In the present work, Lyapunov stability theory, nonlinear adaptive control law and the parameter update
law were utilized to derive the state of two new chaotic reversal systems after being synchronized by the
function projective method. Using this technique allows for a scaling function instead of a constant thereby
giving a better method in applications in secure communication. Numerical simulations are presented to
demonstrate the effective nature of the proposed scheme of synchronization for the new chaotic reversal
system.
ADAPTIVE CONTROL AND SYNCHRONIZATION OF SPROTT-I SYSTEM WITH UNKNOWN PARAMETERSijscai
This paper derives new results for the adaptive control and synchronization design of the Sprott-I chaotic system (1994), when the system parameters are unknown. First, we build an adaptive controller to stabilize the Sprott-I chaotic system to its unstable equilibrium at the origin. Then we build an adaptive
synchronizer to achieve global chaos synchronization of the identical Sprott-I chaotic systems with unknown parameters. The results derived for adaptive stabilization and adaptive synchronization for the Sprott-I chaotic system have been established using adaptive control theory and Lyapunov stability
theory. Numerical simulations have been shown to demonstrate the effectiveness of the adaptive control and synchronization schemes derived in this paper for the Sprott-I chaotic system.
ADAPTIVE CONTROL AND SYNCHRONIZATION OF HYPERCHAOTIC NEWTON-LEIPNIK SYSTEM ijait
The hyperchaotic Newton-Leipnik system (Ghosh and Bhattacharya, 2010) is one of the recently discovered four-dimensional hyperchaotic systems. This paper investigates the adaptive control and synchronization of hyperchaotic Newton-Leipnik system with unknown parameters. First, adaptive
control laws are designed to stabilize the hyperchaotic Newton-Leipnik system to its unstable equilibrium at the origin based on the adaptive control theory and Lyapunov stability theory. Then adaptive control laws are derived to achieve global chaos synchronization of identical hyperchaotic Newton-Leipnik
systems with unknown parameters. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive stabilization and synchronization schemes.
ADAPTIVE CONTROL AND SYNCHRONIZATION OF LIU’S FOUR-WING CHAOTIC SYSTEM WITH C...IJCSEA Journal
This paper investigates the adaptive chaos control and synchronization of Liu’s four-wing chaotic system with cubic nonlinearity (Liu, 2009) and unknown parameters. First, we design adaptive control laws to stabilize the Liu’s four-wing chaotic system with cubic nonlinearity to its unstable equilibrium at the origin based on the adaptive control theory and Lyapunov stability theory. Next, we derive adaptive control laws to achieve global chaos synchronization of identical Liu’s four-wing chaotic systems with cubic nonlinearity and unknown parameters. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive chaos control and synchronization schemes.
ADAPTIVE CONTROL AND SYNCHRONIZATION OF RÖSSLER PROTOTYPE-4 SYSTEMijait
This paper investigates the adaptive control and synchronization of Rössler prototype-4 system with unknown parameters. The Rössler prototype-4 system is a classical three-dimensional chaotic system studied by O.E. Rössler (1979). First, adaptive control laws are designed to stabilize the Rössler prototype-4 system to its unstable equilibrium at the origin based on the adaptive control theory and Lyapunov stability theory. Then adaptive control laws are derived to achieve global chaos synchronization of identical Rössler prototype-4 systems with unknown parameters. Numerical simulations are shown to
validate and illustrate the effectiveness of the proposed adaptive control and synchronization schemes for the Rössler prototype-4 system.
ADAPTIVE CHAOS CONTROL AND SYNCHRONIZATION OF HYPERCHAOTIC LIU SYSTEM ijcseit
The hyperchaotic Liu system (Wang and Liu, 2006) is one of the important models of four-dimensional
hyperchaotic systems. This paper investigates the adaptive chaos control and synchronization of
hyperchaotic Liu system with unknown parameters. First, adaptive control laws are designed to stabilize
the hyperchaotic Liu system to its unstable equilibrium at the origin based on the adaptive control theory
and Lyapunov stability theory. Then adaptive control laws are derived to achieve global chaos
synchronization of identical hyperchaotic Liu systems with unknown parameters. Numerical simulations
are presented to demonstrate the effectiveness of the proposed adaptive chaos control and
synchronization schemes.
GLOBAL CHAOS SYNCHRONIZATION OF UNCERTAIN LORENZ-STENFLO AND QI 4-D CHAOTIC S...ijistjournal
In this paper, we apply adaptive control method to derive new results for the global chaos synchronization of 4-D chaotic systems, viz. identical Lorenz-Stenflo(LS) systems (Stenflo, 2001), identical Qi systems (Qi, Chen and Du, 2005) and non-identical LS and Qi systems. In this paper, we shall assume that the parameters of both master and slave systems are unknown and we devise adaptive control schemes for synchronization using the estimates of parameters for both master and slave systems. Our adaptive synchronization schemes derived in this paper are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the adaptive control method is very effective and convenient to synchronize identical and non-identical LS and Qi systems.
Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive synchronization schemes for the identical and non-identical, uncertain LS and Qi 4-D chaotic systems.
Adaptive Control of a Robotic Arm Using Neural Networks Based ApproachWaqas Tariq
A new neural networks and time series prediction based method has been discussed to control the complex nonlinear multi variable robotic arm motion system in 3d environment without engaging the complicated and voluminous dynamic equations of robotic arms in controller design stage, the proposed method gives such compatibility to the manipulator that it could have significant changes in its dynamic properties, like getting mechanical loads, without need to change designs of the controller.
An Automatic Clustering Technique for Optimal ClustersIJCSEA Journal
This paper proposes a simple, automatic and efficient clustering algorithm, namely, Automatic Merging for Optimal Clusters (AMOC) which aims to generate nearly optimal clusters for the given datasets automatically. The AMOC is an extension to standard k-means with a two phase iterative procedure combining certain validation techniques in order to find optimal clusters with automation of merging of clusters. Experiments on both synthetic and real data have proved that the proposed algorithm finds nearly optimal clustering structures in terms of number of clusters, compactness and separation.
ADAPTIVE CONTROL AND SYNCHRONIZATION OF SPROTT-I SYSTEM WITH UNKNOWN PARAMETERSijscai
This paper derives new results for the adaptive control and synchronization design of the Sprott-I chaotic system (1994), when the system parameters are unknown. First, we build an adaptive controller to stabilize the Sprott-I chaotic system to its unstable equilibrium at the origin. Then we build an adaptive
synchronizer to achieve global chaos synchronization of the identical Sprott-I chaotic systems with unknown parameters. The results derived for adaptive stabilization and adaptive synchronization for the Sprott-I chaotic system have been established using adaptive control theory and Lyapunov stability
theory. Numerical simulations have been shown to demonstrate the effectiveness of the adaptive control and synchronization schemes derived in this paper for the Sprott-I chaotic system.
ADAPTIVE CONTROL AND SYNCHRONIZATION OF HYPERCHAOTIC NEWTON-LEIPNIK SYSTEM ijait
The hyperchaotic Newton-Leipnik system (Ghosh and Bhattacharya, 2010) is one of the recently discovered four-dimensional hyperchaotic systems. This paper investigates the adaptive control and synchronization of hyperchaotic Newton-Leipnik system with unknown parameters. First, adaptive
control laws are designed to stabilize the hyperchaotic Newton-Leipnik system to its unstable equilibrium at the origin based on the adaptive control theory and Lyapunov stability theory. Then adaptive control laws are derived to achieve global chaos synchronization of identical hyperchaotic Newton-Leipnik
systems with unknown parameters. Numerical simulations are presented to demonstrate the effectiveness of the proposed adaptive stabilization and synchronization schemes.
ADAPTIVE CONTROL AND SYNCHRONIZATION OF LIU’S FOUR-WING CHAOTIC SYSTEM WITH C...IJCSEA Journal
This paper investigates the adaptive chaos control and synchronization of Liu’s four-wing chaotic system with cubic nonlinearity (Liu, 2009) and unknown parameters. First, we design adaptive control laws to stabilize the Liu’s four-wing chaotic system with cubic nonlinearity to its unstable equilibrium at the origin based on the adaptive control theory and Lyapunov stability theory. Next, we derive adaptive control laws to achieve global chaos synchronization of identical Liu’s four-wing chaotic systems with cubic nonlinearity and unknown parameters. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive chaos control and synchronization schemes.
ADAPTIVE CONTROL AND SYNCHRONIZATION OF RÖSSLER PROTOTYPE-4 SYSTEMijait
This paper investigates the adaptive control and synchronization of Rössler prototype-4 system with unknown parameters. The Rössler prototype-4 system is a classical three-dimensional chaotic system studied by O.E. Rössler (1979). First, adaptive control laws are designed to stabilize the Rössler prototype-4 system to its unstable equilibrium at the origin based on the adaptive control theory and Lyapunov stability theory. Then adaptive control laws are derived to achieve global chaos synchronization of identical Rössler prototype-4 systems with unknown parameters. Numerical simulations are shown to
validate and illustrate the effectiveness of the proposed adaptive control and synchronization schemes for the Rössler prototype-4 system.
ADAPTIVE CHAOS CONTROL AND SYNCHRONIZATION OF HYPERCHAOTIC LIU SYSTEM ijcseit
The hyperchaotic Liu system (Wang and Liu, 2006) is one of the important models of four-dimensional
hyperchaotic systems. This paper investigates the adaptive chaos control and synchronization of
hyperchaotic Liu system with unknown parameters. First, adaptive control laws are designed to stabilize
the hyperchaotic Liu system to its unstable equilibrium at the origin based on the adaptive control theory
and Lyapunov stability theory. Then adaptive control laws are derived to achieve global chaos
synchronization of identical hyperchaotic Liu systems with unknown parameters. Numerical simulations
are presented to demonstrate the effectiveness of the proposed adaptive chaos control and
synchronization schemes.
GLOBAL CHAOS SYNCHRONIZATION OF UNCERTAIN LORENZ-STENFLO AND QI 4-D CHAOTIC S...ijistjournal
In this paper, we apply adaptive control method to derive new results for the global chaos synchronization of 4-D chaotic systems, viz. identical Lorenz-Stenflo(LS) systems (Stenflo, 2001), identical Qi systems (Qi, Chen and Du, 2005) and non-identical LS and Qi systems. In this paper, we shall assume that the parameters of both master and slave systems are unknown and we devise adaptive control schemes for synchronization using the estimates of parameters for both master and slave systems. Our adaptive synchronization schemes derived in this paper are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the adaptive control method is very effective and convenient to synchronize identical and non-identical LS and Qi systems.
Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive synchronization schemes for the identical and non-identical, uncertain LS and Qi 4-D chaotic systems.
Adaptive Control of a Robotic Arm Using Neural Networks Based ApproachWaqas Tariq
A new neural networks and time series prediction based method has been discussed to control the complex nonlinear multi variable robotic arm motion system in 3d environment without engaging the complicated and voluminous dynamic equations of robotic arms in controller design stage, the proposed method gives such compatibility to the manipulator that it could have significant changes in its dynamic properties, like getting mechanical loads, without need to change designs of the controller.
An Automatic Clustering Technique for Optimal ClustersIJCSEA Journal
This paper proposes a simple, automatic and efficient clustering algorithm, namely, Automatic Merging for Optimal Clusters (AMOC) which aims to generate nearly optimal clusters for the given datasets automatically. The AMOC is an extension to standard k-means with a two phase iterative procedure combining certain validation techniques in order to find optimal clusters with automation of merging of clusters. Experiments on both synthetic and real data have proved that the proposed algorithm finds nearly optimal clustering structures in terms of number of clusters, compactness and separation.
RELIABILITY ASSESSMENT OF EMBEDDED SYSTEMS USING STOPWATCH PETRI NETSIJCSEA Journal
In this paper, we propose a reliability approach in which feared events define reliability requirements and
taking them into account allows to design systems which will be able to avoid the drift towards a feared
state. The description of feared scenarios since the system design phase enables us to understand the
reasons of the feared behavior in order to envisage the necessary reconfigurations and choose safe
architectures. In order to face the increasing complexity of embedded systems and to represent the
suspension and resumption of task execution we propose to extract directly feared scenarios from
Stopwatch Petri net model avoiding the generation of the associated reachability graph and the eternal
combinative explosion problem.
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
SYNCHRONIZATION OF A FOUR-WING HYPERCHAOTIC SYSTEMijccmsjournal
This paper presents synchronization of a four-dimensional autonomous hyperchaotic system based on the generalized augmented Lü system. Based on the Lyapunov stability theory an active control law is derived such that the two four-dimensional autonomous hyper-chaotic systems are to be synchronized. Numerical simulations are presented to demonstrate the effectiveness of the synchronization schemes.
In this paper, a new 3D chaotic system is controlled by generalized backstepping method. Generalized
backstepping method is similarity to backstepping method but generalized backstepping method is more
applications in systems than it. Backstepping method is used only to strictly feedback systems but
generalized backsteppingmethod expand this class. New 3D chaotic system is controlled in two participate
sections; stabilization and tracking reference input. Numerical simulations are presented to demonstrate
the effectiveness of the controlschemes.
Adaptive tracking control of sprott h systemZac Darcy
This paper investigates the tracking problem of Sprott-H chaotic system which is three-dimensional chaotic systems discovered by Sprott (1994). New nonlinear control laws are derived for the tracking problem of uncertain Sprott-H chaotic system with unknown parameters. The adaptive generalized backstepping method is applied to control of uncertain Sprott-H chaotic system. Numerical simulations are presented to demonstrate the effectiveness of the control schemes.
A new two-scroll chaotic system with two nonlinearities: dynamical analysis a...TELKOMNIKA JOURNAL
Chaos theory has several applications in science and engineering. In this work, we announce a
new two-scroll chaotic system with two nonlinearities. The dynamical properties of the system such as
dissipativity, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension and bifurcation diagram are
explored in detail. The presence of coexisting chaotic attractors, coexisting chaotic and periodic attractors
in the system is also investigated. In addition, the offset boosting of a variable in the new chaotic system is
achieved by adding a single controlled constant. It is shown that the new chaotic system has rotation
symmetry about the z-axis. An electronic circuit simulation of the new two-scroll chaotic system is built
using Multisim to check the feasibility of the theoretical model.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
SLIDING CONTROLLER DESIGN FOR THE GLOBAL CHAOS SYNCHRONIZATION OF IDENTICAL H...ijait
This paper establishes new results for the sliding controller design for the global chaos synchronization of identical hyperchaotic Yujun systems (2010). Hyperchaotic systems are chaotic nonlinear systems having more than one positive Lyapunov exponent. Because of the complex dynamics properties of hyperchaotic system such as high capacity, high security and high efficiency, they are very useful in secure
communication devices and data encryption. Using sliding mode control theory and Lyapunov stability theory, a general result has been obtained for the global chaos synchronization of identical chaotic nonlinear systems. As an application of this general result, this paper designs a sliding controller for the
global chaos synchronization of hyperchaotic Yujun systems. Numerical results and simulations are shown to validate the proposed sliding controller design and demonstrate its effectiveness in achieving global chaos synchronization of hyperchaotic Yujun systems.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Design of Kalman filter for Airborne ApplicationsIJERA Editor
Today multiple multi-sensor airborne surveillance systems are available which comprises of primary radar and
secondary surveillance radar as the active sensor on board. The electronics and communication support measure
system (ECSMS) will aid in identification, detection and classification of targets. These systems will detect,
identify, classify the different threats present in the surveillance area and supports defense operation. These
systems contain multiple functional operations as detection of air borne and surface target, tracking, and Multisensor
data fusion. This paper presents the multi-sensor data fusion technique and how to detect and track
moving target in the surveillance area.
The advent of multi-core architecture has highly influenced the area of high performance computing.
Parallel compilation is the area which still needs significant improvement by the use of this architecture.
Recent research has shown some improvement in lexical analysis phase. But it is difficult to implement the
same technique in parsing phase. This paper highlights some issues related to implementation of parallel
parsing on multi-core machines.
RELIABILITY ASSESSMENT OF EMBEDDED SYSTEMS USING STOPWATCH PETRI NETSIJCSEA Journal
In this paper, we propose a reliability approach in which feared events define reliability requirements and
taking them into account allows to design systems which will be able to avoid the drift towards a feared
state. The description of feared scenarios since the system design phase enables us to understand the
reasons of the feared behavior in order to envisage the necessary reconfigurations and choose safe
architectures. In order to face the increasing complexity of embedded systems and to represent the
suspension and resumption of task execution we propose to extract directly feared scenarios from
Stopwatch Petri net model avoiding the generation of the associated reachability graph and the eternal
combinative explosion problem.
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
SYNCHRONIZATION OF A FOUR-WING HYPERCHAOTIC SYSTEMijccmsjournal
This paper presents synchronization of a four-dimensional autonomous hyperchaotic system based on the generalized augmented Lü system. Based on the Lyapunov stability theory an active control law is derived such that the two four-dimensional autonomous hyper-chaotic systems are to be synchronized. Numerical simulations are presented to demonstrate the effectiveness of the synchronization schemes.
In this paper, a new 3D chaotic system is controlled by generalized backstepping method. Generalized
backstepping method is similarity to backstepping method but generalized backstepping method is more
applications in systems than it. Backstepping method is used only to strictly feedback systems but
generalized backsteppingmethod expand this class. New 3D chaotic system is controlled in two participate
sections; stabilization and tracking reference input. Numerical simulations are presented to demonstrate
the effectiveness of the controlschemes.
Adaptive tracking control of sprott h systemZac Darcy
This paper investigates the tracking problem of Sprott-H chaotic system which is three-dimensional chaotic systems discovered by Sprott (1994). New nonlinear control laws are derived for the tracking problem of uncertain Sprott-H chaotic system with unknown parameters. The adaptive generalized backstepping method is applied to control of uncertain Sprott-H chaotic system. Numerical simulations are presented to demonstrate the effectiveness of the control schemes.
A new two-scroll chaotic system with two nonlinearities: dynamical analysis a...TELKOMNIKA JOURNAL
Chaos theory has several applications in science and engineering. In this work, we announce a
new two-scroll chaotic system with two nonlinearities. The dynamical properties of the system such as
dissipativity, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension and bifurcation diagram are
explored in detail. The presence of coexisting chaotic attractors, coexisting chaotic and periodic attractors
in the system is also investigated. In addition, the offset boosting of a variable in the new chaotic system is
achieved by adding a single controlled constant. It is shown that the new chaotic system has rotation
symmetry about the z-axis. An electronic circuit simulation of the new two-scroll chaotic system is built
using Multisim to check the feasibility of the theoretical model.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
SLIDING CONTROLLER DESIGN FOR THE GLOBAL CHAOS SYNCHRONIZATION OF IDENTICAL H...ijait
This paper establishes new results for the sliding controller design for the global chaos synchronization of identical hyperchaotic Yujun systems (2010). Hyperchaotic systems are chaotic nonlinear systems having more than one positive Lyapunov exponent. Because of the complex dynamics properties of hyperchaotic system such as high capacity, high security and high efficiency, they are very useful in secure
communication devices and data encryption. Using sliding mode control theory and Lyapunov stability theory, a general result has been obtained for the global chaos synchronization of identical chaotic nonlinear systems. As an application of this general result, this paper designs a sliding controller for the
global chaos synchronization of hyperchaotic Yujun systems. Numerical results and simulations are shown to validate the proposed sliding controller design and demonstrate its effectiveness in achieving global chaos synchronization of hyperchaotic Yujun systems.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Design of Kalman filter for Airborne ApplicationsIJERA Editor
Today multiple multi-sensor airborne surveillance systems are available which comprises of primary radar and
secondary surveillance radar as the active sensor on board. The electronics and communication support measure
system (ECSMS) will aid in identification, detection and classification of targets. These systems will detect,
identify, classify the different threats present in the surveillance area and supports defense operation. These
systems contain multiple functional operations as detection of air borne and surface target, tracking, and Multisensor
data fusion. This paper presents the multi-sensor data fusion technique and how to detect and track
moving target in the surveillance area.
The advent of multi-core architecture has highly influenced the area of high performance computing.
Parallel compilation is the area which still needs significant improvement by the use of this architecture.
Recent research has shown some improvement in lexical analysis phase. But it is difficult to implement the
same technique in parsing phase. This paper highlights some issues related to implementation of parallel
parsing on multi-core machines.
Presentación utilizada en la Ponencia titulada "Subvertir la normalidad en la Escuela Pública", durante el III Encuentro Estatal de Mareas por la Educación Pública: "La educación que queremos", desarrollado en Málaga del 7 al 9 de Julio de 2015.
FUNCTION PROJECTIVE SYNCHRONIZATION OF NEW CHAOTIC REVERSAL SYSTEMSijcseit
In the present work, Lyapunov stability theory, nonlinear adaptive control law and the parameter update
law were utilized to derive the state of two new chaotic reversal systems after being synchronized by the
function projective method. Using this technique allows for a scaling function instead of a constant thereby
giving a better method in applications in secure communication. Numerical simulations are presented to
demonstrate the effective nature of the proposed scheme of synchronization for the new chaotic reversal
system.
FUNCTION PROJECTIVE SYNCHRONIZATION OF NEW CHAOTIC REVERSAL SYSTEMSijcseit
In the present work, Lyapunov stability theory, nonlinear adaptive control law and the parameter update
law were utilized to derive the state of two new chaotic reversal systems after being synchronized by the
function projective method. Using this technique allows for a scaling function instead of a constant thereby
giving a better method in applications in secure communication. Numerical simulations are presented to
demonstrate the effective nature of the proposed scheme of synchronization for the new chaotic reversal
system.
SYNCHRONIZATION OF A FOUR-WING HYPERCHAOTIC SYSTEMijccmsjournal
This paper presents synchronization of a four-dimensional autonomous hyperchaotic system based on the
generalized augmented Lü system. Based on the Lyapunov stability theory an active control law is derived
such that the two four-dimensional autonomous hyper-chaotic systems are to be synchronized. Numerical
simulations are presented to demonstrate the effectiveness of the synchronization schemes.
SYNCHRONIZATION OF A FOUR-WING HYPERCHAOTIC SYSTEMijccmsjournal
This paper presents synchronization of a four-dimensional autonomous hyperchaotic system based on the
generalized augmented Lü system. Based on the Lyapunov stability theory an active control law is derived
such that the two four-dimensional autonomous hyper-chaotic systems are to be synchronized. Numerical
simulations are presented to demonstrate the effectiveness of the synchronization schemes.
A New Chaotic System with Line of Equilibria: Dynamics, Passive Control and C...IJECEIAES
A new chaotic system with line equilibrium is introduced in this paper. This system consists of five terms with two transcendental nonlinearities and two quadratic nonlinearities. Various tools of dynamical system such as phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, bifurcation diagram and Poincarè map are used. It is interesting that this system has a line of fixed points and can display chaotic attractors. Next, this paper discusses control using passive control method. One example is given to insure the theoretical analysis. Finally, for the new chaotic system, An electronic circuit for realizing the chaotic system has been implemented. The numerical simulation by using MATLAB 2010 and implementation of circuit simulations by using MultiSIM 10.0 have been performed in this study.
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.
Fault tolerant synchronization of chaotic heavy symmetric gyroscope systems v...ISA Interchange
In this paper, fault tolerant synchronization of chaotic gyroscope systems versus external disturbances via Lyapunov rule-based fuzzy control is investigated. Taking the general nature of faults in the slave system into account, a new synchronization scheme, namely, fault tolerant synchronization, is proposed, by which the synchronization can be achieved no matter whether the faults and disturbances occur or not. By making use of a slave observer and a Lyapunov rule-based fuzzy control, fault tolerant synchronization can be achieved. Two techniques are considered as control methods: classic Lyapunov-based control and Lyapunov rule-based fuzzy control. On the basis of Lyapunov stability theory and fuzzy rules, the nonlinear controller and some generic sufficient conditions for global asymptotic synchronization are obtained. The fuzzy rules are directly constructed subject to a common Lyapunov function such that the error dynamics of two identical chaotic motions of symmetric gyros satisfy stability in the Lyapunov sense. Two proposed methods are compared. The Lyapunov rule-based fuzzy control can compensate for the actuator faults and disturbances occurring in the slave system. Numerical simulation results demonstrate the validity and feasibility of the proposed method for fault tolerant synchronization.
This paper presents synchronization of a new autonomous hyperchaotic system. The generalized
backstepping technique is applied to achieve hyperchaos synchronization for the two new hyperchaotic
systems. Generalized backstepping method is similarity to backstepping. Backstepping method is used only
to strictly feedback systems but generalized backstepping method expands this class. Numerical simulations
are presented to demonstrate the effectiveness of the synchronization schemes.
This paper presents synchronization of a new autonomous hyperchaotic system. The generalized backstepping technique is applied to achieve hyperchaos synchronization for the two new hyperchaotic systems. Generalized backstepping method is similarity to backstepping. Backstepping method is used only to strictly feedback systems but generalized backstepping method expands this class. Numerical simulations are presented to demonstrate the effectiveness of the synchronization schemes.
This paper presents synchronization of a new autonomous hyperchaotic system. The generalized
backstepping technique is applied to achieve hyperchaos synchronization for the two new hyperchaotic systems. Generalized back-stepping method is similarity to backstepping. Backstepping method is used only
to strictly feedback systems but generalized back-stepping method expands this class. Numerical simulations are presented to demonstrate the effectiveness of the synchronization schemes.
This paper presents synchronization of a new autonomous hyperchaotic system. The generalized
backstepping technique is applied to achieve hyperchaos synchronization for the two new hyperchaotic
systems. Generalized backstepping method is similarity to backstepping. Backstepping method is used only
to strictly feedback systems but generalized backstepping method expands this class. Numerical simulations
are presented to demonstrate the effectiveness of the synchronization schemes.
GLOBAL CHAOS SYNCHRONIZATION OF UNCERTAIN LORENZ-STENFLO AND QI 4-D CHAOTIC S...ijistjournal
In this paper, we apply adaptive control method to derive new results for the global chaos synchronization of 4-D chaotic systems, viz. identical Lorenz-Stenflo(LS) systems (Stenflo, 2001), identical Qi systems (Qi, Chen and Du, 2005) and non-identical LS and Qi systems. In this paper, we shall assume that the parameters of both master and slave systems are unknown and we devise adaptive control schemes for synchronization using the estimates of parameters for both master and slave systems. Our adaptive synchronization schemes derived in this paper are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the adaptive control method is very effective and convenient to synchronize identical and non-identical LS and Qi systems. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive synchronization schemes for the identical and non-identical, uncertain LS and Qi 4-D chaotic systems.
Adaptive Stabilization and Synchronization of Hyperchaotic QI SystemCSEIJJournal
The hyperchaotic Qi system (Chen, Yang, Qi and Yuan, 2007) is one of the important models of four-
dimensional hyperchaotic systems. This paper investigates the adaptive stabilization and synchronization
of hyperchaotic Qi system with unknown parameters. First, adaptive control laws are designed to
stabilize the hyperchaotic Qi system to its equilibrium point at the origin based on the adaptive control
theory and Lyapunov stability theory. Then adaptive control laws are derived to achieve global chaos
synchronization of identical hyperchaotic Qi systems with unknown parameters. Numerical simulations
are shown to demonstrate the effectiveness of the proposed adaptive stabilization and synchronization
schemes.
Adaptive Controller Design For The Synchronization Of Moore-Spiegel And Act S...ijcsa
In this paper, we design adaptive controllers for the global chaos synchronization of identical MooreSpiegel systems (1966), identical ACT systems (1981) and non-identical Moore-Spiegel and ACT chaotic systems with unknown parameters. Our adaptive synchronization results derived in this paper for
uncertain Moore-Spiegel and ACT systems are established using Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the adaptive control method is very effective and convenient to synchronize identical and non-identical uncertain Moore-Spiegel and ACT chaotic
systems. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive synchronization schemes for the global chaos synchronization of the uncertain chaotic systems derived in this paper.
A New Chaotic System with a Pear-Shaped Equilibrium and Its Circuit Simulation IJECEIAES
This paper reports the finding a new chaotic system with a pear-shaped equilibrium curve and makes a valuable addition to existing chaotic systems with infinite equilibrium points in the literature. The new chaotic system has a total of five nonlinearities. Lyapunov exponents of the new chaotic system are studied for verifying chaos properties and phase portraits of the new system are unveiled. An electronic circuit simulation of the new chaotic system with pear-shaped equilibrium curve is shown using Multisim to check the model feasibility
Feedback linearization and Backstepping controllers for Coupled Tanksieijjournal
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exponentialasymptotic stability, with very short time response, no significant overshooting is recordedand with a negligible norm of the error. The second control procedure is the approaches of Backsteppingcontrol (BC) which is a recursive procedure that interlaces the choice of a Lyapunov functionwith 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 beencountered in other methods. Finally both of the proposed control schemes guarantee theasymptoticstability of the closed loop system meeting trajectory tracking objectives
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1. International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol. 4, No.5, October 2014
FUNCTION PROJECTIVE SYNCHRONIZATION
OF NEW CHAOTIC REVERSAL SYSTEMS
Olurotimi S. Ojoniyi
Department of Physics and Telecommunications, Tai Solarin University of Education,
Ijagun, Ogun State Nigeria.
ABSTRACT
In the present work, Lyapunov stability theory, nonlinear adaptive control law and the parameter update
law were utilized to derive the state of two new chaotic reversal systems after being synchronized by the
function projective method. Using this technique allows for a scaling function instead of a constant thereby
giving a better method in applications in secure communication. Numerical simulations are presented to
demonstrate the effective nature of the proposed scheme of synchronization for the new chaotic reversal
system.
KEYWORDS
Function projective synchronization, Lyapunov stability theory, chaotic system, new chaotic reversal
system.
1. INTRODUCTION
The chaotic dynamics observed only in nonlinear systems have been largely defined by
oscillations which are sensitive to initial conditions [1]. Lorenz and Rossler systems are
pioneering simple chaotic systems discovered with a lot of interesting properties that can model
physical systems [1]-[2]. This relatively new dynamical behaviour has since been discovered in
other disciplines such as engineering, science and economics. In order to understand fully most
nonlinear phenomenon in nature through interaction of systems, the control and synchronization
of chaotic oscillations is vital.
The process of controlling and synchronising chaotic systems has attracted much attention since
its discovery in less than twenty years [3]. The work of Pecora and Caroll [4] generated a wider
research in synchronization since it entails the synchronization of two identical chaotic systems
with different initial conditions.A number of methods of synchronization have been proposed
since the pioneering work of Pecora and Caroll such as complete synchronization, generalized
synchronization, phase synchronization, lag synchronization, adaptive synchronization, time-scale
synchronization, intermittent synchronization, projective synchronization and function
projective synchronization [5]-[9]. Function projective synchronization deserves much attention
since it has been found applicable and better in secure communication.
Function projective synchronization implies that the master and slave oscillators could be
synchronized up to a scaling function unlike a constant in the projective synchronization. The
DOI : 10.5121/ijcseit.2014.4503 33
2. International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol. 4, No.5, October 2014
advantage is that it becomes more complex to determine the function used and as a result more
secure communication is achieved under this scheme.
In the present work, function projective synchronization of new chaotic reversal systems [10]
with uncertain parameters using nonlinear adaptive controller has been investigated to
demonstrate the effectiveness of this scheme as it applies in secure communication. The
remaining part of this work is arranged as follows: section 2 is on the nonlinear adaptive
controller designed to synchronize the new chaotic reversal systems, section 3 is on numerical
simulations presented to demonstrate the robust nature of the scheme, and section 4 is the
conclusion of the paper.
In the present section, we examine briefly the dynamics of the new deterministic model for
chaotic reversal [10].
34
2. ADAPTIVE CONTROL SCHEME
We have a new deterministic model for chaotic reversal by C. Gissinger [10] given by:
………. (1)
Where and are the states and are unknown parameters.
The system (1) is chaotic when the parameter values are taken as:
and as shown in figure 1.
Strange Attractor of the New Chaotic Reversal System
-5
0
5
-5
0
4
2
0
-2
5
x
1
3
x
2 x
Figure 1:
The system (1) is taken as master system, and the slave system with the adaptive control scheme
is taken as
………. (2)
3. International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol. 4, No.5, October 2014
Where are the parameters of the slave which needs to be estimated and are
the nonlinear controllers such that the two new chaotic reversal systems are function projective
synchronized in the sense that
35
……… (3)
Where is the scaling function.
From system (1) and (2) we get the error dynamical system which can be written as
……… (4)
Where
In order to stabilize the error variables of system (3) at the origin, we propose the adaptive control
law and the parameter update law for system (3) as follows
…….(5)
And the update rule for the three uncertain parameters are
……….. (6)
Where and
Theorem For the given scaling function , the function projective synchronization between
the master system (1) and the slave system (2) can be achieved if the nonlinear controller (5) and
the update law (6) are adopted.
Proof We construct the following Lyapunov function
Calculating the time derivative of V along the trajectory of error system (4), we have
4. International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol. 4, No.5, October 2014
36
… (8)
+
+
+ [
Where , and .
It is evident that is negative definite and if and only if . By the Lyapunov
stability theory, the function projective synchronization is achieved. This ends the proof.
3. NUMERICAL SIMULATIONS
The numerical simulations to verify the effectiveness of the proposed function projective
synchronization using the adaptive controllers are carried out by the fourth-order Runge-Kutta
method. This method is used to solve the master system (1) and the slave system (2) with time
step size . The initial conditions of the master system are
. The scaling function is chosen as and . The figure
2 shows that the error variables tend to zero with . Figure 3 shows that the
estimated values of the uncertain parameters converge to as
.
300
250
200
150
100
50
0
0 2 4 6 8 10 12 14 16 18 20
Time / s
e
1
5. International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol. 4, No.5, October 2014
37
5
4
3
2
1
0
-1
0 2 4 6 8 10 12 14 16 18 20
Time /s
e
2
10
8
6
4
2
0
0 2 4 6 8 10 12 14 16 18 20
Time /s
e
3
Figure 2: Error dynamics between master system (1) and the slave system (2)
100
0
-100
-200
-300
0 2 4 6 8 10 12 14 16 18 20
Time /s
a
1
6. International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol. 4, No.5, October 2014
38
4
3
2
1
0
-1
0 2 4 6 8 10 12 14 16 18 20
Time /s
b
1
12
10
8
6
4
2
0
0 2 4 6 8 10 12 14 16 18 20
Time /s
c
1
Figure 3: The time evolution of the estimated parameters
4. CONCLUSION
In the present work we have demonstrated the application of function projective synchronization
in synchronizing the new chaotic reversal systems with uncertain parameters. The Lyapunov
stability theory was used to design the adaptive synchronization controllers with associated
parameter update laws to stabilize the error dynamics between the master and the slave chaotic
oscillators. All the theoretical investigations have been verified by numerical simulations to proof
the effectiveness of the scheme.
REFERENCES
[1] Lorenz, E.N. (1963) “Deterministic nonperiodic flow,” J. Atmos. Phys. Vol. 20, pp 131-141.
[2] Rössler, O.E. (1976) “An equation for continuous chaos,” Physics Letters A, Vol. 57, pp 397-398.
[3] Junbiao Guan, (2012 )‘’Function projective synchronization of a class of chaotic systems with
uncertain parameters’’, Hindawi Publishing Corp., Article ID 431752,
[4] L. M. Pecora and T. L. Carroll, (1990) “Synchronization in chaotic systems,” Physical Review
Letters, vol. 64, no. 8, pp. 821–824,.
[5] M. Rosenblum, A. Pikovsky, and J. Kurths, (1996) “Phase synchronization of chaotic oscillators,”
Physical Review Letters, vol. 76, pp. 1804–1807,.
[6] H. Taghvafard and G. H. Erjaee, (2011)“Phase and anti-phase synchronization of fractional order
chaotic systems via active control,” Communications in Nonlinear Science and Numerical
Simulation, vol. 16, no. 10, pp. 4079–4088,.
[7] R. Mainieri and J. Rehacek, (1999)“Projective synchronization in three-dimensional chaotic systems,”
Physical Review Letters, vol. 82, pp. 3042–3045,.
7. International Journal of Computer Science, Engineering and Information Technology (IJCSEIT), Vol. 4, No.5, October 2014
[8] Junbiao Guan, (2010) “Synchronization control of two different chaotic systems with known and
39
unknown parameters,” Chinese Physics Letters, vol. 27, Article ID 020502,.
[9] L. Runzi, (2008) “Adaptive function project synchronization of Rossler hyperchaotic system with
uncertain parameters,” Physics Letters. A, vol. 372, no. 20, pp. 3667–3671,
[10] Gissinger, C. (2012) ‘’ A new deterministic model for chaotic reversals, ’’ Euro. Phy. J. B 85:137, pp
1-12.
Author
Ojoniyi, Olurotimi Seyi is currently on a Ph.D programme in nonlinear dynamics and chaos
at the department of Physics of the University of Agriculture, Abeokuta, Ogun State, Nigeria.
He holds a M.Sc, degree in Physics from the University of Ibadan, Ibadan, Nigeria and is
currently an academic Staff of Physics and Telecommunications department of Tai Solarin
University of Education, Ijagun, Ogun State, Nigeria.