If a manufacturing system enters into a state where
a task enters into a state of suspended animation
for
perpetuity, we say it is in a livelocked state. In
contrast, all tasks of the system remain suspended
for
perpetuity in a deadlocked state of the system. A l
ivelock-free manufacturing system can never experie
nce
deadlocks, but the converse is not necessarily true
. A livelock-prone manufacturing system can be
regulated using a supervisory policy such that the
resulting supervised system is livelock-free. If a
liveness
enforcing supervisory policy (LESP) prevents the oc
currence of an event at given state of the
manufacturing system, and every other LESP, irrespe
ctive of the implementation paradigm, prescribes the
same control for that state, we say the original LE
SP is minimally restrictive.
A Software Tool for Live-Lock Avoidance in Systems Modelled Using a Class of ...IJCSEA Journal
If a manufacturing system enters into a state where a task enters into a state of suspended animation for perpetuity, we say it is in a livelocked state. In contrast, all tasks of the system remain suspended for perpetuity in a deadlocked state of the system. A livelock-free manufacturing system can never experience deadlocks, but the converse is not necessarily true. A livelock-prone manufacturing system can be regulated using a supervisory policy such that the resulting supervised system is livelock-free. If a liveness enforcing supervisory policy (LESP) prevents the occurrence of an event at given state of the manufacturing system, and every other LESP, irrespective of the implementation paradigm, prescribes the same control for that state, we say the original LESP is minimally restrictive.
This paper is about two enhancements to an existing software tool that synthesizes the minimally restrictive LESP for a manufacturing system modelled using a class of weighted Petri nets (PNs). The first enhancement is about broadening the scope of the software tool to a larger class of PNs. The second enhancement is about improving the running time of the software tool using a property identified in this paper.
We identify a class, ℋ, of general Petri net (PN) structures where the existence of a liveness enforcing supervisory policy (LESP) for an instance of this class, initialized at a marking, is sufficient to infer the existence of an LESP when the same instance is initialized at a larger marking. As a consequence, the existence of an LESP for the PN that results when a member of this class is initialized with a marking, is decidable. Additionally, the maximally permissive LESP, when it exists, can be synthesized using a software tool described in an earlier paper. We also highlight a property that plays a critical role in the speed of convergence of the iterative procedure for the synthesis of the minimally restrictive LESP, when it exits, for any instance of ℋ that uses the aforementioned software package.
This document presents a summary of the paper "System Theory over Random Networks: Control and Estimation" by Marzieh Nabi Abdolyousefi and Mehran Mesbahi. The paper explores system-theoretic properties like controllability and observability of systems operating over random networks. It examines control and estimation of diffusion-like protocols over random graphs and decentralized control and estimation schemes involving randomness. The main results analyze controllability and stability properties of control systems defined over random networks.
Cellular automata are algorithms that model the discrete spatial and temporal evolution of complex systems using local transformation rules. They consist of a lattice of cells that can have different states, with the state of each cell updated synchronously based on the states of neighboring cells. There are various types of cellular automata depending on factors like the neighborhood considered and whether the rules are deterministic or probabilistic. Cellular automata have been widely used to model microstructure evolution in materials science applications like recrystallization simulation.
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
This document summarizes research on controlling unstable periodic orbits that coexist with a strange attractor using periodic proportional pulses. The technique is demonstrated on the nonlinear dynamics model xn+1 = axn - bxn2, which exhibits chaos for certain parameter values. Control curves are plotted and used to stabilize periodic orbits of periods 1, 2, 3 and 4 by applying proportional pulses every q iterations with a kicking factor λ. The results show this technique can stabilize unstable periodic orbits embedded in the chaotic attractor.
On The Transition Probabilities for the Fuzzy States of a Fuzzy Markov ChainIJERA Editor
In this paper the theory of fuzzy logic is mixed with the theory of Markov systems and the abstraction of a
Markov system with fuzzy states introduced. The notions such as fuzzy transient, fuzzy recurrent etc., were
introduced. The results based on these notions are introduced.
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
The document summarizes a queueing model with two component mixture of doubly truncated exponential service times. The service time distribution is a two component mixture of doubly truncated exponential distributions, which can characterize heterogeneous and finite range service times. Assuming Poisson arrivals, the embedded Markov chain technique is used to analyze the system. Explicit expressions are derived for performance measures like average number of customers, average waiting time, throughput, and probability of idleness. Numerical analysis studies the sensitivity of performance measures to parameter changes. The model includes two component mixture of exponential, doubly truncated exponential, and exponential service time models as special cases.
The document summarizes key concepts about the Hopfield model, an attractor neural network model inspired by physics. It discusses how memory is stored in the symmetric connectivity matrix through Hebbian learning of stored patterns. During recall, the network dynamics relax toward one of the stored memory patterns as an attractor state. This can be modeled deterministically or stochastically. The number of memories an N-neuron network can reliably store is approximately 0.15N.
JAISTサマースクール2016「脳を知るための理論」講義01 Single neuron modelshirokazutanaka
This document provides an overview of topics to be covered in a lecture on single neuron models. It will discuss:
1) The basic anatomy and physiology of neurons including their morphology and membrane properties.
2) Phenomenological models of subthreshold dynamics like the integrate-and-fire, quadratic-and-fire, and resonate-and-fire models.
3) Biophysical models of spiking mechanisms including the Hodgkin-Huxley model and its use of ion channels and master equations.
4) Analysis techniques like phase plots and bifurcation analysis applied to models like FitzHugh-Nagumo and Hindmarsh-Rose.
5) Modern single neuron models such
A Software Tool for Live-Lock Avoidance in Systems Modelled Using a Class of ...IJCSEA Journal
If a manufacturing system enters into a state where a task enters into a state of suspended animation for perpetuity, we say it is in a livelocked state. In contrast, all tasks of the system remain suspended for perpetuity in a deadlocked state of the system. A livelock-free manufacturing system can never experience deadlocks, but the converse is not necessarily true. A livelock-prone manufacturing system can be regulated using a supervisory policy such that the resulting supervised system is livelock-free. If a liveness enforcing supervisory policy (LESP) prevents the occurrence of an event at given state of the manufacturing system, and every other LESP, irrespective of the implementation paradigm, prescribes the same control for that state, we say the original LESP is minimally restrictive.
This paper is about two enhancements to an existing software tool that synthesizes the minimally restrictive LESP for a manufacturing system modelled using a class of weighted Petri nets (PNs). The first enhancement is about broadening the scope of the software tool to a larger class of PNs. The second enhancement is about improving the running time of the software tool using a property identified in this paper.
We identify a class, ℋ, of general Petri net (PN) structures where the existence of a liveness enforcing supervisory policy (LESP) for an instance of this class, initialized at a marking, is sufficient to infer the existence of an LESP when the same instance is initialized at a larger marking. As a consequence, the existence of an LESP for the PN that results when a member of this class is initialized with a marking, is decidable. Additionally, the maximally permissive LESP, when it exists, can be synthesized using a software tool described in an earlier paper. We also highlight a property that plays a critical role in the speed of convergence of the iterative procedure for the synthesis of the minimally restrictive LESP, when it exits, for any instance of ℋ that uses the aforementioned software package.
This document presents a summary of the paper "System Theory over Random Networks: Control and Estimation" by Marzieh Nabi Abdolyousefi and Mehran Mesbahi. The paper explores system-theoretic properties like controllability and observability of systems operating over random networks. It examines control and estimation of diffusion-like protocols over random graphs and decentralized control and estimation schemes involving randomness. The main results analyze controllability and stability properties of control systems defined over random networks.
Cellular automata are algorithms that model the discrete spatial and temporal evolution of complex systems using local transformation rules. They consist of a lattice of cells that can have different states, with the state of each cell updated synchronously based on the states of neighboring cells. There are various types of cellular automata depending on factors like the neighborhood considered and whether the rules are deterministic or probabilistic. Cellular automata have been widely used to model microstructure evolution in materials science applications like recrystallization simulation.
IJCER (www.ijceronline.com) International Journal of computational Engineerin...ijceronline
This document summarizes research on controlling unstable periodic orbits that coexist with a strange attractor using periodic proportional pulses. The technique is demonstrated on the nonlinear dynamics model xn+1 = axn - bxn2, which exhibits chaos for certain parameter values. Control curves are plotted and used to stabilize periodic orbits of periods 1, 2, 3 and 4 by applying proportional pulses every q iterations with a kicking factor λ. The results show this technique can stabilize unstable periodic orbits embedded in the chaotic attractor.
On The Transition Probabilities for the Fuzzy States of a Fuzzy Markov ChainIJERA Editor
In this paper the theory of fuzzy logic is mixed with the theory of Markov systems and the abstraction of a
Markov system with fuzzy states introduced. The notions such as fuzzy transient, fuzzy recurrent etc., were
introduced. The results based on these notions are introduced.
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
The document summarizes a queueing model with two component mixture of doubly truncated exponential service times. The service time distribution is a two component mixture of doubly truncated exponential distributions, which can characterize heterogeneous and finite range service times. Assuming Poisson arrivals, the embedded Markov chain technique is used to analyze the system. Explicit expressions are derived for performance measures like average number of customers, average waiting time, throughput, and probability of idleness. Numerical analysis studies the sensitivity of performance measures to parameter changes. The model includes two component mixture of exponential, doubly truncated exponential, and exponential service time models as special cases.
The document summarizes key concepts about the Hopfield model, an attractor neural network model inspired by physics. It discusses how memory is stored in the symmetric connectivity matrix through Hebbian learning of stored patterns. During recall, the network dynamics relax toward one of the stored memory patterns as an attractor state. This can be modeled deterministically or stochastically. The number of memories an N-neuron network can reliably store is approximately 0.15N.
JAISTサマースクール2016「脳を知るための理論」講義01 Single neuron modelshirokazutanaka
This document provides an overview of topics to be covered in a lecture on single neuron models. It will discuss:
1) The basic anatomy and physiology of neurons including their morphology and membrane properties.
2) Phenomenological models of subthreshold dynamics like the integrate-and-fire, quadratic-and-fire, and resonate-and-fire models.
3) Biophysical models of spiking mechanisms including the Hodgkin-Huxley model and its use of ion channels and master equations.
4) Analysis techniques like phase plots and bifurcation analysis applied to models like FitzHugh-Nagumo and Hindmarsh-Rose.
5) Modern single neuron models such
JAISTサマースクール2016「脳を知るための理論」講義04 Neural Networks and Neuroscience hirokazutanaka
This document summarizes key concepts from a lecture on neural networks and neuroscience:
- Single-layer neural networks like perceptrons can only learn linearly separable patterns, while multi-layer networks can approximate any function. Backpropagation enables training multi-layer networks.
- Recurrent neural networks incorporate memory through recurrent connections between units. Backpropagation through time extends backpropagation to train recurrent networks.
- The cerebellum functions similarly to a perceptron for motor learning and control. Its feedforward circuitry from mossy fibers to Purkinje cells maps to the layers of a perceptron.
This lecture discusses synaptic learning rules in neural networks. It introduces the basic anatomy and physiology of synapses and different coding schemes neurons use, such as rate coding and spike timing coding. It then covers several synaptic plasticity rules, including Hebbian learning, spike-timing dependent plasticity (STDP), and the Bienenstock-Cooper-Munro (BCM) rule. It also discusses modeling synapses using the conductance-based model and implementations of STDP learning through online learning rules and weight dependence mechanisms.
The feedback-control-for-distributed-systemsCemal Ardil
The document summarizes a study on feedback control synthesis for distributed systems. The study proposes a zone control approach, where the state space is partitioned into zones defined by observable points. Control actions are piecewise constant functions that only change when the system transitions between zones. An optimization problem is formulated to determine the optimal constant control value for each zone. Gradient formulas are derived to solve this using numerical optimization methods. The zone control approach was tested on heat exchanger process control problems and showed more robust performance than alternative methods.
Senior Seminar: Systems of Differential EquationsJDagenais
This document discusses solving systems of differential equations. It begins by introducing systems of differential equations and their importance in modeling natural processes. It then outlines the key concepts needed to solve systems, including matrices, eigenvalues, and diagonalization. The document focuses on solving homogeneous systems where the eigenvalues are distinct and real. It presents the process of writing systems in matrix form and looking for solutions of the form x=e^rt to find the eigenvalues from the characteristic equation.
Fractional Newton-Raphson Method and Some Variants for the Solution of Nonlin...mathsjournal
The following document presents some novel numerical methods valid for one and several variables, which
using the fractional derivative, allow us to find solutions for some nonlinear systems in the complex space using
real initial conditions. The origin of these methods is the fractional Newton-Raphson method, but unlike the
latter, the orders proposed here for the fractional derivatives are functions. In the first method, a function is
used to guarantee an order of convergence (at least) quadratic, and in the other, a function is used to avoid the
discontinuity that is generated when the fractional derivative of the constants is used, and with this, it is possible
that the method has at most an order of convergence (at least) linear.
Backstepping Controller Synthesis for Piecewise Polynomial Systems: A Sum of ...Behzad Samadi
This document outlines a method for synthesizing backstepping controllers for piecewise polynomial (PWP) systems using sum of squares (SOS) optimization. It introduces PWP systems in strict feedback form and formulates controller synthesis as a convex feasibility problem by constructing SOS Lyapunov functions. An example application to a single-link flexible-joint robot partitions variables to create regions and designs a stabilizing PWP controller.
This document provides an introduction to Markov jump linear systems (MJLS). It begins by discussing how dynamical systems are increasingly complex due to technological advances, requiring more efficient control systems. MJLS are introduced as a class of models that can account for abrupt changes in system dynamics by allowing the system to switch among a set of linear models based on a Markov process. Key characteristics of MJLS are described, including that the overall system behavior depends on the switching rate between models. Examples are provided to illustrate how MJLS can exhibit different properties than traditional linear systems due to switching dynamics.
Optical sensing techniques and signal processing 5ali alavi
This document discusses frequency analysis of optical imaging systems. It begins with a generalized treatment of imaging systems and defines the amplitude transfer function and impulse response. For coherent systems, the image is a convolution of the ideal image and amplitude impulse response. For incoherent systems, the image intensity is a convolution with the intensity impulse response, which is the squared amplitude impulse response. It then examines the frequency responses of coherent and incoherent systems, defining the amplitude transfer function and optical transfer function respectively.
Computational Motor Control: Optimal Control for Deterministic Systems (JAIST...hirokazutanaka
This is lecure 2 note for JAIST summer school on computational motor control (Hirokazu Tanaka & Hiroyuki Kambara). Lecture video: https://www.youtube.com/watch?v=lNH1q4y1m-U
This document discusses dynamics of structures with uncertainties. It begins with an introduction to stochastic single degree of freedom systems and how natural frequency variability can be modeled using probability distributions. It then discusses how to extend this approach to stochastic multi degree of freedom systems using stochastic finite element formulations and modal projections. Key challenges with statistical overlap of eigenvalues are noted. The document provides mathematical models of equivalent damping in stochastic systems and examples of stochastic frequency response functions.
FEEDBACK LINEARIZATION AND BACKSTEPPING CONTROLLERS FOR COUPLED TANKSieijjournal
This paper investigates the usage of some sophisticated and advanced nonlinear control algorithms in order to control a nonlinear Coupled Tanks System. The first control procedure is called the Feedback linearisation control (FLC), this type of control has been found a successful in achieving a global exponential asymptotic stability, with very short time response, no significant overshooting is recorded and with a negligible norm of the error. The second control procedure is the approaches of Back stepping control (BC) which is a recursive procedure that interlaces the choice of a Lyapunov function with the design of feedback control, from simulation results it shown that this method preserves tracking, robust control and it can often solve stabilization problems with less restrictive conditions may been countered in other methods. Finally both of the proposed control schemes guarantee the asymptoticstability of the closed loop system meeting trajectory tracking objectives.
Active Controller Design for Regulating the Output of the Sprott-P Systemijccmsjournal
This document summarizes research on controlling the output of the Sprott-P chaotic system. It begins by introducing the output regulation problem for nonlinear control systems and the solution approach of Byrnes and Isidori. It then applies this approach to regulate the output of the Sprott-P system for constant tracking problems. Explicit state feedback control laws are derived to regulate each of the three state variables x1, x2, and x3 to track a constant reference signal ω. Theorems are provided stating the control laws solve the output regulation problem for each tracking case.
This document describes a method for numerically computing quasi-discrete Hankel transforms of integer order for propagating optical wave fields. The method generalizes an existing zero-order Hankel transform method to higher orders. It approximates input functions using Fourier-Bessel series over a finite integration interval, resulting in a symmetric transformation matrix that satisfies the discrete form of the Parseval theorem. This allows for energy conservation during successive applications of the Hankel transform and inverse Hankel transform. The method is applied to propagating an optical field through axially symmetric systems. Numerical tests demonstrate the accuracy of computing Hankel transforms of different orders for a sinc function input field.
An Exponential Observer Design for a Class of Chaotic Systems with Exponentia...ijtsrd
In this paper, a class of generalized chaotic systems with exponential nonlinearity is studied and the state observation problem of such systems is explored. Using differential inequality with time domain analysis, a practical state observer for such generalized chaotic systems is constructed to ensure the global exponential stability of the resulting error system. Besides, the guaranteed exponential decay rate can be correctly estimated. Finally, several numerical simulations are given to demonstrate the validity, effectiveness, and correctness of the obtained result. Yeong-Jeu Sun "An Exponential Observer Design for a Class of Chaotic Systems with Exponential Nonlinearity" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-1 , December 2020, URL: https://www.ijtsrd.com/papers/ijtsrd38233.pdf Paper URL : https://www.ijtsrd.com/engineering/electrical-engineering/38233/an-exponential-observer-design-for-a-class-of-chaotic-systems-with-exponential-nonlinearity/yeongjeu-sun
This document discusses applying Newton's method and continuation methods to reduce optimal control problems to boundary value problems. It begins by introducing Newton's method and the implicit function theorem, which defines a curve of solutions. It then discusses the continuous analogue of Newton's method, which transforms the equations into an initial value problem that is integrated. Finally, it shows how an optimal control problem can be reduced to a boundary value problem by applying the Pontryagin maximum principle, yielding equations that can be solved using continuation methods.
1. Logo MTQ Provinsi di Kabupaten Seram Bagian Barat menggunakan berbagai simbol yang merepresentasikan makna Islam dan budaya lokal untuk membangun semangat persatuan.
2. Unsur-unsurnya meliputi kaligrafi nama Allah, tulisan Quran, peta Kabupaten Seram Bagian Barat, dan burung yang merepresentasikan semangat kemajemukan dan pembangunan berkelanjutan.
3. Logo ini bertujuan memperkuat jiwa kebersamaan m
Este documento es un cuestionario de planeación para la asignatura de Administración de los recursos y función informática del 4to semestre del Instituto Tecnológico de Tuxtepec. Fue realizado por el alumno Albino López Cervantes y revisado por la catedrática María de los Ángeles Martínez morales en mayo de 2015.
Federico C. Ortiz Jr. is applying for a sales representative position. He has a background in civil engineering and architecture and has worked in drafting, tax mapping, and as a deliveryman. He has extensive training in AutoCAD, Microsoft Office, and multimedia programs. Ortiz aims to utilize his educational background and skills to obtain knowledge relevant to his field. He highlights his ability to liaise at different levels, adaptability, willingness to take on various tasks, and computer literacy as strengths for the role.
Ringkasan dokumen tersebut adalah:
1. LPTQ Provinsi Maluku berupaya meningkatkan mutu peserta dan pengurus MTQ melalui peningkatan kapasitas dewan hakim dan guru TPQ.
2. LPTQ bergerak sejalan dengan visi pembangunan kepulauan dan pariwisata berwawasan Al-Quran di kawasan timur Indonesia.
3. Rakorda merekomendasikan peraturan daerah tentang pembinaan MTQ dan pendidikan agama untuk meningkat
Buku ini membahasakan konsep Fiqh Dakwah dalam Al-Quran dengan menganalisis beberapa ayat Al-Quran yang terkait dengan dakwah. Ringkasannya adalah: (1) Dakwah harus didasarkan pada pemikiran kritis dan kejelasan, (2) Hendaklah menawarkan alternatif dan solusi, bukan hanya kritik, dan (3) Perlu melindungi dakwah dengan mencari dukungan kelompok kuat.
JAISTサマースクール2016「脳を知るための理論」講義04 Neural Networks and Neuroscience hirokazutanaka
This document summarizes key concepts from a lecture on neural networks and neuroscience:
- Single-layer neural networks like perceptrons can only learn linearly separable patterns, while multi-layer networks can approximate any function. Backpropagation enables training multi-layer networks.
- Recurrent neural networks incorporate memory through recurrent connections between units. Backpropagation through time extends backpropagation to train recurrent networks.
- The cerebellum functions similarly to a perceptron for motor learning and control. Its feedforward circuitry from mossy fibers to Purkinje cells maps to the layers of a perceptron.
This lecture discusses synaptic learning rules in neural networks. It introduces the basic anatomy and physiology of synapses and different coding schemes neurons use, such as rate coding and spike timing coding. It then covers several synaptic plasticity rules, including Hebbian learning, spike-timing dependent plasticity (STDP), and the Bienenstock-Cooper-Munro (BCM) rule. It also discusses modeling synapses using the conductance-based model and implementations of STDP learning through online learning rules and weight dependence mechanisms.
The feedback-control-for-distributed-systemsCemal Ardil
The document summarizes a study on feedback control synthesis for distributed systems. The study proposes a zone control approach, where the state space is partitioned into zones defined by observable points. Control actions are piecewise constant functions that only change when the system transitions between zones. An optimization problem is formulated to determine the optimal constant control value for each zone. Gradient formulas are derived to solve this using numerical optimization methods. The zone control approach was tested on heat exchanger process control problems and showed more robust performance than alternative methods.
Senior Seminar: Systems of Differential EquationsJDagenais
This document discusses solving systems of differential equations. It begins by introducing systems of differential equations and their importance in modeling natural processes. It then outlines the key concepts needed to solve systems, including matrices, eigenvalues, and diagonalization. The document focuses on solving homogeneous systems where the eigenvalues are distinct and real. It presents the process of writing systems in matrix form and looking for solutions of the form x=e^rt to find the eigenvalues from the characteristic equation.
Fractional Newton-Raphson Method and Some Variants for the Solution of Nonlin...mathsjournal
The following document presents some novel numerical methods valid for one and several variables, which
using the fractional derivative, allow us to find solutions for some nonlinear systems in the complex space using
real initial conditions. The origin of these methods is the fractional Newton-Raphson method, but unlike the
latter, the orders proposed here for the fractional derivatives are functions. In the first method, a function is
used to guarantee an order of convergence (at least) quadratic, and in the other, a function is used to avoid the
discontinuity that is generated when the fractional derivative of the constants is used, and with this, it is possible
that the method has at most an order of convergence (at least) linear.
Backstepping Controller Synthesis for Piecewise Polynomial Systems: A Sum of ...Behzad Samadi
This document outlines a method for synthesizing backstepping controllers for piecewise polynomial (PWP) systems using sum of squares (SOS) optimization. It introduces PWP systems in strict feedback form and formulates controller synthesis as a convex feasibility problem by constructing SOS Lyapunov functions. An example application to a single-link flexible-joint robot partitions variables to create regions and designs a stabilizing PWP controller.
This document provides an introduction to Markov jump linear systems (MJLS). It begins by discussing how dynamical systems are increasingly complex due to technological advances, requiring more efficient control systems. MJLS are introduced as a class of models that can account for abrupt changes in system dynamics by allowing the system to switch among a set of linear models based on a Markov process. Key characteristics of MJLS are described, including that the overall system behavior depends on the switching rate between models. Examples are provided to illustrate how MJLS can exhibit different properties than traditional linear systems due to switching dynamics.
Optical sensing techniques and signal processing 5ali alavi
This document discusses frequency analysis of optical imaging systems. It begins with a generalized treatment of imaging systems and defines the amplitude transfer function and impulse response. For coherent systems, the image is a convolution of the ideal image and amplitude impulse response. For incoherent systems, the image intensity is a convolution with the intensity impulse response, which is the squared amplitude impulse response. It then examines the frequency responses of coherent and incoherent systems, defining the amplitude transfer function and optical transfer function respectively.
Computational Motor Control: Optimal Control for Deterministic Systems (JAIST...hirokazutanaka
This is lecure 2 note for JAIST summer school on computational motor control (Hirokazu Tanaka & Hiroyuki Kambara). Lecture video: https://www.youtube.com/watch?v=lNH1q4y1m-U
This document discusses dynamics of structures with uncertainties. It begins with an introduction to stochastic single degree of freedom systems and how natural frequency variability can be modeled using probability distributions. It then discusses how to extend this approach to stochastic multi degree of freedom systems using stochastic finite element formulations and modal projections. Key challenges with statistical overlap of eigenvalues are noted. The document provides mathematical models of equivalent damping in stochastic systems and examples of stochastic frequency response functions.
FEEDBACK LINEARIZATION AND BACKSTEPPING CONTROLLERS FOR COUPLED TANKSieijjournal
This paper investigates the usage of some sophisticated and advanced nonlinear control algorithms in order to control a nonlinear Coupled Tanks System. The first control procedure is called the Feedback linearisation control (FLC), this type of control has been found a successful in achieving a global exponential asymptotic stability, with very short time response, no significant overshooting is recorded and with a negligible norm of the error. The second control procedure is the approaches of Back stepping control (BC) which is a recursive procedure that interlaces the choice of a Lyapunov function with the design of feedback control, from simulation results it shown that this method preserves tracking, robust control and it can often solve stabilization problems with less restrictive conditions may been countered in other methods. Finally both of the proposed control schemes guarantee the asymptoticstability of the closed loop system meeting trajectory tracking objectives.
Active Controller Design for Regulating the Output of the Sprott-P Systemijccmsjournal
This document summarizes research on controlling the output of the Sprott-P chaotic system. It begins by introducing the output regulation problem for nonlinear control systems and the solution approach of Byrnes and Isidori. It then applies this approach to regulate the output of the Sprott-P system for constant tracking problems. Explicit state feedback control laws are derived to regulate each of the three state variables x1, x2, and x3 to track a constant reference signal ω. Theorems are provided stating the control laws solve the output regulation problem for each tracking case.
This document describes a method for numerically computing quasi-discrete Hankel transforms of integer order for propagating optical wave fields. The method generalizes an existing zero-order Hankel transform method to higher orders. It approximates input functions using Fourier-Bessel series over a finite integration interval, resulting in a symmetric transformation matrix that satisfies the discrete form of the Parseval theorem. This allows for energy conservation during successive applications of the Hankel transform and inverse Hankel transform. The method is applied to propagating an optical field through axially symmetric systems. Numerical tests demonstrate the accuracy of computing Hankel transforms of different orders for a sinc function input field.
An Exponential Observer Design for a Class of Chaotic Systems with Exponentia...ijtsrd
In this paper, a class of generalized chaotic systems with exponential nonlinearity is studied and the state observation problem of such systems is explored. Using differential inequality with time domain analysis, a practical state observer for such generalized chaotic systems is constructed to ensure the global exponential stability of the resulting error system. Besides, the guaranteed exponential decay rate can be correctly estimated. Finally, several numerical simulations are given to demonstrate the validity, effectiveness, and correctness of the obtained result. Yeong-Jeu Sun "An Exponential Observer Design for a Class of Chaotic Systems with Exponential Nonlinearity" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-5 | Issue-1 , December 2020, URL: https://www.ijtsrd.com/papers/ijtsrd38233.pdf Paper URL : https://www.ijtsrd.com/engineering/electrical-engineering/38233/an-exponential-observer-design-for-a-class-of-chaotic-systems-with-exponential-nonlinearity/yeongjeu-sun
This document discusses applying Newton's method and continuation methods to reduce optimal control problems to boundary value problems. It begins by introducing Newton's method and the implicit function theorem, which defines a curve of solutions. It then discusses the continuous analogue of Newton's method, which transforms the equations into an initial value problem that is integrated. Finally, it shows how an optimal control problem can be reduced to a boundary value problem by applying the Pontryagin maximum principle, yielding equations that can be solved using continuation methods.
1. Logo MTQ Provinsi di Kabupaten Seram Bagian Barat menggunakan berbagai simbol yang merepresentasikan makna Islam dan budaya lokal untuk membangun semangat persatuan.
2. Unsur-unsurnya meliputi kaligrafi nama Allah, tulisan Quran, peta Kabupaten Seram Bagian Barat, dan burung yang merepresentasikan semangat kemajemukan dan pembangunan berkelanjutan.
3. Logo ini bertujuan memperkuat jiwa kebersamaan m
Este documento es un cuestionario de planeación para la asignatura de Administración de los recursos y función informática del 4to semestre del Instituto Tecnológico de Tuxtepec. Fue realizado por el alumno Albino López Cervantes y revisado por la catedrática María de los Ángeles Martínez morales en mayo de 2015.
Federico C. Ortiz Jr. is applying for a sales representative position. He has a background in civil engineering and architecture and has worked in drafting, tax mapping, and as a deliveryman. He has extensive training in AutoCAD, Microsoft Office, and multimedia programs. Ortiz aims to utilize his educational background and skills to obtain knowledge relevant to his field. He highlights his ability to liaise at different levels, adaptability, willingness to take on various tasks, and computer literacy as strengths for the role.
Ringkasan dokumen tersebut adalah:
1. LPTQ Provinsi Maluku berupaya meningkatkan mutu peserta dan pengurus MTQ melalui peningkatan kapasitas dewan hakim dan guru TPQ.
2. LPTQ bergerak sejalan dengan visi pembangunan kepulauan dan pariwisata berwawasan Al-Quran di kawasan timur Indonesia.
3. Rakorda merekomendasikan peraturan daerah tentang pembinaan MTQ dan pendidikan agama untuk meningkat
Buku ini membahasakan konsep Fiqh Dakwah dalam Al-Quran dengan menganalisis beberapa ayat Al-Quran yang terkait dengan dakwah. Ringkasannya adalah: (1) Dakwah harus didasarkan pada pemikiran kritis dan kejelasan, (2) Hendaklah menawarkan alternatif dan solusi, bukan hanya kritik, dan (3) Perlu melindungi dakwah dengan mencari dukungan kelompok kuat.
Tulisan ini membahas peran kearifan lokal seperti pela gandong dalam menyelesaikan konflik keagamaan di Maluku. Kearifan lokal seperti pela gandong berperan penting dalam proses rekonsiliasi dengan menyatukan kembali solidaritas masyarakat yang terpecah selama konflik. Representasi dalam birokrasi juga berperan dalam mengurangi kesenjangan antar elemen masyarakat.
Buku ini memberikan ringkasan tentang penghitungan dan analisis Indeks Pembangunan Manusia Kota Lhokseumawe tahun 2012. Buku ini menjelaskan metodologi pengumpulan data, pengolahan data, dan penghitungan IPM serta menganalisis perkembangan IPM Kota Lhokseumawe dari tahun ke tahun berdasarkan indikator kesehatan, pendidikan, dan daya beli.
Sam Houser es el presidente de Rockstar Games, la compañía que cofundó con su hermano Dan y Terry Donovan. Dirigió y produjo los juegos de Grand Theft Auto desde GTA III, llevando la serie a la era 3D con ciudades recreadas de forma realista. Se le atribuye el éxito de convertir GTA en una de las franquicias más exitosas financieramente durante la sexta generación de consolas.
El documento presenta los pasos para resolver un sistema de ecuaciones de dos variables. Primero se igualan los valores de x obtenidos al despejar x de cada ecuación. Luego se pasan los denominadores al otro lado y se resuelve la ecuación resultante para encontrar el valor de y. Finalmente, se sustituye en una de las ecuaciones originales para hallar el valor de x y se comprueba que satisfacen ambas ecuaciones originales.
Lewis Loyi Wei is offering two types of table tennis training courses:
1) Private one-on-one lessons for all ages and skill levels for $12-25 per hour. Students will learn techniques and strategies and can practice for $5 per hour with instruction.
2) A 4-8 hour service and return training course for intermediate to advanced players rated 1400-2600 for $120-360. Lewis Loyi Wei will teach serving techniques from different angles while Andrew Liu focuses on returning serves both defensively and offensively.
The courses will take place in San Francisco on Saturdays and at other Bay Area locations on weekdays and Sundays. Lewis Loyi Wei and Andrew Liu
Buku ini membahas tentang dakwah di era digital. Pembahasan dimulai dari pengertian dakwah dan ilmu dakwah, sejarah dakwah dari masa Rasulullah hingga kontemporer, dasar-dasar dakwah, pelaku, sasaran dan pesan dakwah. Selanjutnya membahas metode dakwah, pengertian ma'ruf dan munkar serta kaidah amar ma'ruf nahi munkar. Terakhir membahas peran media massa dalam d
Tiga kalimat ringkasan dokumen tersebut adalah:
Jurnalistik dakwah diperlukan untuk memberikan pencerahan kepada media massa agar dapat menghindari benturan peradaban dengan menyampaikan berita secara bijak dan mempertimbangkan keragaman sosial. Nabi Muhammad mencontohkan bagaimana umat Islam dapat hidup berdampingan dengan kelompok lain secara damai melalui Piagam Madinah yang menghormati perbedaan. Peran jurnalist
Dokumen tersebut membahas metode desain logo IAIN Ambon dengan menggunakan teori AISYATEK. Teori ini menekankan pada lima unsur yaitu Aqidah, Intelektual, Syariah, Teknologi, dan Kewirausahaan. Logo dirancang berdasarkan visi dan misi IAIN Ambon serta budaya lokal Maluku. Unsur-unsur seperti alif, kearifan lokal, dan falsafah lebah dimasukkan ke dalam desain logo.
1. Jurnalisme perdamaian bertujuan untuk mengurangi konflik dan meningkatkan pemahaman antar kelompok dengan menekankan hal-hal yang menghubungkan mereka daripada yang memisahkan.
2. Jurnalis harus melihat konflik sebagai proses sosial kompleks yang melibatkan banyak pihak dan tujuan, bukan hanya dua pihak yang saling bertentangan.
3. Analisis sosial diperlukan untuk memahami konteks ruang
Este documento resume las normas legales que rigen la declaración jurada anual de personas naturales para el año 2014. Detalla quiénes están obligados a presentar la declaración jurada según la categoría de renta, así como los casos en los que no se está obligado. También indica el vencimiento para la presentación de la declaración jurada anual.
Simulation and stability analysis of neural network based control scheme for ...ISA Interchange
This paper proposes a new adaptive neural network based control scheme for switched linear systems with parametric uncertainty and external disturbance. A key feature of this scheme is that the prior information of the possible upper bound of the uncertainty is not required. A feedforward neural network is employed to learn this upper bound. The adaptive learning algorithm is derived from Lyapunov stability analysis so that the system response under arbitrary switching laws is guaranteed uniformly ultimately bounded. A comparative simulation study with robust controller given in [Zhang L, Lu Y, Chen Y, Mastorakis NE. Robust uniformly ultimate boundedness control for uncertain switched linear systems. Computers and Mathematics with Applications 2008; 56: 1709–14] is presented.
A Mixed Binary-Real NSGA II Algorithm Ensuring Both Accuracy and Interpretabi...IJECEIAES
In this work, a Neuro-Fuzzy Controller network, called NFC that implements a Mamdani fuzzy inference system is proposed. This network includes neurons able to perform fundamental fuzzy operations. Connections between neurons are weighted through binary and real weights. Then a mixed binaryreal Non dominated Sorting Genetic Algorithm II (NSGA II) is used to perform both accuracy and interpretability of the NFC by minimizing two objective functions; one objective relates to the number of rules, for compactness, while the second is the mean square error, for accuracy. In order to preserve interpretability of fuzzy rules during the optimization process, some constraints are imposed. The approach is tested on two control examples: a single input single output (SISO) system and a multivariable (MIMO) system.
Simple Exponential Observer Design for the Generalized Liu Chaotic Systemijtsrd
In this paper, the generalized Liu chaotic system is firstly introduced and the state observation problem of such a system is investigated. Based on the time-domain approach with differential and integral equalities, a novel state observer for the generalized Liu chaotic system is constructed to ensure the global exponential stability of the resulting error system. Besides, the guaranteed exponential convergence rate can be precisely calculated. Finally, numerical simulations are presented to exhibit the effectiveness and feasibility of the obtained results. Yeong-Jeu Sun"Simple Exponential Observer Design for the Generalized Liu Chaotic System" Published in International Journal of Trend in Scientific Research and Development (ijtsrd), ISSN: 2456-6470, Volume-2 | Issue-1 , December 2017, URL: http://www.ijtsrd.com/papers/ijtsrd7126.pdf http://www.ijtsrd.com/engineering/engineering-maths/7126/simple-exponential-observer-design-for-the-generalized-liu-chaotic-system/yeong-jeu-sun
ACTIVE CONTROLLER DESIGN FOR THE GENERALIZED PROJECTIVE SYNCHRONIZATION OF TH...ijait
This paper discusses the design of active controllers for generalized projective synchronization (GPS) of identical Wang 3-scroll chaotic systems (Wang, 2009), identical Dadras 3-scroll chaotic systems (Dadras and Momeni, 2009) and non-identical Wang 3-scroll system and Dadras 3-scroll system. The synchronization results (GPS) derived in this paper for the 3 scroll chaotic systems have been derived using active control method and established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active control method is very effective and convenient for
achieving the generalized projective synchronization (GPS) of the 3-scroll chaotic systems addressed in this paper. Numerical simulations are provided to illustrate the effectiveness of the GPS synchronization results derived in this paper.
THE ACTIVE CONTROLLER DESIGN FOR ACHIEVING GENERALIZED PROJECTIVE SYNCHRONIZA...ijait
This paper discusses the design of active controllers for achieving generalized projective synchronization (GPS) of identical hyperchaotic Lü systems (Chen, Lu, Lü and Yu, 2006), identical hyperchaotic Cai systems (Wang and Cai, 2009) and non-identical hyperchaotic Lü and hyperchaotic Cai systems. The synchronization results (GPS) for the hyperchaotic systems have been derived using active control method and established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active control method is very effective and convenient for achieving the GPS of the
hyperchaotic systems addressed in this paper. Numerical simulations are provided to illustrate the effectiveness of the GPS synchronization results derived in this paper.
Hybrid Chaos Synchronization of Hyperchaotic Newton-Leipnik Systems by Slidin...ijctcm
This paper investigates the hybrid chaos synchronization of identical hyperchaotic Newton-Leipnik systems (Ghosh and Bhattacharya, 2010) by sliding mode control. The stability results derived in this paper for the hybrid chaos synchronization of identical hyperchaotic Newton-Leipnik systems are established using Lyapunov stability theory. Hybrid synchronization of hyperchaotic Newton-Leipnik systems is achieved through the complete synchronization of first and third states of the systems and the anti-synchronization of second and fourth states of the master and slave systems. Since the Lyapunov exponents are not required for these calculations, the sliding mode control is very effective and convenient to achieve hybrid chaos synchronization of the identical hyperchaotic Newton-Leipnik systems. Numerical simulations are shown to validate and demonstrate the effectiveness of the synchronization schemes derived in this paper.
Global stabilization of a class of nonlinear system based on reduced order st...ijcisjournal
The problem of global stabilization for a class of nonlinear system is considered in this paper.The sufficient
condition of the global stabilization of this class of system is obtained by deducing thestabilization of itself
from the stabilization of its subsystems. This paper will come up with a designmethod of state feedback
control law to make this class of nonlinear system stable, and indicate the efficiency of the conclusion of
this paper via a series of examples and simulations at the end. Theresults presented in this paper improve
and generalize the corresponding results of recent works.
Control theorists have extensively studied stability
as well as relative stability of LTI systems. In this research
paper we attempt to answer the question. How unstable is an
unstable system? In that effort we define instability exponents
dealing with the impulse response. Using these instability
exponents, we characterize unstable systems.
The document discusses various applications of artificial neural networks (ANNs) including electrical load forecasting, system identification, control systems, and pattern recognition. It provides details on ANN approaches for each application area. For electrical load forecasting, ANNs can be used to classify forecasting into time spans and discuss techniques like fuzzy logic and regression models. ANNs are also discussed for system identification to determine system parameters from input-output data and for control system applications like predictive control and feedback linearization. The document concludes with ANN approaches for pattern recognition tasks involving classification, clustering, and regression.
Hierarchical algorithms of quasi linear ARX Neural Networks for Identificatio...Yuyun Wabula
This document summarizes a research paper on hierarchical algorithms for training a quasi-linear ARX neural network model for identification of nonlinear systems. The key points are:
1) A hierarchical algorithm is proposed that first estimates the system using a linear sub-model and least squares estimation to obtain linear parameters. It then trains a neural network nonlinear sub-model to refine the errors of the linear sub-model.
2) The linear parameter estimates are fixed and used as biases for the neural network, which is trained to minimize the residual errors of the linear sub-model.
3) This hierarchical approach separates the identification into linear and nonlinear parts, allowing analysis of the system linearly while also capturing nonlinearities. The neural
ANTI-SYNCHRONIZATION OF HYPERCHAOTIC BAO AND HYPERCHAOTIC XU SYSTEMS VIA ACTI...IJCSEIT Journal
This paper investigates the anti-synchronization of identical hyperchaotic Bao systems (Bao and Liu,
2008), identical hyperchaotic Xu systems (Xu, Cai and Zheng, 2009) and non-identical hyperchaotic Bao
and hyperchaotic Xu systems. Active nonlinear control has been deployed for the anti- synchronization of
the hyperchaotic systems addressed in this paper and the main results have been established using
Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the active
nonlinear control method is very effective and convenient to achieve anti-synchronization of identical and
non-identical hyperchaotic Bao and hyperchaotic Xu systems. Numerical simulations have been provided to
validate and demonstrate the effectiveness of the anti-synchronization results for the hyperchaotic Cao and
hyperchaotic Xu systems.
On the Principle of Optimality for Linear Stochastic Dynamic System ijfcstjournal
In this work, processes represented by linear stochastic dynamic system are investigated and by
considering optimal control problem, principle of optimality is proven. Also, for existence of optimal
control and corresponding optimal trajectory, proofs of theorems of necessity and sufficiency condition are
attained.
APPROXIMATE CONTROLLABILITY RESULTS FOR IMPULSIVE LINEAR FUZZY STOCHASTIC DIF...ijfls
In this paper, the approximate controllability of impulsive linear fuzzy stochastic differential equations with nonlocal conditions in Banach space is studied. By using the Banach fixed point
theorems, stochastic analysis, fuzzy process and fuzzy solution, some sufficient conditions are given for
the approximate controllability of the system.
APPROXIMATE CONTROLLABILITY RESULTS FOR IMPULSIVE LINEAR FUZZY STOCHASTIC DIF...Wireilla
This summary provides the key details about the document in 3 sentences:
The document discusses approximate controllability results for impulsive linear fuzzy stochastic differential equations under nonlocal conditions. It presents sufficient conditions for the approximate controllability of such systems using Banach fixed point theorems, stochastic analysis, and fuzzy processes. The main result establishes approximate controllability of impulsive linear fuzzy stochastic differential equations by verifying assumptions on the system using fixed point theorems.
M.G.Goman, A.V.Khramtsovsky (1997) - Global Stability Analysis of Nonlinear A...Project KRIT
М.Г.Гоман, А.В.Храмцовский "Анализ устойчивости "в большом" в нелинейных задачах динамики", доклад на конференции AIAA Guidance, Navigation, and Control Conf., AIAA Paper 97-3721, 1997 г.
В статье описываются численные методы анализа устойчивости "в большом". Представлены результаты расчетов областей устойчивости стационарных установившихся режимов движения для различных нелинейных задач динамики пол\"ета, таких как инерционное вращение, сваливание, штопор и др.
M.G.Goman, A.V.Khramtsovsky "Global Stability Analysis of Nonlinear Aircraft Dynamics", presented at AIAA Guidance, Navigation, and Control Conf., AIAA Paper 97-3721, 1997.
Global stability analysis of dynamical system implies determination of all the system's attractors and their regions of asymptotic stability. Numerical methods necessary for global stability analysis are outlined: SSNE algorithm for systematic search of all the solutions of nonlinear system of equations, and two algorithms for computing cross-sections of asymptotic stability region boundaries. Results obtained during investigation of aircraft roll-coupling problem are presented as an example of global stability analysis.
Approximate Solution of a Linear Descriptor Dynamic Control System via a non-...IOSR Journals
This document discusses approximate solutions for linear descriptor dynamic control systems using a non-classical variational approach. It begins by introducing descriptor systems and their importance in applications. It then discusses making irregular systems regular through computational algorithms. The paper focuses on consistent initial conditions and their characterization. It proposes using a non-classical variational approach to obtain approximate solutions with a high degree of accuracy and freedom of choice for the bilinear form.
On the Cryptographic Measures and Chaotic Dynamical Complexity Measuresijcisjournal
The relationship between cryptographic measures and chaotic dynamical complexity measures is studied in
this paper, including linear complexity and measure entropy, nonlinear complexity and source entropy.
Moreover, a method is presented to guarantee the complexity of chaos-based pseudorandom sequence due
to this relationship. This is important to the development of chaos-based cryptography.
This document describes a study using artificial neural networks (ANNs) to model complex nonlinear systems. Specifically, it discusses:
1) Using an ANN to predict pressure distributions on a rotor wing during ramping motion, with results showing accurate prediction of spatial and temporal evolution.
2) Applying the same ANN model to predict performance of a bank stock based on trends in the stock and stock market index.
3) Proposing a framework combining ANNs with mathematical models to obtain better predictions and representations of financial data trends.
This document summarizes an academic paper that proposes modifying well-known local linear models for system identification by replacing their original recursive learning rules with outlier-robust variants based on M-estimation. It describes three existing local linear models - local linear map (LLM), radial basis function network (RBFN), and local model network (LMN) - and then introduces the concept of M-estimation as a way to make the learning rules of these models more robust to outliers. The performance of the proposed outlier-robust variants is evaluated on three benchmark datasets and is found to provide considerable improvement in the presence of outliers compared to the original models.
Similar to A S OFTWARE T OOL FOR L IVE - LOCK A VOIDANCE IN S YSTEMS M ODELLED USING A C LASS OF P ETRI N ETS (20)
GraphSummit Singapore | The Future of Agility: Supercharging Digital Transfor...Neo4j
Leonard Jayamohan, Partner & Generative AI Lead, Deloitte
This keynote will reveal how Deloitte leverages Neo4j’s graph power for groundbreaking digital twin solutions, achieving a staggering 100x performance boost. Discover the essential role knowledge graphs play in successful generative AI implementations. Plus, get an exclusive look at an innovative Neo4j + Generative AI solution Deloitte is developing in-house.
For the full video of this presentation, please visit: https://www.edge-ai-vision.com/2024/06/building-and-scaling-ai-applications-with-the-nx-ai-manager-a-presentation-from-network-optix/
Robin van Emden, Senior Director of Data Science at Network Optix, presents the “Building and Scaling AI Applications with the Nx AI Manager,” tutorial at the May 2024 Embedded Vision Summit.
In this presentation, van Emden covers the basics of scaling edge AI solutions using the Nx tool kit. He emphasizes the process of developing AI models and deploying them globally. He also showcases the conversion of AI models and the creation of effective edge AI pipelines, with a focus on pre-processing, model conversion, selecting the appropriate inference engine for the target hardware and post-processing.
van Emden shows how Nx can simplify the developer’s life and facilitate a rapid transition from concept to production-ready applications.He provides valuable insights into developing scalable and efficient edge AI solutions, with a strong focus on practical implementation.
GraphSummit Singapore | The Art of the Possible with Graph - Q2 2024Neo4j
Neha Bajwa, Vice President of Product Marketing, Neo4j
Join us as we explore breakthrough innovations enabled by interconnected data and AI. Discover firsthand how organizations use relationships in data to uncover contextual insights and solve our most pressing challenges – from optimizing supply chains, detecting fraud, and improving customer experiences to accelerating drug discoveries.
Full-RAG: A modern architecture for hyper-personalizationZilliz
Mike Del Balso, CEO & Co-Founder at Tecton, presents "Full RAG," a novel approach to AI recommendation systems, aiming to push beyond the limitations of traditional models through a deep integration of contextual insights and real-time data, leveraging the Retrieval-Augmented Generation architecture. This talk will outline Full RAG's potential to significantly enhance personalization, address engineering challenges such as data management and model training, and introduce data enrichment with reranking as a key solution. Attendees will gain crucial insights into the importance of hyperpersonalization in AI, the capabilities of Full RAG for advanced personalization, and strategies for managing complex data integrations for deploying cutting-edge AI solutions.
Driving Business Innovation: Latest Generative AI Advancements & Success StorySafe Software
Are you ready to revolutionize how you handle data? Join us for a webinar where we’ll bring you up to speed with the latest advancements in Generative AI technology and discover how leveraging FME with tools from giants like Google Gemini, Amazon, and Microsoft OpenAI can supercharge your workflow efficiency.
During the hour, we’ll take you through:
Guest Speaker Segment with Hannah Barrington: Dive into the world of dynamic real estate marketing with Hannah, the Marketing Manager at Workspace Group. Hear firsthand how their team generates engaging descriptions for thousands of office units by integrating diverse data sources—from PDF floorplans to web pages—using FME transformers, like OpenAIVisionConnector and AnthropicVisionConnector. This use case will show you how GenAI can streamline content creation for marketing across the board.
Ollama Use Case: Learn how Scenario Specialist Dmitri Bagh has utilized Ollama within FME to input data, create custom models, and enhance security protocols. This segment will include demos to illustrate the full capabilities of FME in AI-driven processes.
Custom AI Models: Discover how to leverage FME to build personalized AI models using your data. Whether it’s populating a model with local data for added security or integrating public AI tools, find out how FME facilitates a versatile and secure approach to AI.
We’ll wrap up with a live Q&A session where you can engage with our experts on your specific use cases, and learn more about optimizing your data workflows with AI.
This webinar is ideal for professionals seeking to harness the power of AI within their data management systems while ensuring high levels of customization and security. Whether you're a novice or an expert, gain actionable insights and strategies to elevate your data processes. Join us to see how FME and AI can revolutionize how you work with data!
HCL Notes and Domino License Cost Reduction in the World of DLAUpanagenda
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-and-domino-license-cost-reduction-in-the-world-of-dlau/
The introduction of DLAU and the CCB & CCX licensing model caused quite a stir in the HCL community. As a Notes and Domino customer, you may have faced challenges with unexpected user counts and license costs. You probably have questions on how this new licensing approach works and how to benefit from it. Most importantly, you likely have budget constraints and want to save money where possible. Don’t worry, we can help with all of this!
We’ll show you how to fix common misconfigurations that cause higher-than-expected user counts, and how to identify accounts which you can deactivate to save money. There are also frequent patterns that can cause unnecessary cost, like using a person document instead of a mail-in for shared mailboxes. We’ll provide examples and solutions for those as well. And naturally we’ll explain the new licensing model.
Join HCL Ambassador Marc Thomas in this webinar with a special guest appearance from Franz Walder. It will give you the tools and know-how to stay on top of what is going on with Domino licensing. You will be able lower your cost through an optimized configuration and keep it low going forward.
These topics will be covered
- Reducing license cost by finding and fixing misconfigurations and superfluous accounts
- How do CCB and CCX licenses really work?
- Understanding the DLAU tool and how to best utilize it
- Tips for common problem areas, like team mailboxes, functional/test users, etc
- Practical examples and best practices to implement right away
In the rapidly evolving landscape of technologies, XML continues to play a vital role in structuring, storing, and transporting data across diverse systems. The recent advancements in artificial intelligence (AI) present new methodologies for enhancing XML development workflows, introducing efficiency, automation, and intelligent capabilities. This presentation will outline the scope and perspective of utilizing AI in XML development. The potential benefits and the possible pitfalls will be highlighted, providing a balanced view of the subject.
We will explore the capabilities of AI in understanding XML markup languages and autonomously creating structured XML content. Additionally, we will examine the capacity of AI to enrich plain text with appropriate XML markup. Practical examples and methodological guidelines will be provided to elucidate how AI can be effectively prompted to interpret and generate accurate XML markup.
Further emphasis will be placed on the role of AI in developing XSLT, or schemas such as XSD and Schematron. We will address the techniques and strategies adopted to create prompts for generating code, explaining code, or refactoring the code, and the results achieved.
The discussion will extend to how AI can be used to transform XML content. In particular, the focus will be on the use of AI XPath extension functions in XSLT, Schematron, Schematron Quick Fixes, or for XML content refactoring.
The presentation aims to deliver a comprehensive overview of AI usage in XML development, providing attendees with the necessary knowledge to make informed decisions. Whether you’re at the early stages of adopting AI or considering integrating it in advanced XML development, this presentation will cover all levels of expertise.
By highlighting the potential advantages and challenges of integrating AI with XML development tools and languages, the presentation seeks to inspire thoughtful conversation around the future of XML development. We’ll not only delve into the technical aspects of AI-powered XML development but also discuss practical implications and possible future directions.
Building Production Ready Search Pipelines with Spark and MilvusZilliz
Spark is the widely used ETL tool for processing, indexing and ingesting data to serving stack for search. Milvus is the production-ready open-source vector database. In this talk we will show how to use Spark to process unstructured data to extract vector representations, and push the vectors to Milvus vector database for search serving.
Unlock the Future of Search with MongoDB Atlas_ Vector Search Unleashed.pdfMalak Abu Hammad
Discover how MongoDB Atlas and vector search technology can revolutionize your application's search capabilities. This comprehensive presentation covers:
* What is Vector Search?
* Importance and benefits of vector search
* Practical use cases across various industries
* Step-by-step implementation guide
* Live demos with code snippets
* Enhancing LLM capabilities with vector search
* Best practices and optimization strategies
Perfect for developers, AI enthusiasts, and tech leaders. Learn how to leverage MongoDB Atlas to deliver highly relevant, context-aware search results, transforming your data retrieval process. Stay ahead in tech innovation and maximize the potential of your applications.
#MongoDB #VectorSearch #AI #SemanticSearch #TechInnovation #DataScience #LLM #MachineLearning #SearchTechnology
HCL Notes und Domino Lizenzkostenreduzierung in der Welt von DLAUpanagenda
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-und-domino-lizenzkostenreduzierung-in-der-welt-von-dlau/
DLAU und die Lizenzen nach dem CCB- und CCX-Modell sind für viele in der HCL-Community seit letztem Jahr ein heißes Thema. Als Notes- oder Domino-Kunde haben Sie vielleicht mit unerwartet hohen Benutzerzahlen und Lizenzgebühren zu kämpfen. Sie fragen sich vielleicht, wie diese neue Art der Lizenzierung funktioniert und welchen Nutzen sie Ihnen bringt. Vor allem wollen Sie sicherlich Ihr Budget einhalten und Kosten sparen, wo immer möglich. Das verstehen wir und wir möchten Ihnen dabei helfen!
Wir erklären Ihnen, wie Sie häufige Konfigurationsprobleme lösen können, die dazu führen können, dass mehr Benutzer gezählt werden als nötig, und wie Sie überflüssige oder ungenutzte Konten identifizieren und entfernen können, um Geld zu sparen. Es gibt auch einige Ansätze, die zu unnötigen Ausgaben führen können, z. B. wenn ein Personendokument anstelle eines Mail-Ins für geteilte Mailboxen verwendet wird. Wir zeigen Ihnen solche Fälle und deren Lösungen. Und natürlich erklären wir Ihnen das neue Lizenzmodell.
Nehmen Sie an diesem Webinar teil, bei dem HCL-Ambassador Marc Thomas und Gastredner Franz Walder Ihnen diese neue Welt näherbringen. Es vermittelt Ihnen die Tools und das Know-how, um den Überblick zu bewahren. Sie werden in der Lage sein, Ihre Kosten durch eine optimierte Domino-Konfiguration zu reduzieren und auch in Zukunft gering zu halten.
Diese Themen werden behandelt
- Reduzierung der Lizenzkosten durch Auffinden und Beheben von Fehlkonfigurationen und überflüssigen Konten
- Wie funktionieren CCB- und CCX-Lizenzen wirklich?
- Verstehen des DLAU-Tools und wie man es am besten nutzt
- Tipps für häufige Problembereiche, wie z. B. Team-Postfächer, Funktions-/Testbenutzer usw.
- Praxisbeispiele und Best Practices zum sofortigen Umsetzen
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdfPaige Cruz
Monitoring and observability aren’t traditionally found in software curriculums and many of us cobble this knowledge together from whatever vendor or ecosystem we were first introduced to and whatever is a part of your current company’s observability stack.
While the dev and ops silo continues to crumble….many organizations still relegate monitoring & observability as the purview of ops, infra and SRE teams. This is a mistake - achieving a highly observable system requires collaboration up and down the stack.
I, a former op, would like to extend an invitation to all application developers to join the observability party will share these foundational concepts to build on:
TrustArc Webinar - 2024 Global Privacy SurveyTrustArc
How does your privacy program stack up against your peers? What challenges are privacy teams tackling and prioritizing in 2024?
In the fifth annual Global Privacy Benchmarks Survey, we asked over 1,800 global privacy professionals and business executives to share their perspectives on the current state of privacy inside and outside of their organizations. This year’s report focused on emerging areas of importance for privacy and compliance professionals, including considerations and implications of Artificial Intelligence (AI) technologies, building brand trust, and different approaches for achieving higher privacy competence scores.
See how organizational priorities and strategic approaches to data security and privacy are evolving around the globe.
This webinar will review:
- The top 10 privacy insights from the fifth annual Global Privacy Benchmarks Survey
- The top challenges for privacy leaders, practitioners, and organizations in 2024
- Key themes to consider in developing and maintaining your privacy program
Essentials of Automations: The Art of Triggers and Actions in FMESafe Software
In this second installment of our Essentials of Automations webinar series, we’ll explore the landscape of triggers and actions, guiding you through the nuances of authoring and adapting workspaces for seamless automations. Gain an understanding of the full spectrum of triggers and actions available in FME, empowering you to enhance your workspaces for efficient automation.
We’ll kick things off by showcasing the most commonly used event-based triggers, introducing you to various automation workflows like manual triggers, schedules, directory watchers, and more. Plus, see how these elements play out in real scenarios.
Whether you’re tweaking your current setup or building from the ground up, this session will arm you with the tools and insights needed to transform your FME usage into a powerhouse of productivity. Join us to discover effective strategies that simplify complex processes, enhancing your productivity and transforming your data management practices with FME. Let’s turn complexity into clarity and make your workspaces work wonders!
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...SOFTTECHHUB
The choice of an operating system plays a pivotal role in shaping our computing experience. For decades, Microsoft's Windows has dominated the market, offering a familiar and widely adopted platform for personal and professional use. However, as technological advancements continue to push the boundaries of innovation, alternative operating systems have emerged, challenging the status quo and offering users a fresh perspective on computing.
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A S OFTWARE T OOL FOR L IVE - LOCK A VOIDANCE IN S YSTEMS M ODELLED USING A C LASS OF P ETRI N ETS
1. International Journal of Computer Science, Engineering and Applications (IJCSEA) Vol.5, No.2, April 2015
DOI : 10.5121/ijcsea.2015.5201 1
A SOFTWARE TOOL FOR LIVE-LOCK AVOIDANCE IN
SYSTEMS MODELLED USING A CLASS OF PETRI
NETS
E. Salimi1
, N. Somnath1
and R.S. Sreenivas1
1
Department of Industrial and Enterprise Systems Engineering, University of Illinois at
Urbana-Champaign, Urbana, IL, USA
ABSTRACT
If a manufacturing system enters into a state where a task enters into a state of suspended animation for
perpetuity, we say it is in a livelocked state. In contrast, all tasks of the system remain suspended for
perpetuity in a deadlocked state of the system. A livelock-free manufacturing system can never experience
deadlocks, but the converse is not necessarily true. A livelock-prone manufacturing system can be
regulated using a supervisory policy such that the resulting supervised system is livelock-free. If a liveness
enforcing supervisory policy (LESP) prevents the occurrence of an event at given state of the
manufacturing system, and every other LESP, irrespective of the implementation paradigm, prescribes the
same control for that state, we say the original LESP is minimally restrictive.
This paper is about two enhancements to an existing software tool that synthesizes the minimally restrictive
LESP for a manufacturing system modelled using a class of weighted Petri nets (PNs). The first
enhancement is about broadening the scope of the software tool to a larger class of PNs. The second
enhancement is about improving the running time of the software tool using a property identified in this
paper.
We identify a class, ℋ, of general Petri net (PN) structures where the existence of a liveness enforcing
supervisory policy (LESP) for an instance of this class, initialized at a marking, is sufficient to infer the
existence of an LESP when the same instance is initialized at a larger marking. As a consequence, the
existence of an LESP for the PN that results when a member of this class is initialized with a marking, is
decidable. Additionally, the maximally permissive LESP, when it exists, can be synthesized using a software
tool described in an earlier paper. We also highlight a property that plays a critical role in the speed of
convergence of the iterative procedure for the synthesis of the minimally restrictive LESP, when it exits, for
any instance of ℋ that uses the aforementioned software package.
KEYWORDS
Manufacturing Systems, Livelock Avoidance &Petri Nets
1. INTRODUCTION
Manufacturing systems belong to a class of systems called Discrete-Event/Discrete-State (DEDS)
systems. The (discrete-)states of these systems have a logical, as opposed to numerical,
interpretation. At each state, there are potential (discrete-)events that can occur, the occurrence of
any one of them would change the state of the system, which then results in a new set of potential
events, and this process can be repeated as often as necessary. DEDS systems are regulated by a
supervisory policy, which determines which event is to be permitted at each state, in such a
2. International Journal of Computer Science, Engineering and Applications (IJCSEA) Vol.5, No.2, April 2015
2
manner that some behavioural specification is satisfied. Our focus is on livelock-avoidance. A
manufacturing system is in a livelocked-state if a task enters into a state of suspended animation
for perpetuity. If all tasks in the manufacturing system are prevented from progressing to
completion, we say the manufacturing system has entered a deadlocked-state (cf. [1], for
example). A livelock-free manufacturing system does not have deadlocked-states, but a deadlock-
free manufacturing system can still experience livelocks. Livelock freedom is harder to achieve,
compared to deadlock freedom.
Petri nets (PNs) have been extensively used to model manufacturing systems (cf. [2,3], for
example). In this paper we consider the synthesis of liveness enforcing supervisory policies
(LESPs) in PN models of manufacturing systems. The results in the literature range from heuristic
procedures to provably correct methods that can synthesize LESPs for a variety of PN classes.
Since the existence of an LESP in an arbitrary PN instance is not even semi-decidable, it is
imperative that any provably correct scheme restrictsits attention to a sub-class of PN structures.
This paper identifies one such a class, ℋ, which strictly includes all other classes of PNs for
which a LESP can be automatically synthesized (cf. [4–6], for example). Additionally, the
software tool identified in reference [7] can be used to synthesize the minimally restrictive LESP,
when it exists, for any member of the class ℋ, thus broadening its scope. We also identify a
characterization of the minimally restrictive LESP for any instance of ℋ, which can be used to
improve the running time of the aforementioned software tool.
This paper is organized as follows – section 2 introduces the notations and definitions used in this
paper. This section also reviews the supervisory control paradigm for PN models, along with a
brief review of the relevant results from the literature. The main results are presented in section 3.
Section 4 presents the conclusions.
2. NOTATIONS AND DEFINITIONS AND SOME PRELIMINARY OBSERVATIONS
ℕ (ℕା
)denotes the set of non-negative (positive) integers. The cardinality of a set A is
represented as card(A). A Petri net (PN) structure ܰ = (ߎ, ܶ, ߔ, ߁) is an ordered 4-tuple,
whereߎ = ሼଵ ⋯ ሽis a set of nplaces, ܶ = ሼݐଵ ⋯ ݐሽ is a collection ofmtransitions,Φ ⊆ (Π ×
ܶ) ∪ (ܶ × Π)isasetofarcs,andΓ: Φ → ℕା
isthe weight associated with each arc. The weight of an
arc is represented by an integer that is placed alongside the arc. If an arc has a unitary weight, it is
not represented in its graphical representation in this paper.
If all arcs of a PN are unitary, it is said to be an ordinary PN, otherwise it is a general PN. The
initial marking of a PN structure N is a function
: Π → ℕ, which identifies the number of
tokens in each place. A Petri net (PN), N(m0
), is a PN structure N together with its initial marking
m0
.
ܶ∗
represents the set of all finite-length strings of transitions. For ߪ ∈ ܶ∗
, we use࢞(ߪ) to denote
the Parikh vector of σ. That is, the ith
entry, ࢞(ߪ), corresponds to the number of occurrences of
transition ti in σ.
Let ݔ•
≔ ሼ,ݕ(|ݕ )ݔ ∈ Φሽ and ݔ•
≔ ሼ,ݔ(|ݕ )ݕ ∈ Φሽ. If ∀ ∈ ,ݐ•
() ≥ Γ((, ))ݐfor some
ݐ ∈ ܶ and some marking mi
, then ݐ ∈ ܶ is said to be enabled at marking mi
. The set of enabled
transitions at marking mi
is denoted by the symbol Te(N, mi
). An enabled transition ݐ ∈ ܶ(ܰ,
)
can fire, which changes the marking mi
to mi+1
according to ାଵ() = () − Γ(, )ݐ +
Γ(,ݐ .)
Asetofmarkingsℳ ⊆ ℕ
issaidtoberight-closed[8]if((ଵ
∈ ℳ)⋀(ଶ
≥ ଵ) ⇒ (ଶ
∈ ℳ)),
and is uniquely defined by its finite set of minimal-elements.
3. International Journal of Computer Science, Engineering and Applications (IJCSEA) Vol.5, No.2, April 2015
3
When the marking is interpreted as a nonnegative integer-valued vector, it is useful to definethe
input matrix IN (output matrix OUT) as an n×m matrix, where INi, j (OUTi,j) equals Γ((pi,tj))
(Γ((pi,tj))) if pi∈•
tj, (pi∈t•
j) and is zero-valued otherwise. The incidence matrix C of the PN N is an
n×m matrix, where C = OUT−IN.
2.1. Supervisory Control of PNs
Under this paradigm, the set of transitions in the PN is partitioned into a set of
controllabletransitions (ܶ ⊆ ܶ)and a set of uncontrollable transitions (ܶ௨ ⊆ ܶ). Thecontrollable
(uncontrollable) transitions are represented as filled (unfilled) boxes ingraphical representation of
PNs.
A supervisory policy ℘: ℕ
× ܶ → ሼ0,1ሽ, is a function that returns a 0 or 1for each transition and
each reachable marking. Transition ݐ ∈ ܶis control-enabled(state-enabled) if ℘(, )ݐ = 1
(ݐ ∈ ܶ(ܰ, )) for some marking m. A transition that isstate- and control-enabled can fire, which
results in a new marking as indicated in theprevious section. Since uncontrollable transitions
cannot be prevented from firing bythe supervisory policy, we require the following condition to
be true of all supervisorypolicies: ∀ ∈ ℕ
, ℘(, )ݐ = 1, if ݐ ∈ ܶ௨.
A valid firing stringߪ = ݐଵݐଶ ⋯ ݐ ∈ ܶ∗
for a marking mi
satisfies the followingconditions:
(1)ݐଵ ∈ ܶ൫ܰ, ܕ
൯, ℘൫ܕ
, ݐଵ൯ = 1,and (2) for ݆ ∈ ሼ1,2, ⋯ ݇ − 1ሽthe firingof transition tj produces
a markingmi+j
,ݐାଵ ∈ ܶ൫ܰ, ܕା
൯, and ℘൫ܕା
, ݐାଵ൯ = 1.
ℜ(ܰ,
, ℘)denotes the set of markings that are reachable from m0
under thesupervision of ℘in
N. We use
ఙ
→
to denote that mj
results from the firing ofߪ ∈ ܶ∗
from mi
.
A transition tk is live under the supervision of ℘ if ∀
∈ ℜ(ܰ,
, ℘), ∃
∈ ℜ൫ܰ,
, ℘൯such
thatݐ ∈ ܶ൫ܰ, ܕ
൯ and ℘൫ܕ
, ݐ൯ = 1. If all transitions in N(m0
)are live under ℘, then it is a
liveness enforcing supervisory policy (LESP) for N(m0
).The policy ℘ is said to be minimally
restrictive if for every LESP℘ෝ: ℕ
× ܶ → ሼ0,1ሽ, the following condition holds∀
∈ ℕ
, ∀ ݐ ∈
ܶ, ℘൫ܕ
, ݐ൯ ≥ ℘ෝ൫ܕ
, ݐ൯.
There is an LESP for N(m0
)if and only if
∈ ∆(ࡺ),
whereΔ(ܰ) = ሼ
∈ ℕௗ(ஈ)
|∃ ܽ݊ (ܰ ݎ݂ ܲܵܧܮ)ሽ is the set of initial markings m0
for
which there is aLESP for N(m0
). It follows that Δ(ܰ) is control invariant (cf. [9,10]) with respect
toN; that is, if ଵ
∈ Δ(ܰ), ݐ௨ ∈ ܶ௨ ∩ ܶ(ܰ, ଵ
) and ଵ
௧ೠ
→ ଶ
in N, then ଶ
∈
Δ(ܰ).Equivalently, only the firing of a controllable transition at any marking in Δ(ܰ) canresult in
a new marking that is not in Δ(ܰ).
If ℘ is an LESP for N(m0
), then ℜ(ܰ,
, ℘) ⊆ ∆(ܰ). Additionally, the LESP℘∗
, that prevents
the firing of a controllable transition at any marking when its firingwould result in a new marking
that is not in ∆(ࡺ), is the minimally restrictive LESPfor N(m0
). That is, there can be no other
LESP, independent of the implementationparadigm, that can be better than ℘∗
.
Neither the existence, nor the non-existence, of an LESP for an arbitrary PN issemi-decidable; the
existence of an LESP is decidable if all transitions in the PNare controllable, or if the PN
structure belongs to specific classes identified in theliterature [4–6,11]. The process of deciding
the existence of an LESP in an arbitraryinstance from these classes is NP-hard.
4. International Journal of Computer Science, Engineering and Applications (IJCSEA) Vol.5, No.2, April 2015
4
2.2. Review of Relevant Prior Work
Monitors were introduced into supervisory control of PNS by Giua [12], and wereused by Moody
et al. [13], and Iordache et al. [14] to derive sufficient conditions forthe existence of certain
classes of PNs. Sufficient conditions for minimally restrictive,closed-loop liveness of a class
Marked Graph PNs supervised by monitors were derivedby Basile et al. [15]. There are necessary
and sufficient conditions for classes ofPNs known as S3
PR and S4
PR nets that can be used to
synthesize liveness enforcingenhancements in instances of these classes [16,17]. Reveliotis et al.
[18] and Ghaffariet al. [19] used the theory of regions to identify minimally restrictive LESPs
forResource Allocation Systems. Marchetti et al. [20] presented a polynomial time sufficient
condition for liveness, for the class of Unitary Weighted Event Graphs. Ferrariniet al [21]
compare the performance of a selection of deadlock avoidance policies inPN models of flexible
manufacturing systems. Chen et al. [22] use Integer LinearProgramming to synthesize invariant
based monitors that enforce liveness in a classof PNs. Hu et al. [23,24] use a set of inequalities to
characterize insufficiently markedsiphons that is subsequently used to develop an algebraic
LESP-synthesis procedure.Li et al [25] develop an iterative siphon-based control scheme for
preventing deadlocksin PN models of manufacturing systems using a mixed integer
programmingapproach involving what are known as necessary siphons.
3. Main Results
Let,Ω()ݐ = ሼݐ̂ ∈ ܶ| ݐ•
∩ ݐ̂•
≠ ∅ሽ, denote the set of transitions that share a common inputplace
with ݐ ∈ ܶfor a PN structure ܰ = (ߎ, ܶ, ߔ, ߁). Consequently,(ݐଵ ∈ Ω(ݐଶ)) ⇒ (ݐଶ ∈ Ω(ݐଵ)). Let
ℋ෩ denote a class of PN structures where the following property is true:
∀ ∈ ∆(ܰ), ∀ݐ௨ ∈ ܶ௨, ∀ݐ ∈ Ω(ݐ௨), ൫ݐ ∈ ܶ(ܰ, )൯ ⇒ ൫ݐ௨ ∈ ܶ(ܰ, )൯. (1)
That is, ℋ෩ is a class of PN structures where, if a transition t is state-enabled, then all
uncontrollable transitions that share a common input place with t are also state enabledat any
marking in ∆(ܰ). The following lemma finds use in the proof of theorem2.
Lemma 1: (Lemma 5.1, [5]) Let ℘ be a LESP for N(m0
), where
∈ ∆(ܰ), for aPN structure
ܰ ∈ ℋ෩. Suppose
ఙ
→
under the supervision of ℘, andෝ
ఙෝ
→ ෝ
without supervision in N,
where the number of occurrences of each controllabletransition in ߪ and ߪො are identical, andෝ
≥
. There exists strings ߪଵ, ߪොଵ ∈ ܶ∗
such that (1)
ఙఙభ
ሱۛሮ
under the supervision of ℘ in N,
(2)ෝ
ఙෝఙෝభ
ሱۛሮ ෝ
withoutsupervision in N, and (3) ࢞(ߪߪଵ) = ࢞(ߪොߪොଵ). Consequently,ෝ
≥ ෝ
.
Proof: Let ܶ௨ ⊆ ܶ௨denote the set of uncontrollable transitions that appear more oftenin ߪොas
compared to ߪ. If ܶ௨ = ∅, thenߪො = ߪ and the result holds trivially. If ܶ௨ ≠ ∅,,there is a stringߪଵ
such
ఙభ
→ ାଵ
under the supervision of the LESP ℘ suchthat (1) at least one member of
ݐ௨ ∈ ܶ௨ is state-enabled atାଵ
, and (2) none ofthe members of ܶ௨ are state-enabled at any
marking that results from the firing of aproper prefix of ߪଵ at
. It follows that ෝ
ఙభ
→ ෝ ାଵ
,
without any supervision, in N.If this were not the case, there must be a proper prefix of ߪଵ, of the
form ߪതݐ, suchthat ෝ
ఙഥ
→ ഥ in N, butݐ ∉ ܶ(ܰ, ഥ ). Additionally, ݐ ∈ Ω(ݐ̅௨)for some ݐ̅௨ ∈ ܶ.
Sinceܰ ∈ ℋ෩, and ഥ ∈ ∆(ܰ), it follows that ݐ௨ ∈ ܶ(ܰ, ഥ ), which contradicts requirement (2).
Suppose
ఙభೠ
ሱۛሮ ାଵ
under ℘ in N, and ෝ
ఙభ
→ ෝ ାଵ
without supervision inN. We let
←
ାଵ
, ෝ
← ෝ ାଵ
, ߪ ← ߪߪଵݐ௨,andߪො ← ߪߪଵݐ௨. The result followsby repeating the above
construction as often as necessary till ܶ௨ = ߶. ♣
5. International Journal of Computer Science, Engineering and Applications (IJCSEA) Vol.5, No.2, April 2015
5
The following theorem notes that ∆(ܰ) is right-closed if ܰ ∈ ℋ෩.
Theorem 2:ቀ൫
∈ ∆(ܰ)൯⋀(ෝ
≥ )ቁ ⇒ ൫ෝ
∈ ∆(ܰ)൯,ifܰ ∈ ℋ෩ .
Proof: Since
∈ ∆(ܰ), there is an LESP ℘ for N(m0
). Following reference [5],we define an
LESP ℘ෝfor N(ෝ
) as follows (1)∀ݐ ∈ ܶ, ℘ෝ(ෝ
, )ݐ = ℘(
, ,)ݐ (2) ifෝ
ఙෝ
→ ෝ
under ℘ෝ, then
(2a) ∀ݐ௨ ∈ ܶ௨, ℘ෝ൫ෝ
, ݐ௨൯ = 1, and (2b) ∀ݐ ∈ ܶ, ൫℘ෝ൫ෝ
, ݐ൯ = 1൯ ⟺ (∃ߪ ∈ ܶ∗
,suchthat
ఙ
→ under ℘, and the number of occurrences of eachcontrollable transition in ߪ and ߪොݐ are
identical).
If ෝ
ఙෝ
→ ෝ
under ℘ෝ, then ∃ߪ ∈ ܶ∗
such that
ఙ
→
under ℘, and the numberof occurrences of
each controllable transition in ߪ and ߪො are identical. Using lemma1, and the definition of ℘ෝ, we
know ∃ߪොଵ, ߪଵ ∈ ܶ∗
such that ෝ
ఙෝఙෝభ
ሱۛሮ ෝ ାଵ
under ℘ෝ,
ఙఙభ
ሱۛሮ ାଵ
under ℘, andෝ ାଵ
≥ ାଵ
.
Consequently, for any ߪଶ ∈ ܶ∗
such thatାଵ
ఙమ
→ ାଶ
under ℘, we have ෝ ାଵ
ఙమ
→ ෝ ାଶ
under ℘ෝ as
well. Since ℘ is an LESPfor N(m0
), it follows that℘ෝis an LESP for N(ෝ
). ♣
Lemma 1 and theorem 2 together imply the following theorem.
Theorem 3:∆(ܰ) is right-closed if ܰ ∈ ℋ෩.
The above condition is not necessary for the right-closure of ∆(ܰ). For instance,∆(ܰଵ) is right-
closed for the general PN ܰଵ shown in figure 1(a), butܰଵ ∉ ℋ෩. Specifically,∆(ܰଵ) is identified by
the inequality (1 1 1 1 1)m≥ 1, and m = (1 0 000)T
∈ ∆(ܰଵ), ݐଶ ∈ ܶ௨,ݐଷ ∈ ܶ(ܰଵ, ), butݐଶ ∉
ܶ(ܰଵ, ).
There is an LESP for the PN N(m0
)if and only if
∈ ∆(ܰ), and the existence ofan LESP is
undecidable for a general PN (cf. corollary 5.2, [11]). This would meanthat the set ∆(ܰ) cannot
be computed for an arbitrary PN structure N. To overcome this limitation, we modify the
requirement of equation 1 as
∀ ∈ ℕ
, ∀ݐ௨ ∈ ܶ௨, ∀ݐ ∈ Ω(ݐ௨), ൫ݐ ∈ ܶ(ܰ, )൯ ⇒ ൫ݐ௨ ∈ ܶ(ܰ, )൯ (2)
This requirement defines a class of PNs, which we denote asℋ(⊆ ℋ෩), and fromtheorem 3, we
conclude ∆(ܰ)is right-closed for anyܰ ∈ ℋ.
Theorem 4: A PN structure ܰ = (ߎ, ܶ, ߔ, ߁) belongs to the class ℋ if and only if∀ ∈ Π, ∀ݐ௨ ∈
•
∩ ܶ௨,
ቆΓ(, ݐ௨) =
݉݅݊
ݐ ∈ •Γ(, )ݐቇ ∧ (∀ݐ ∈ Ω(ݐ௨), ݐ௨
•
⊆ ݐ•
).
Proof:(If) Suppose, ݐ ∈ ܶ(ܰ, ) for ∈ ℕ
, and∃ݐ௨ ∈ Ω()ݐ ∩ ܶ௨(⇒ ݐ ∈ Ω(ݐ௨)).Since
ݐ௨
•
⊆ ݐ•
and∀ ∈ ݐ௨
•
, Γ(, ݐ௨) = ݉݅݊௧∈•Γ(, ,)ݐ it follows thatݐ௨ ∈ ܶ(ܰ, ).
(Only If) We will show that the violation of requirement in the statement of thetheorem for a PN
structure N would imply thatܰ ∉ ℋ.Suppose ∃ ∈ Π, ∃ݐ௨ ∈ •
∩ ܶ௨ such that either
1. Γ(, ݐ௨) > ݉݅݊௧∈•Γ(, ,)ݐ or
6. International Journal of Computer Science, Engineering and Applications (IJCSEA) Vol.5, No.2, April 2015
2. ∃ݐ ∈ Ω(ݐ௨), ݐ௨
•
− ݐ•
≠
In each of these cases we construct a marking
ܶ(ܰ, ), which leads to the conclusion that
For the first-case, the marking m
tokens in the input places of any transition
result inݐ̂ ∈ ܶ(ܰ, ) and ݐ௨ ∉ ܶ
Similarly, for the second-case, the marking
thatݐ ∈ ܶ(ܰ, ), while ensuring that the places in
ݐ ∈ ܶ(ܰ, ) and ݐ௨ ∉ ܶ(ܰ, )
♣
There is an O(n2
m2
) algorithm that decides if an
where ݊ = ܿܽ)ߎ(݀ݎand m = card(T)
results in reference [5] implies that the existenceof an LESP for
the software package described inreference [7] can be used to compute the minimally restrictive
LESP for N(m0
), whenit exists. As noted in the introduction section, each decidable class of PN
structuresidentified in references [4
PN structure N2 shown in figure 1(b) is a member of
theorem 4, and it does not belong to any of the classes of structuresidentified in references [4
Additionally,
min൫∆(ܰଶ)൯ = ሼ(0 0 0 1
(0 1 2 0 1)்
, (2 1
There is an LESP for ܰଶ(ଶ
)if and only if
Figure 1. (a) The PN structure ܰଵ
figure1, [4]). (b) The PN structure N
4(cf. figure 2a, [6]). (c) The PN structure
ℕ
|((ଵ) + (ଶ) + (ଷ) +
International Journal of Computer Science, Engineering and Applications (IJCSEA) Vol.5, No.2, April 2015
≠ ∅
In each of these cases we construct a marking ∈ ℕ
such that ∃ݐ ∈ Ω(ݐ௨) ∩ ܶ(ܰ
, which leads to the conclusion thatܰ ∉ ℋ.
m places exactly (݉݅݊௧∈•Γ(, -))ݐmany tokensin p, and su
ens in the input places of any transitionݐ̂ ∈ Ω(ݐ௨)such thatΓ(, ݐ̂) = ݉݅݊௧∈•Γ(
ܶ(ܰ, ).
case, the marking mplaces sufficient tokens in the inputplaces of
le ensuring that the places in ( ݐ௨
•
− )ݐ•
remain empty. Consequently,
).
algorithm that decides if an arbitrary PN structure belongs to the class
m = card(T). The right-closure of ∆(ܰ)for any ܰ ∈ ℋ, along with the
results in reference [5] implies that the existenceof an LESP for N(m0
) is decidable.
the software package described inreference [7] can be used to compute the minimally restrictive
, whenit exists. As noted in the introduction section, each decidable class of PN
identified in references [4–6] are strictly contained in the class ℋ. As an illustration,
shown in figure 1(b) is a member of ℋ as it meets the structuralrequirements of
theorem 4, and it does not belong to any of the classes of structuresidentified in references [4
0)்
, (1 0 1 0 2)்
, (0 0 2 0 2)்
, (2 0 0 0 2)்
, (1 1 1
1 0 0 1)்
, (0 2 2 0 0)்
, (1 2 1 0 0)்
, (2 2 0 0 0)்
ሽ
if and only ifଶ
∈ ∆(ܰଶ).
ଵ is not a member of the class ℋ෩. However, ∆(ܰଵ) is right
N2is a member of ℋ as it meets the structural requirements of theorem
4(cf. figure 2a, [6]). (c) The PN structure N3 is not a member of the class ℋ, and ∆
(ସ) ≥ 1) ∨ ((ହ)ௗଶ = 1)ሽis not right-closed.
International Journal of Computer Science, Engineering and Applications (IJCSEA) Vol.5, No.2, April 2015
6
(ܰ, ) andݐ௨ ∉
, and sufficient
(, )ݐthat will
cient tokens in the inputplaces of t such
Consequently,
to the class ℋ,
, along with the
is decidable. Furthermore,
the software package described inreference [7] can be used to compute the minimally restrictive
, whenit exists. As noted in the introduction section, each decidable class of PN
. As an illustration, the
as it meets the structuralrequirements of
theorem 4, and it does not belong to any of the classes of structuresidentified in references [4–6].
0 1)்
,
is right-closed (cf.
as it meets the structural requirements of theorem
∆(ܰଷ) = ሼ ∈
7. International Journal of Computer Science, Engineering and Applications (IJCSEA) Vol.5, No.2, April 2015
7
A transitionݐ ∈ ܶ is said to be a choice-transition (resp. non-choice transition) if ( ݐ•
)• ≠ ሼݐሽ
(resp. ( ݐ•
)•
= ሼݐሽ). In reference [26] it is shown that the minimally restrictive LESP for a class of
ordinary PNs called Free-choice PNs does not control-disable a non-choice (controllable)
transition. The following result shows that a similar observation holds for any minimally
restrictive LESP for N(m0
) where ܰ ∈ ℋ.
Theorem 5: [26] Suppose ∈ ∆(ܰ) for a PN N(m0
), where ܰ ∈ ℋ, then theminimally
restrictive LESP ℘∗
for N(m0
) does not disable any controllable transitionݐ ∈ ܶ that satisfies the
requirement ( ݐ
•
)•
= ሼݐሽ.
Proof: (Sketch) Suppose ∃ଵ
∈ ℜ(ܰ,
, ℘∗)൫⊆ ∆(ܰ)൯, ∃ଶ
∈ ℜ(ܰ, ), such thatଵ
௧
→ ଶ
in N for some ݐ ∈ ܶ that satisfies the requirement ( ݐ
•
)•
= ሼݐሽ. We willshow that
1. ∃߱ ∈ ܶ∗
such that ଶ
ఠ
→ in N, where ∈ ∆(ܰ).
2. Additionally, if ߱ = ߱ଵ߱ଶ, ଶ
ఠభ
ሱሮ ෝ ଵ
ఠమ
ሱሮ ,෦ andෝ ଵ
௧ೠ
→ ෝ ଶ
in N for someݐ௨ ∈ ܶ௨, then
∃߱ෝ ∈ ܶ∗
, ∃ෝ ଷ
∈ ℜ(ܰ, ෝ ଶ), such thatෝ ଵ
௧ೠ
→ ෝ ଶ
ఠෝ
→ ෝ ଷ
andෝ ଷ
∈ ∆(ܰ).
Following the repeated application of the above observation, we conclude thatଶ
∈ ∆(ܰ).
Since ℘∗
is an LESP, ∃߱ଵ ∈ (ܶ − ሼݐሽ)∗
, andଵ
ఠభ
ሱሮ ଷ
௧
→ ସ
in N underthe supervision of℘∗
.
Since( ݐ
•
)•
= ሼݐሽ , it follows that ଶ
ఠభ
ሱሮ ସ
in N, andሼଵ
, ଷ
, ସ
ሽ ⊆ ∆(ܰ)(cf. figure 2(a)).
Suppose߱ଵ = ߱ଶ߱ଷ, ଶ
ఠమ
ሱሮ ଽ
ఠయ
ሱሮ ସ
,and ݐ௨ ∈ ܶ௨ such thatଽ
௧ೠ
→ ଵ
. Also,∃ଶ
(∈ ∆(ܰ)) such
thatଵ
ఠమ
ሱሮ ହ
. There aretwo cases to consider – (i) ݐ௨ ∈ ܶ(ܰ, ହ), and (ii) ݐ௨ ∉ ܶ(ܰ, ହ).
In the first case, ∃
(∈ ∆(ܰ)) such that ହ
௧ೠ
→
(cf. figure 2(b)). Since ℘∗
isan LESP,
∃߱ସ ∈ (ܶ − ሼݐሽ)∗
, ∃
, ଼
∈ ∆(ܰ),such that
ఠర
ሱሮ
௧
→ ଼
. Since ( ݐ
•
)•
= ሼݐሽ, we have
ଵ
ఠర
ሱሮ ସ
, whereସ
∈ ∆(ܰ).
For the second case where ݐ௨ ∉ ܶ(ܰ, ହ), since ݐ௨ ∈ ܶ(ܰ, ଽ), it follows that∃ ∈ Π such
thatሼ(ݐ, ,) (, ݐ௨)ሽ ⊆ Φ, and the prior-firing of ݐ is necessary to place sufficient tokens in
∈ Π, for ݐ௨ to be state-enabled at ହ
(cf. figure 2(c)). Sinceܰ ∈ ℋ, it follows that none of the
transitions in Ω(ݐ௨) can fire at any marking thatis reachable in the segment identified by
ଵ
ఠభ
ሱሮ ଷ
. Consequently, ݐ௨ ∈ ܶ(ܰ, ସ),and ସ
௧ೠ
→ ଵଵ
under the supervision of ℘∗
, where
ଵଵ
∈ ∆(ܰ). Consequently,ଵ
ఠర
ሱሮ ଵଵ
. ♣
Theorem 5 does not hold for general PN structures. The PN structure ܰଷ shownin figure 1(c) does
not belong to the class ℋ. This is becausemin௧∈ఱ
• Γ(ହ, )ݐ = 1,while Γ(ହ, ݐ) = 2, andݐ ∈ ହ
•
∩
ܶ௨. dditionally, Δ(ܰଷ) = ሼ ∈ ℕ
|((ଵ) + (ଶ) + (ଷ) + (ସ) ≥ 1) ∨ ((ହ)ௗଶ =
1)ሽ, which is not right-closed. Theminimally restrictive LESP forܰଷ()for any ଷ
∈ Δ(ܰଷ)
control-disables a controllabletransition at a marking in Δ(ܰଷ) only if its firing results in a new
marking thatis not in Δ(ܰଷ). The minimally restrictive LESP would control-disable the non-
choicetransition ݐଶ ∈ ܶ at the marking(0 1 0 0 1)்
∈ Δ(ܰଷ).
As a consequence of theorem 5, without loss of generality, we can assume all non-choice
transitions are uncontrollable, even when they are not, for any instance ofthe class of PN
structures ℋ. This is formally stated in the following theorem.
8. International Journal of Computer Science, Engineering and Applications (IJCSEA) Vol.5, No.2, April 2015
Figure 2. A graphical illustration used in the proof of theorem 5.
Theorem 6: Let ܰ = (ߎ, ܶ, ߔ,
transitions is partitioned into the set of uncontrollable transitions
ܶ (i.e. ܶ = ܶ ∪ ܶ௨andܶ௨ ∩ ܶ
structurally identical to N, but the set of transitions in
uncontrollable- and controllable-
andܶ = ܶ − ܶ௨. Then ∆(ܰ) = ∆
Proof: Sinceܶ ⊆ ܶ, it follows that
bycontradiction. Suppose,∆൫ܰ൯ ⊂
is, ∃ଵ
∈ ∆(ܰ), ∃ݐ̂௨ ∈ ܶ௨such that
with respect to N, it must be that
thatଶ
∈ ∆(ܰ), which establishes the result.
As an illustration, the non-choice, controllable transition
can be considered to be uncontrollable, which e
controllable transitions. There is an LESP for a PN
only if the PN is live. This leads to the observationthat the PN
International Journal of Computer Science, Engineering and Applications (IJCSEA) Vol.5, No.2, April 2015
Figure 2. A graphical illustration used in the proof of theorem 5.
, ߁) be a PN structure from the familyℋ, where the set
transitions is partitioned into the set of uncontrollable transitions ܶ௨, and controllabletransitions
= ∅). Suppose ܰis another memberof the family
, but the set of transitions in ܰ arepartitioned into a di
-transitions, where
ܶ௨ = ܶ௨ ∪ {ݐ ∈ ܶ| ቀ ݐ•
)•
= {}ݐቅ,
∆൫ܰ൯.
, it follows that ∆൫ܰ൯ ⊆ ∆(ܰ). The reverse inclusion is shown
൫ ൯ ⊂ ∆(ܰ), then∆(ܰ) is not control invariant with respectto
such that ଵ
௧ೠ
→ ଶ
and ଶ
∉ ∆(ܰ). Since ⊆ ∆(ܰ)is control invariant
, it must be thatݐ̂ ∈ {ݐ ∈ ܶ| ቀ ݐ•
)•
= {}ݐቅ. But,from theorem 5, we know
which establishes the result. ♣
choice, controllable transition ݐଶin the PN structure ܰଶof figure 1(b)
can be considered to be uncontrollable, which effectively results in aPN structure with no
e is an LESP for a PN N(m0
)withno controllable transitions if and
only if the PN is live. This leads to the observationthat the PNܰଶ(ଶ
)is live for any
International Journal of Computer Science, Engineering and Applications (IJCSEA) Vol.5, No.2, April 2015
8
, where the set of
, and controllabletransitions
is another memberof the family ℋ that is
arepartitioned into a different set of
. The reverse inclusion is shown
is not control invariant with respectto ܰ. That
is control invariant
. But,from theorem 5, we know
of figure 1(b)
ectively results in aPN structure with no
withno controllable transitions if and
ଶ
∈ ∆(ܰଶ).
9. International Journal of Computer Science, Engineering and Applications (IJCSEA) Vol.5, No.2, April 2015
9
The observation that we can assume all non-choice transitions are uncontrollable,even when they
are not for any ܰ ∈ ℋ, is critical to the speeding-up the execution ofthe software package
described in reference [7]. This is illustrated in subsequent text.
The PN structures ܰସ and ܰହ shown in figure 3(a) and 3(b) are FCPN structures,and consequently
they belong to the class ℋ. The only difference between them isthat the non-choice transition ݐହ
is controllable (resp. uncontrollable) in ܰସ (resp. ܰହ).
As a consequence of theorem 6, the sets Δ(ܰସ) and Δ(ܰହ) are identical, and areidentified by the
twenty-four minimal elements shown in figure 4, which shows theoutput generated by the above
mentioned software for ܰହ. The algorithm in references[5,7], finds a series of outer-
approximations Ψ for ∆(ܰ) for an appropriate PNstructure N, that are control invariant with
respect to N.
The iteration starts with Ψ, the largest controllable, right-closed subset of the setof initial
markings for which there is an LESP for the fully-controlled version of N.In the context of this
example, eight minimal elements identify the right-closed ofinitial markings for which there is an
LESP for the fully-controllable version of ܰହshown in figure 4. The second and third among this
list of eight minimal elements arenot control invariant asݐହ, ݐ ∈ ܶ௨ and
(0 0 1 0 0 0 0 0 0)்
௧ఱ
→ (0 0 0 1 0 0 0 0 0)்
௧ళ
→ (0 0 0 0 0 0 0 0 0)்
.
The largest controllable subset of this right-closed set is Ψ,which is identified by the six minimal
elements shown immediately afterwards in thesame figure.
For any right-closed set of markings Ψ that is control invariant with respect toa PN structure N,
we can envisage a supervisory policy ℘ஏ that disables the firingof a controllable transition at a
marking if its firing would result in a new marking that is not in Ψ. It is possible to construct the
coverability graph for the PN N(m0
),under the influence of this supervisory policy. The loop-test
procedure of reference[7] checks if there is a closed-path identified by ߪ ∈ ܶ∗
in this coverability
graph,where (1) every transition in T appears at least once in ߪ, and (2) ۱)ߪ(ܠ ≥ , that is,the net
token-load change after the execution of the string ߪ is non-negative.
With reference to the examples at hand, the loop-test checks if the above mentioned path-
conditionis satisfied in the coverability graph that is generated by each minimal element
ofΨunder the influence of the supervisory policy ℘ஏ. If a minimal element fails this test,it is
elevated by a set of unit-vectors, which defines a right-closed proper subset ofΨ. The largest
controllable subset of this right-closed set is Ψାଵ, which used in lieu of Ψ in the next iteration.
As shown in figure 4, four minimal elements,
(1 0 0 0 0 0 0 0 0)்
, (0 0 0 0 0 0 1 0 0)்
, (0 0 0 0 0 0 0 1 0)்
, and(0 0 0 0 0 0 0 0 1)்
that define Ψ for ܰହ, fail this test. The loop-test will fail for the first minimal
element(1 0 0 0 0 0 0 0 0)்
∈ min (Ψ), as ܶ(ܰହ, (1 0 0 0 0 0 0 0 0)்) = {ݐଵ, ݐଷ}(⊆ ܶ).
But,
(1 0 0 0 0 0 0 0 0)்
௧భ
→ (0 1 0 0 0 0 0 0 0)்
and
(1 0 0 0 0 0 0 0 0)்
௧య
→ (0 0 1 1 0 0 0 0 0)்
.
Since, (0 1 0 0 0 0 0 0 0)்
, (0 0 1 1 0 0 0 0 0)்
∉ Ψ, the supervisorypolicy ℘ஏబ
would disable
these transitions at the marking (1 0 0 0 0 0 0 0 0)்
,which effectively creates a policy-induced
deadlock state. The test fails for second,third and fourth minimal elements
10. International Journal of Computer Science, Engineering and Applications (IJCSEA) Vol.5, No.2, April 2015
10
(0 0 0 0 0 0 1 0 0)்
, (0 0 0 0 0 0 0 1 0)்
, (0 0 0 0 0 0 0 0 1)்
∈ min(Ψ),
as the marking (1 0 0 0 0 0 0 0 0)்
is inevitably reached after the firing of an appropriate set of
transitions. Specifically,
(0 0 0 0 0 0 1 0 0)்
௧వ௧భభ
ሱۛۛሮ (1 0 0 0 0 0 0 0 0)்
,
(0 0 0 0 0 0 0 1 0)்
௧భబ௧భభ
ሱۛۛሮ (1 0 0 0 0 0 0 0 0)்
,
and (0 0 0 0 0 0 0 0 1)்
௧భభ
ሱሮ (1 0 0 0 0 0 0 0 0)்
.
Since the marking (1 0 0 0 0 0 0 0 0)்
failed the loop-test,it follows that these three marking
would fail the test, as well.
The four minimal elements, that failed the loop-test, are elevated by nine unitvectors, and the
largest controllable, right-closed set of this newly constructed set isidentified by the twenty-four
minimal elements shown in figure 4, which identifiesthe next iterate Ψଵ. Each of these twenty-
four minimal elements pass the loop-testreferred to earlier, implying that Δ(ܰହ) = Ψଵ. From
theorem 6, we infer Δ(ܰସ) = Ψଵ,as well.
We turn our attention to the iteration scheme for ܰସ where ݐହ is left as a controllabletransition.
The right-closed set of initial markings for which there is an LESPfor the fully-controlled version
of ܰସ is identified by the same set of eight minimalelements shown in the initial part of the output
of figure 4. The largest controllablesubset of this set (Ψ) is identified by the six minimal
elements of figure 4 along withthe vector (0 0 1 0 0 0 0 0 0)்
. This extra minimal element is due
to the fact thatݐହ is controllable in ܰସ, which fails the loop-test along with the four that failed
thetest in figure 4. After the elevation by unit-vectors as described above, the next iterateΨଵ has
the twenty-four minimal elements shown in figure 4 together with eight newelements
(1 0 1 0 0 0 0 0 0)்
, (0 1 1 0 0 0 0 0 0)்
, (0 0 2 0 0 0 0 0 0)்
, (0 0 1 1 0 0 0 0 0)்
,
(0 0 1 0 1 0 0 0 0)்
, (0 0 1 0 0 0 1 0 0)்
, (0 0 1 0 0 0 0 1 0)்
, (0 0 1 0 0 0 0 0 1)்
That is, the minimal element (0 0 1 0 0 0 0 0 0)்
of Ψis replaced by these eightelements, which
defines Ψଵ. These eight elements fail the loop-test, and are replacedwith additional elevated
vectors, and so on. The right-closed set that is defined by thisiteration scheme, in the limit, is the
set Δ(ܰହ) described earlier. But, as a computationscheme this procedure will not terminate. This
issue is mitigated by ensuringthat all controllable, non-choice transitions are interpreted as being
a part of the setof uncontrollable transitions. This has theoretical sanction as per theorems 5 and
6.There are other examples where the improvement in runtime is not as dramatic as
thisillustrative example.
The method isNetFreeChoice() within the class PetriNet of the previous version of the code (cf.
reference [7]),is replaced by isNetHClass() instead. The program terminates if the PN
structureunder consideration does not belong to the class H. If the the PN structure belongsto the
class ℋ, the method relabelNonChoiceTransitions() is used to relabel all controllablenon-choice
transitions in the PN structure as uncontrollable transitions. Following this, the procedures
outlined in reference [7] are executed to synthesize theminimally restrictive LESP for the PN
structure at hand.
11. International Journal of Computer Science, Engineering and Applications (IJCSEA) Vol.5, No.2, April 2015
Figure 3. (a) The PN structure ܰସ is a member of
also a member of ℋ. The non-choice transition
Fromtheorem 6, we infer that ∆(ܰସ)
4. Concluding Remarks
If some process in a manufacturing system enters into a state of suspended animationfor
perpetuity, while other events proceed towards completion with no impediment,we say the system
is in a livelocked-state. Procedures that can
manufacturing system from entering into livelockedstatesare highly desirable.
In this paper we identified two enhancements to the software tool [7] that synthesizesthe
minimally restrictive, liveness enf
systems modeled using a class of weighted
For the first enhancement, we identified a class of PN structures,
classes of PN structures where the existe
sufficient to conclude that there is an LESP when the sameinstance is initialized with a larger
marking. This broadens the scope of the softwaretool of reference [7]. For the second
enhancement, we showed that the minimallyrestrictive LESP does not control
transitions in the PN model ofthe manufacturing system. This observation plays a crucial role in
improving thespeed of convergence of the iterative scheme used in the software des
above,which was illustrated by an example.
International Journal of Computer Science, Engineering and Applications (IJCSEA) Vol.5, No.2, April 2015
is a member of ℋ as it is an FCPN structure. (b) The PN structure
choice transition ݐହ is controllable (resp. uncontrollable) in
( ) = ∆(ܰହ).
If some process in a manufacturing system enters into a state of suspended animationfor
perpetuity, while other events proceed towards completion with no impediment,we say the system
state. Procedures that can synthesize supervisorypolicies that can prevent the
manufacturing system from entering into livelockedstatesare highly desirable.
In this paper we identified two enhancements to the software tool [7] that synthesizesthe
liveness enforcing supervisory policy (LESP) for aclass of manufacturing
systems modeled using a class of weighted Petri nets (PNs).
For the first enhancement, we identified a class of PN structures, ℋ, that includesall known
classes of PN structures where the existence of a LESP for an instanceinitialized at a marking is
cient to conclude that there is an LESP when the sameinstance is initialized with a larger
marking. This broadens the scope of the softwaretool of reference [7]. For the second
howed that the minimallyrestrictive LESP does not control-disable non
transitions in the PN model ofthe manufacturing system. This observation plays a crucial role in
improving thespeed of convergence of the iterative scheme used in the software des
above,which was illustrated by an example.
International Journal of Computer Science, Engineering and Applications (IJCSEA) Vol.5, No.2, April 2015
11
as it is an FCPN structure. (b) The PN structure ܰହis
is controllable (resp. uncontrollable) in ܰସ (resp. ܰହ).
If some process in a manufacturing system enters into a state of suspended animationfor
perpetuity, while other events proceed towards completion with no impediment,we say the system
synthesize supervisorypolicies that can prevent the
In this paper we identified two enhancements to the software tool [7] that synthesizesthe
(LESP) for aclass of manufacturing
, that includesall known
nce of a LESP for an instanceinitialized at a marking is
cient to conclude that there is an LESP when the sameinstance is initialized with a larger
marking. This broadens the scope of the softwaretool of reference [7]. For the second
disable non-choice
transitions in the PN model ofthe manufacturing system. This observation plays a crucial role in
improving thespeed of convergence of the iterative scheme used in the software described
12. International Journal of Computer Science, Engineering and Applications (IJCSEA) Vol.5, No.2, April 2015
Figure 4. The output file generated by the software described in reference [7] for the FCPN structure
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