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 STABILIZATION AND SYNCHRONIZATION OF HYPERCHAOTIC QI SYSTEM cseij
The hyperchaotic Qi system (Chen, Yang, Qi and Yuan, 2007) is one of the important models of fourdimensional 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 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.
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 Hyperchaotic Cai Systemijctcm
The hyperchaotic Cai system (Wang, Cai, Miao and Tian, 2010) is one of the important paradigms of fourdimensional hyperchaotic systems. This paper investigates the adaptive control and synchronization of hyperchaotic Cai system with unknown parameters. First, adaptive control laws are designed to stabilize the hyperchaotic Cai system to its unstable 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 Cai systems with unknown parameters. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive control 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.
THE DESIGN OF ADAPTIVE CONTROLLER AND SYNCHRONIZER FOR QI-CHEN SYSTEM WITH UN...IJCSEA Journal
This paper investigates the design problem of adaptive controller and synchronizer for the Qi-Chen system (2005), when the system parameters are unknown. First, we build an adaptive controller to stabilize the QiChen chaotic system to its unstable equilibrium at the origin. Then we build an adaptive synchronizer to achieve global chaos synchronization of the identical Qi-Chen chaotic systems with unknown parameters. The results derived for adaptive stabilization and adaptive synchronization for the Qi-Chen chaotic system are 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 Qi-Chen chaotic system.
Adaptive Controller and Synchronizer Design for Hyperchaotic Zhou System with...Zac Darcy
In this paper, we establish new results for the adaptive controller and synchronizer design for the
hyperchaotic Zhou system (2009), when the parameters of the system are unknown. Using adaptive control theory and Lyapunov stability theory, we first design an adaptive controller to stabilize the hyperchaotic Zhou system to its unstable equilibrium at the origin. Next, using adaptive control theory and Lyapunov stability theory, we design an adaptive controller to achieve global chaos synchronization
of the identical hyperchaotic Zhou systems with unknown parameters. Simulations have been provided for adaptive controller and synchronizer designs to validate and illustrate the effectiveness of the schemes.
GLOBAL CHAOS SYNCHRONIZATION OF HYPERCHAOTIC QI AND HYPERCHAOTIC JHA SYSTEMS ...ijistjournal
This paper derives new results for the global chaos synchronization of identical hyperchaotic Qi systems (2008), identical hyperchaotic Jha systems (2007) and non-identical hyperchaotic Qi and Jha systems. Active nonlinear control is the method adopted to achieve the complete synchronization of the identical and different hyperchaotic Qi and Jha systems. Our stability results derived in this paper are established using Lyapunov stability theory. Numerical simulations are shown to validate and illustrate the effectiveness of the synchronization results derived in this paper.
ADAPTIVE STABILIZATION AND SYNCHRONIZATION OF HYPERCHAOTIC QI SYSTEM cseij
The hyperchaotic Qi system (Chen, Yang, Qi and Yuan, 2007) is one of the important models of fourdimensional 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 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.
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 Hyperchaotic Cai Systemijctcm
The hyperchaotic Cai system (Wang, Cai, Miao and Tian, 2010) is one of the important paradigms of fourdimensional hyperchaotic systems. This paper investigates the adaptive control and synchronization of hyperchaotic Cai system with unknown parameters. First, adaptive control laws are designed to stabilize the hyperchaotic Cai system to its unstable 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 Cai systems with unknown parameters. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive control 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.
THE DESIGN OF ADAPTIVE CONTROLLER AND SYNCHRONIZER FOR QI-CHEN SYSTEM WITH UN...IJCSEA Journal
This paper investigates the design problem of adaptive controller and synchronizer for the Qi-Chen system (2005), when the system parameters are unknown. First, we build an adaptive controller to stabilize the QiChen chaotic system to its unstable equilibrium at the origin. Then we build an adaptive synchronizer to achieve global chaos synchronization of the identical Qi-Chen chaotic systems with unknown parameters. The results derived for adaptive stabilization and adaptive synchronization for the Qi-Chen chaotic system are 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 Qi-Chen chaotic system.
Adaptive Controller and Synchronizer Design for Hyperchaotic Zhou System with...Zac Darcy
In this paper, we establish new results for the adaptive controller and synchronizer design for the
hyperchaotic Zhou system (2009), when the parameters of the system are unknown. Using adaptive control theory and Lyapunov stability theory, we first design an adaptive controller to stabilize the hyperchaotic Zhou system to its unstable equilibrium at the origin. Next, using adaptive control theory and Lyapunov stability theory, we design an adaptive controller to achieve global chaos synchronization
of the identical hyperchaotic Zhou systems with unknown parameters. Simulations have been provided for adaptive controller and synchronizer designs to validate and illustrate the effectiveness of the schemes.
GLOBAL CHAOS SYNCHRONIZATION OF HYPERCHAOTIC QI AND HYPERCHAOTIC JHA SYSTEMS ...ijistjournal
This paper derives new results for the global chaos synchronization of identical hyperchaotic Qi systems (2008), identical hyperchaotic Jha systems (2007) and non-identical hyperchaotic Qi and Jha systems. Active nonlinear control is the method adopted to achieve the complete synchronization of the identical and different hyperchaotic Qi and Jha systems. Our stability results derived in this paper are established using Lyapunov stability theory. Numerical simulations are shown to validate and illustrate the effectiveness of the synchronization results derived in this paper.
GLOBAL CHAOS SYNCHRONIZATION OF HYPERCHAOTIC QI AND HYPERCHAOTIC JHA SYSTEMS ...ijistjournal
This paper derives new results for the global chaos synchronization of identical hyperchaotic Qi systems (2008), identical hyperchaotic Jha systems (2007) and non-identical hyperchaotic Qi and Jha systems. Active nonlinear control is the method adopted to achieve the complete synchronization of the identical and different hyperchaotic Qi and Jha systems. Our stability results derived in this paper are established using Lyapunov stability theory. Numerical simulations are shown to validate and illustrate the effectiveness of the synchronization results derived in this paper.
ADAPTIVE STABILIZATION AND SYNCHRONIZATION OF LÜ-LIKE ATTRACTORijcseit
This paper derives new results for the adaptive chaos stabilization and synchronization of Lü-like attractor
with unknown parameters. The Lü-like attractor is one of the recently discovered 3-scroll chaotic systems,
which was proposed by D. Li (2007). First, adaptive control laws are determined to stabilize the Lü-like
attractor to its unstable equilibrium at the origin. These adaptive laws are established using Lyapunov
stability theory. Then adaptive synchronization laws are determined so as to achieve global chaos
synchronization of identical Lü-like attractors with unknown parameters. Numerical simulations are
presented to validate and demonstrate the effectiveness of the proposed adaptive control and
synchronization schemes for the Lü-like attractor.
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.
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 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.
ACTIVE CONTROLLER DESIGN FOR THE HYBRID SYNCHRONIZATION OF HYPERCHAOTIC XU AN...Zac Darcy
The synchronization of chaotic systems treats a pair of chaotic systems, which are usually called as master
and slave systems. In the chaos synchronization problem, the goal of the design is to synchronize the states
of master and slave systems asymptotically. In the hybrid synchronization design of master and slave
systems, one part of the systems, viz. their odd states, are completely synchronized (CS), while the other
part, viz. their even states, are completely anti-synchronized (AS) so that CS and AS co-exist in the process
of synchronization. This research work deals with the hybrid synchronization of hyperchaotic Xi systems
(2009) and hyperchaotic Li systems (2005). The main results of this hybrid research work are established
with Lyapunov stability theory. MATLAB simulations of the hybrid synchronization results are shown for
the hyperchaotic Xu and Li systems.
Global Chaos Synchronization of Hyperchaotic Pang and Hyperchaotic Wang Syste...CSEIJJournal
This paper investigates the global chaos synchronization of identical hyperchaotic Wang systems, identical
hyperchaotic Pang systems, and non-identical hyperchaotic Wang and hyperchaotic Pang systems via
adaptive control method. Hyperchaotic Pang system (Pang and Liu, 2011) and hyperchaotic Wang system
(Wang and Liu, 2006) are recently discovered hyperchaotic systems. Adaptive control method is deployed
in this paper for the general case when the system parameters are unknown. Sufficient conditions for global
chaos synchronization of identical hyperchaotic Pang systems, identical hyperchaotic Wang systems and
non-identical hyperchaotic Pang and Wang systems are derived via adaptive control theory and Lyapunov
stability theory. Since the Lyapunov exponents are not required for these calculations, the adaptive control
method is very convenient for the global chaos synchronization of the hyperchaotic systems discussed in
this paper. Numerical simulations are presented to validate and demonstrate the effectiveness of the
proposed synchronization schemes.
ADAPTIVE CONTROL AND SYNCHRONIZATION OF A HIGHLY CHAOTIC ATTRACTORijistjournal
Recently, a novel three-dimensional highly chaotic attractor has been discovered by Srisuchinwong and Munmuangsaen (2010). This paper investigates the adaptive control and synchronization of this highly chaotic attractor with unknown parameters. First, adaptive control laws are designed to stabilize the highly chaotic system to its unstable 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 highly chaotic systems with unknown parameters. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive control and synchronization schemes.
ADAPTIVE CONTROL AND SYNCHRONIZATION OF A HIGHLY CHAOTIC ATTRACTORijistjournal
Recently, a novel three-dimensional highly chaotic attractor has been discovered by Srisuchinwong and Munmuangsaen (2010). This paper investigates the adaptive control and synchronization of this highly chaotic attractor with unknown parameters. First, adaptive control laws are designed to stabilize the highly chaotic system to its unstable 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 highly chaotic systems with unknown parameters. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive control and synchronization schemes.
ACTIVE CONTROLLER DESIGN FOR THE HYBRID SYNCHRONIZATION OF HYPERCHAOTIC ZHEN...ijscai
This paper deals with a new research problem in the chaos literature, viz. hybrid synchronization of a
pair of chaotic systems called the master and slave systems. In the hybrid synchronization design of
master and slave systems, one part of the systems, viz. their odd states, are completely synchronized (CS),
while the other part, viz. their even states, are completely anti-synchronized (AS) so that CS and AS coexist in the process of synchronization. This research work deals with the hybrid synchronization of
hyperchaotic Zheng systems (2010) and hyperchaotic Yu systems (2012). The main results of this hybrid
synchronization research work have been proved using Lyapunov stability theory. Numerical examples of
the hybrid synchronization results are shown along with MATLAB simulations for the hyperchaotic
Zheng and hyperchaotic Yu systems.
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 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.
ADAPTIVESYNCHRONIZER DESIGN FOR THE HYBRID SYNCHRONIZATION OF HYPERCHAOTIC ZH...ijitcs
This paper derives new adaptive synchronizers for the hybrid synchronization of hyperchaotic Zheng
systems (2010) and hyperchaotic Yu systems (2012). In the hybrid synchronization design of master and
slave systems, one part of the systems, viz. their odd states, are completely synchronized (CS), while the
other part, viz. their even states, are completely anti-synchronized (AS) so that CS and AS co-exist in the
process of synchronization. The research problem gets even more complicated, when the parameters of the
hyperchaotic systems are not known and we handle this complicate problem using adaptive control. The
main results of this research work are established via adaptive control theory andLyapunov stability
theory. MATLAB plotsusing classical fourth-order Runge-Kutta method have been depictedfor the new
adaptive hybrid synchronization results for the hyperchaotic Zheng and hyperchaotic Yu systems.
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.
International Journal of Computer Science, Engineering and Information Techno...ijcseit
In chaos theory, the problem anti-synchronization of chaotic systems deals with a pair of chaotic systems
called drive and response systems. In this problem, the design goal is to drive the sum of their respective
states to zero asymptotically. This problem gets even more complicated and requires special attention when
the parameters of the drive and response systems are unknown. This paper uses adaptive control theory
and Lyapunov stability theory to derive new results for the anti-synchronization of hyperchaotic Wang
system (2008) and hyperchaotic Li system (2005) with uncertain parameters. Hyperchaotic systems are
nonlinear dynamical systems exhibiting chaotic behaviour with two or more positive Lyapunov exponents.
The hyperchaotic systems have applications in areas like oscillators, lasers, neural networks, encryption,
secure transmission and secure communication. The main results derived in this paper are validated and
demonstrated with MATLAB simulations.
ANTI-SYNCHRONIZATION OF HYPERCHAOTIC WANG AND HYPERCHAOTIC LI SYSTEMS WITH UN...ijcseit
In chaos theory, the problem anti-synchronization of chaotic systems deals with a pair of chaotic systems
called drive and response systems. In this problem, the design goal is to drive the sum of their respective
states to zero asymptotically. This problem gets even more complicated and requires special attention when
the parameters of the drive and response systems are unknown. This paper uses adaptive control theory
and Lyapunov stability theory to derive new results for the anti-synchronization of hyperchaotic Wang
system (2008) and hyperchaotic Li system (2005) with uncertain parameters. Hyperchaotic systems are
nonlinear dynamical systems exhibiting chaotic behaviour with two or more positive Lyapunov exponents.
The hyperchaotic systems have applications in areas like oscillators, lasers, neural networks, encryption,
secure transmission and secure communication. The main results derived in this paper are validated and
demonstrated with MATLAB simulations.
ADAPTIVE CONTROLLER DESIGN FOR THE HYBRID SYNCHRONIZATION OF HYPERCHAOTIC XU ...ijait
This paper derives new adaptive results for the hybrid synchronization of hyperchaotic Xi systems (2009)
and hyperchaotic Li systems (2005). In the hybrid synchronization design of master and slave systems, one
part of the systems, viz. their odd states, are completely synchronized (CS), while the other part, viz. their
even states, are completely anti-synchronized (AS) so that CS and AS co-exist in the process of
synchronization. The research problem gets even more complicated, when the parameters of the
hyperchaotic systems are unknown and we tackle this problem using adaptive control. The main results of
this research work are proved using adaptive control theory and Lyapunov stability theory. MATLAB
simulations using classical fourth-order Runge-Kutta method are shown for the new adaptive hybrid
synchronization results for the hyperchaotic Xu and hyperchaotic Li systems.
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.
HYBRID SLIDING SYNCHRONIZER DESIGN OF IDENTICAL HYPERCHAOTIC XU SYSTEMS ijitjournal
In this paper, new results have been obtained via sliding mode control for the hybrid chaos synchronization
of identical hyperchaotic Xu systems (Xu, Cai and Zheng, 2009). In hybrid synchronization of master and
slave systems, the odd states are completely synchronized, while the even states are anti-synchronized. The
stability results derived in this paper for the hybrid synchronization of identical hyperchaotic Xu systems
are established using Lyapunov stability theory. MATLAB simulations have been shown for the numerical
results to illustrate the hybrid synchronization schemes derived for the identical hyperchaotic Xu systems.
SLIDING MODE CONTROLLER DESIGN FOR GLOBAL CHAOS SYNCHRONIZATION OF COULLET SY...ijistjournal
This paper derives new results for the design of sliding mode controller for the global chaos synchronization of identical Coullet systems (1981). The synchronizer results derived in this paper for the complete chaos synchronization of identical hyperchaotic systems are established using sliding control theory and Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve global chaos synchronization of the identical Coullet systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper for the identical Coullet systems.
IOT SOLUTIONS FOR SMART PARKING- SIGFOX TECHNOLOGYCSEIJJournal
Sigfox technology has emerged as a competitive product in the communication service provider market for
approximately a decade. Widely implemented for smart parking solutions across various European
countries, it has now gained traction in Germany as well. The technology's successful track record and
reputation in the market demonstrate its effectiveness and reliability in addressing the communication
needs of IoT applications, particularly in the context of vehicle parking systems. This is noted in terms of a
city like Berlin-Germany, for on which the study is conducted. The major challenge being on how to relate
the parking techniques in a more user friendly, cost effective and less energy consumpmti0n mode where
the questions had at the beginning of the paper, relatively at the end the answers are sought to it via Sigfox
and its comparison with other related technologies like LoRA WAN and weightless. But more so future
areas of research study is also pointed out on areas which are not clearly identified in this particular
research area.
This paper entails the pros, cons adaptive, emerging and existing technology study in terms of cloud, big
data, Data analytics are all discussed in tandem to Sigfox.
Reliability Improvement with PSP of Web-Based Software ApplicationsCSEIJJournal
In diverse industrial and academic environments, the quality of the software has been evaluated using
different analytic studies. The contribution of the present work is focused on the development of a
methodology in order to improve the evaluation and analysis of the reliability of web-based software
applications. The Personal Software Process (PSP) was introduced in our methodology for improving the
quality of the process and the product. The Evaluation + Improvement (Ei) process is performed in our
methodology to evaluate and improve the quality of the software system. We tested our methodology in a
web-based software system and used statistical modeling theory for the analysis and evaluation of the
reliability. The behavior of the system under ideal conditions was evaluated and compared against the
operation of the system executing under real conditions. The results obtained demonstrated the
effectiveness and applicability of our methodology
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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 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.
ACTIVE CONTROLLER DESIGN FOR THE HYBRID SYNCHRONIZATION OF HYPERCHAOTIC XU AN...Zac Darcy
The synchronization of chaotic systems treats a pair of chaotic systems, which are usually called as master
and slave systems. In the chaos synchronization problem, the goal of the design is to synchronize the states
of master and slave systems asymptotically. In the hybrid synchronization design of master and slave
systems, one part of the systems, viz. their odd states, are completely synchronized (CS), while the other
part, viz. their even states, are completely anti-synchronized (AS) so that CS and AS co-exist in the process
of synchronization. This research work deals with the hybrid synchronization of hyperchaotic Xi systems
(2009) and hyperchaotic Li systems (2005). The main results of this hybrid research work are established
with Lyapunov stability theory. MATLAB simulations of the hybrid synchronization results are shown for
the hyperchaotic Xu and Li systems.
Global Chaos Synchronization of Hyperchaotic Pang and Hyperchaotic Wang Syste...CSEIJJournal
This paper investigates the global chaos synchronization of identical hyperchaotic Wang systems, identical
hyperchaotic Pang systems, and non-identical hyperchaotic Wang and hyperchaotic Pang systems via
adaptive control method. Hyperchaotic Pang system (Pang and Liu, 2011) and hyperchaotic Wang system
(Wang and Liu, 2006) are recently discovered hyperchaotic systems. Adaptive control method is deployed
in this paper for the general case when the system parameters are unknown. Sufficient conditions for global
chaos synchronization of identical hyperchaotic Pang systems, identical hyperchaotic Wang systems and
non-identical hyperchaotic Pang and Wang systems are derived via adaptive control theory and Lyapunov
stability theory. Since the Lyapunov exponents are not required for these calculations, the adaptive control
method is very convenient for the global chaos synchronization of the hyperchaotic systems discussed in
this paper. Numerical simulations are presented to validate and demonstrate the effectiveness of the
proposed synchronization schemes.
ADAPTIVE CONTROL AND SYNCHRONIZATION OF A HIGHLY CHAOTIC ATTRACTORijistjournal
Recently, a novel three-dimensional highly chaotic attractor has been discovered by Srisuchinwong and Munmuangsaen (2010). This paper investigates the adaptive control and synchronization of this highly chaotic attractor with unknown parameters. First, adaptive control laws are designed to stabilize the highly chaotic system to its unstable 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 highly chaotic systems with unknown parameters. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive control and synchronization schemes.
ADAPTIVE CONTROL AND SYNCHRONIZATION OF A HIGHLY CHAOTIC ATTRACTORijistjournal
Recently, a novel three-dimensional highly chaotic attractor has been discovered by Srisuchinwong and Munmuangsaen (2010). This paper investigates the adaptive control and synchronization of this highly chaotic attractor with unknown parameters. First, adaptive control laws are designed to stabilize the highly chaotic system to its unstable 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 highly chaotic systems with unknown parameters. Numerical simulations are shown to demonstrate the effectiveness of the proposed adaptive control and synchronization schemes.
ACTIVE CONTROLLER DESIGN FOR THE HYBRID SYNCHRONIZATION OF HYPERCHAOTIC ZHEN...ijscai
This paper deals with a new research problem in the chaos literature, viz. hybrid synchronization of a
pair of chaotic systems called the master and slave systems. In the hybrid synchronization design of
master and slave systems, one part of the systems, viz. their odd states, are completely synchronized (CS),
while the other part, viz. their even states, are completely anti-synchronized (AS) so that CS and AS coexist in the process of synchronization. This research work deals with the hybrid synchronization of
hyperchaotic Zheng systems (2010) and hyperchaotic Yu systems (2012). The main results of this hybrid
synchronization research work have been proved using Lyapunov stability theory. Numerical examples of
the hybrid synchronization results are shown along with MATLAB simulations for the hyperchaotic
Zheng and hyperchaotic Yu systems.
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 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.
ADAPTIVESYNCHRONIZER DESIGN FOR THE HYBRID SYNCHRONIZATION OF HYPERCHAOTIC ZH...ijitcs
This paper derives new adaptive synchronizers for the hybrid synchronization of hyperchaotic Zheng
systems (2010) and hyperchaotic Yu systems (2012). In the hybrid synchronization design of master and
slave systems, one part of the systems, viz. their odd states, are completely synchronized (CS), while the
other part, viz. their even states, are completely anti-synchronized (AS) so that CS and AS co-exist in the
process of synchronization. The research problem gets even more complicated, when the parameters of the
hyperchaotic systems are not known and we handle this complicate problem using adaptive control. The
main results of this research work are established via adaptive control theory andLyapunov stability
theory. MATLAB plotsusing classical fourth-order Runge-Kutta method have been depictedfor the new
adaptive hybrid synchronization results for the hyperchaotic Zheng and hyperchaotic Yu systems.
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.
International Journal of Computer Science, Engineering and Information Techno...ijcseit
In chaos theory, the problem anti-synchronization of chaotic systems deals with a pair of chaotic systems
called drive and response systems. In this problem, the design goal is to drive the sum of their respective
states to zero asymptotically. This problem gets even more complicated and requires special attention when
the parameters of the drive and response systems are unknown. This paper uses adaptive control theory
and Lyapunov stability theory to derive new results for the anti-synchronization of hyperchaotic Wang
system (2008) and hyperchaotic Li system (2005) with uncertain parameters. Hyperchaotic systems are
nonlinear dynamical systems exhibiting chaotic behaviour with two or more positive Lyapunov exponents.
The hyperchaotic systems have applications in areas like oscillators, lasers, neural networks, encryption,
secure transmission and secure communication. The main results derived in this paper are validated and
demonstrated with MATLAB simulations.
ANTI-SYNCHRONIZATION OF HYPERCHAOTIC WANG AND HYPERCHAOTIC LI SYSTEMS WITH UN...ijcseit
In chaos theory, the problem anti-synchronization of chaotic systems deals with a pair of chaotic systems
called drive and response systems. In this problem, the design goal is to drive the sum of their respective
states to zero asymptotically. This problem gets even more complicated and requires special attention when
the parameters of the drive and response systems are unknown. This paper uses adaptive control theory
and Lyapunov stability theory to derive new results for the anti-synchronization of hyperchaotic Wang
system (2008) and hyperchaotic Li system (2005) with uncertain parameters. Hyperchaotic systems are
nonlinear dynamical systems exhibiting chaotic behaviour with two or more positive Lyapunov exponents.
The hyperchaotic systems have applications in areas like oscillators, lasers, neural networks, encryption,
secure transmission and secure communication. The main results derived in this paper are validated and
demonstrated with MATLAB simulations.
ADAPTIVE CONTROLLER DESIGN FOR THE HYBRID SYNCHRONIZATION OF HYPERCHAOTIC XU ...ijait
This paper derives new adaptive results for the hybrid synchronization of hyperchaotic Xi systems (2009)
and hyperchaotic Li systems (2005). In the hybrid synchronization design of master and slave systems, one
part of the systems, viz. their odd states, are completely synchronized (CS), while the other part, viz. their
even states, are completely anti-synchronized (AS) so that CS and AS co-exist in the process of
synchronization. The research problem gets even more complicated, when the parameters of the
hyperchaotic systems are unknown and we tackle this problem using adaptive control. The main results of
this research work are proved using adaptive control theory and Lyapunov stability theory. MATLAB
simulations using classical fourth-order Runge-Kutta method are shown for the new adaptive hybrid
synchronization results for the hyperchaotic Xu and hyperchaotic Li systems.
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.
HYBRID SLIDING SYNCHRONIZER DESIGN OF IDENTICAL HYPERCHAOTIC XU SYSTEMS ijitjournal
In this paper, new results have been obtained via sliding mode control for the hybrid chaos synchronization
of identical hyperchaotic Xu systems (Xu, Cai and Zheng, 2009). In hybrid synchronization of master and
slave systems, the odd states are completely synchronized, while the even states are anti-synchronized. The
stability results derived in this paper for the hybrid synchronization of identical hyperchaotic Xu systems
are established using Lyapunov stability theory. MATLAB simulations have been shown for the numerical
results to illustrate the hybrid synchronization schemes derived for the identical hyperchaotic Xu systems.
SLIDING MODE CONTROLLER DESIGN FOR GLOBAL CHAOS SYNCHRONIZATION OF COULLET SY...ijistjournal
This paper derives new results for the design of sliding mode controller for the global chaos synchronization of identical Coullet systems (1981). The synchronizer results derived in this paper for the complete chaos synchronization of identical hyperchaotic systems are established using sliding control theory and Lyapunov stability theory. Since the Lyapunov exponents are not required for these calculations, the sliding mode control method is very effective and convenient to achieve global chaos synchronization of the identical Coullet systems. Numerical simulations are shown to illustrate and validate the synchronization schemes derived in this paper for the identical Coullet systems.
Similar to Adaptive Stabilization and Synchronization of Hyperchaotic QI System (20)
IOT SOLUTIONS FOR SMART PARKING- SIGFOX TECHNOLOGYCSEIJJournal
Sigfox technology has emerged as a competitive product in the communication service provider market for
approximately a decade. Widely implemented for smart parking solutions across various European
countries, it has now gained traction in Germany as well. The technology's successful track record and
reputation in the market demonstrate its effectiveness and reliability in addressing the communication
needs of IoT applications, particularly in the context of vehicle parking systems. This is noted in terms of a
city like Berlin-Germany, for on which the study is conducted. The major challenge being on how to relate
the parking techniques in a more user friendly, cost effective and less energy consumpmti0n mode where
the questions had at the beginning of the paper, relatively at the end the answers are sought to it via Sigfox
and its comparison with other related technologies like LoRA WAN and weightless. But more so future
areas of research study is also pointed out on areas which are not clearly identified in this particular
research area.
This paper entails the pros, cons adaptive, emerging and existing technology study in terms of cloud, big
data, Data analytics are all discussed in tandem to Sigfox.
Reliability Improvement with PSP of Web-Based Software ApplicationsCSEIJJournal
In diverse industrial and academic environments, the quality of the software has been evaluated using
different analytic studies. The contribution of the present work is focused on the development of a
methodology in order to improve the evaluation and analysis of the reliability of web-based software
applications. The Personal Software Process (PSP) was introduced in our methodology for improving the
quality of the process and the product. The Evaluation + Improvement (Ei) process is performed in our
methodology to evaluate and improve the quality of the software system. We tested our methodology in a
web-based software system and used statistical modeling theory for the analysis and evaluation of the
reliability. The behavior of the system under ideal conditions was evaluated and compared against the
operation of the system executing under real conditions. The results obtained demonstrated the
effectiveness and applicability of our methodology
DATA MINING FOR STUDENTS’ EMPLOYABILITY PREDICTIONCSEIJJournal
This study has been undertaken to predict the student employability.Assessing student employability
provides a method of integrating student abilities and employer business requirements, which is becoming
an increasingly important concern for academic institutions. Improving student evaluation techniques for
employability can help students to have a better understanding of business organizations and find the right
one for them. The data for the training classification models is gathered through a survey in which students
are asked to fill out a questionnaire in which they may indicate their abilities and academic achievement.
This information may be used to determine their competency in a variety of skill categories, including soft
skills, problem-solving skills and technical abilities and so on.The goal of this research is to use data
mining to predict student employability by considering different factors such as skills that the students have
gained during their diploma level and time duration with respect to the knowledge they have captured
when they expect the placement at the end of graduation. Further during this research most specific skills
with relevant to each job category also was identified. In this research for the prediction of the student
employability different data mining models such as such as KNN, Naive Bayer’s, and Decision Tree were
evaluated and out of that best model also was identified for this institute's student’s employability
prediction.So, in this research classification and association techniques were used and evaluated.
Call for Articles - Computer Science & Engineering: An International Journal ...CSEIJJournal
Computer Science & Engineering: An International Journal (CSEIJ) is a bi-monthly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Computer Science & Computer Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of computer science and computer Engineering.
A Complexity Based Regression Test Selection StrategyCSEIJJournal
Software is unequivocally the foremost and indispensable entity in this technologically driven world.
Therefore quality assurance, and in particular, software testing is a crucial step in the software
development cycle. This paper presents an effective test selection strategy that uses a Spectrum of
Complexity Metrics (SCM). Our aim in this paper is to increase the efficiency of the testing process by
significantly reducing the number of test cases without having a significant drop in test effectiveness. The
strategy makes use of a comprehensive taxonomy of complexity metrics based on the product level (class,
method, statement) and its characteristics.We use a series of experiments based on three applications with
a significant number of mutants to demonstrate the effectiveness of our selection strategy.For further
evaluation, we compareour approach to boundary value analysis. The results show the capability of our
approach to detect mutants as well as the seeded errors.
XML Encryption and Signature for Securing Web ServicesCSEIJJournal
In this research, we have focused on the most challenging issue that Web Services face, i.e. how to secure
their information. Web Services security could be guaranteed by employing security standards, which is the
main focus of this search. Every suggested model related to security design should put in the account the
securities' objectives; integrity, confidentiality, non- repudiation, authentication, and authorization. The
proposed model describes SOAP messages and the way to secure their contents. Due to the reason that
SOAP message is the core of the exchanging information in Web Services, this research has developed a
security model needed to ensure e-business security. The essence of our model depends on XML encryption
and XML signature to encrypt and sign SOAP message. The proposed model looks forward to achieve a
high speed of transaction and a strong level of security without jeopardizing the performance of
transmission information.
Performance Comparison of PCA,DWT-PCA And LWT-PCA for Face Image RetrievalCSEIJJournal
This paper compares the performance of face image retrieval system based on discrete wavelet transforms
and Lifting wavelet transforms with principal component analysis (PCA). These techniques are
implemented and their performances are investigated using frontal facial images from the ORL database.
The Discrete Wavelet Transform is effective in representing image features and is suitable in Face image
retrieval, it still encounters problems especially in implementation; e.g. Floating point operation and
decomposition speed. We use the advantages of lifting scheme, a spatial approach for constructing wavelet
filters, which provides feasible alternative for problems facing its classical counterpart. Lifting scheme has
such intriguing properties as convenient construction, simple structure, integer-to-integer transform, low
computational complexity as well as flexible adaptivity, revealing its potentials in Face image retrieval.
Comparing to PCA and DWT with PCA, Lifting wavelet transform with PCA gives less computation and
DWT-PCA gives high retrieval rate..
Call for Papers - Computer Science & Engineering: An International Journal (C...CSEIJJournal
Computer Science & Engineering: An International Journal (CSEIJ) is a bi-monthly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Computer Science & Computer Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of computer science and computer Engineering.
Paper Submission - Computer Science & Engineering: An International Journal (...CSEIJJournal
Computer Science & Engineering: An International Journal (CSEIJ) is a bi-monthly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Computer Science & Computer Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of computer science and computer Engineering.
Performance Comparison of PCA,DWT-PCA And LWT-PCA for Face Image RetrievalCSEIJJournal
This paper compares the performance of face image retrieval system based on discrete wavelet transforms
and Lifting wavelet transforms with principal component analysis (PCA). These techniques are
implemented and their performances are investigated using frontal facial images from the ORL database.
The Discrete Wavelet Transform is effective in representing image features and is suitable in Face image
retrieval, it still encounters problems especially in implementation; e.g. Floating point operation and
decomposition speed. We use the advantages of lifting scheme, a spatial approach for constructing wavelet
filters, which provides feasible alternative for problems facing its classical counterpart. Lifting scheme has
such intriguing properties as convenient construction, simple structure, integer-to-integer transform, low
computational complexity as well as flexible adaptivity, revealing its potentials in Face image retrieval.
Comparing to PCA and DWT with PCA, Lifting wavelet transform with PCA gives less computation and
DWT-PCA gives high retrieval rate..
Call for Papers - Computer Science & Engineering: An International Journal (C...CSEIJJournal
Computer Science & Engineering: An International Journal (CSEIJ) is a bi-monthly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Computer Science & Computer Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of computer science and computer Engineering.
Data security and privacy are important to prevent the re-
veal, modification and unauthorized usage of sensitive information. The
introduction of using critical power devices for internet of things (IoTs),
e-commerce, e-payment, and wireless sensor networks (WSNs) has brought
a new challenge of security due to the low computation capability of sen-
sors. Therefore, the lightweight authenticated key agreement protocols
are important to protect their security and privacy. Several researches
have been published about authenticated key agreement. However, there
is a need of lightweight schemes that can fit with critical capability de-
vices. Addition to that, a malicious key generation center (KGC) can
become a threat to watch other users, i.e impersonate user by causing
the key escrow problem
Call for Papers - Computer Science & Engineering: An International Journal (C...CSEIJJournal
Computer Science & Engineering: An International Journal (CSEIJ) is a bi-monthly open access peer-reviewed journal that publishes articles which contribute new results in all areas of the Computer Science & Computer Engineering. The journal is devoted to the publication of high quality papers on theoretical and practical aspects of computer science and computer Engineering.
Recommendation System for Information Services Adapted, Over Terrestrial Digi...CSEIJJournal
The development of digital television in Colombia has grown in last year’s, specially the digital terrestrial
television (DTT), which is an essential part to the projects of National Minister of ICT, thanks to the big
distribution and use of the television network and Internet in the country. This article explains how joining
different technologies like social networks, information adaptation and DTT, to get an application that
offers information services to users, based on their data, preferences, inclinations, use and interaction with
others users and groups inside the network.
Reconfiguration Strategies for Online Hardware Multitasking in Embedded SystemsCSEIJJournal
An intensive use of reconfigurable hardware is expected in future embedded systems. This means that the
system has to decide which tasks are more suitable for hardware execution. In order to make an efficient
use of the FPGA it is convenient to choose one that allows hardware multitasking, which is implemented by
using partial dynamic reconfiguration. One of the challenges for hardware multitasking in embedded
systems is the online management of the only reconfiguration port of present FPGA devices. This paper
presents different online reconfiguration scheduling strategies which assign the reconfiguration interface
resource using different criteria: workload distribution or task’ deadline. The online scheduling strategies
presented take efficient and fast decisions based on the information available at each moment. Experiments
have been made in order to analyze the performance and convenience of these reconfiguration strategies.
Performance Comparison and Analysis of Mobile Ad Hoc Routing ProtocolsCSEIJJournal
A mobile ad hoc network (MANET) is a wireless network that uses multi-hop peer-to-peer routing instead
of static network infrastructure to provide network connectivity. MANETs have applications in rapidly
deployed and dynamic military and civilian systems. The network topology in a MANET usually changes
with time. Therefore, there are new challenges for routing protocols in MANETs since traditional routing
protocols may not be suitable for MANETs. Researchers are designing new MANET routing protocols
and comparing and improving existing MANET routing protocols before any routing protocols are
standardized using simulations. However, the simulation results from different research groups are not
consistent with each other. This is because of a lack of consistency in MANET routing protocol models
and application environments, including networking and user traffic profiles. Therefore, the simulation
scenarios are not equitable for all protocols and conclusions cannot be generalized. Furthermore, it is
difficult for one to choose a proper routing protocol for a given MANET application. According to the
aforementioned issues, this paper focuses on MANET routing protocols. Specifically, my contribution
includes the characterization of different routing protocols and compare and analyze the performance of
different routing protocols.
An Energy Efficient Data Secrecy Scheme For Wireless Body Sensor NetworksCSEIJJournal
Data secrecy is one of the key concerns for wireless body sensor networks (WBSNs). Usually, a data
secrecy scheme should accomplish two tasks: key establishment and encryption. WBSNs generally face
more serious limitations than general wireless networks in terms of energy supply. To address this, in this
paper, we propose an energy efficient data secrecy scheme for WBSNs. On one hand, the proposed key
establishment protocol integrates node IDs, seed value and nonce seamlessly for security, then
establishes a session key between two nodes based on one-way hash algorithm SHA-1. On the other hand,
a low-complexity threshold selective encryption technology is proposed. Also, we design a security
selection patter exchange method with low-complexity for the threshold selection encryption. Then, we
evaluate the energy consumption of the proposed scheme. Our scheme shows the great advantage over
the other existing schemes in terms of low energy consumption.
To improve the QoS in MANETs through analysis between reactive and proactive ...CSEIJJournal
A Mobile Ad hoc NETwork (MANET), is a self-configuring infra structure less network of mobile devices
connected by wireless links. ad hoc is Latin and means "for this purpose". Each device in a MANET is free
to move independently in any direction, and will therefore change its links to other devices frequently. Each
must forward traffic unrelated to its own use, and therefore be a router. The primary challenge in building
a MANET is equipping each device to continuously maintain the information required to properly route
traffic. QOS is defined as a set of service requirements to be met by the network while transporting a
packet stream from source to destination. Intrinsic to the notion of QOS is an agreement or a guarantee by
the network to provide a set of measurable pre-specified service attributes to the user in terms of delay,
jitter, available bandwidth, packet loss, and so on. The analysis is mainly between proactive or table-driven
protocols like OLSR (Optimized Link State Routing) viz DSDV (Destination Sequenced Distance Vector) &
CGSR (Cluster Head Gateway Switch Routing) and reactive or source initiated routing protocols viz
AODV (Ad hoc on Demand distance Vector) & DSR (Dynamic Source Routing). The QoS analysis of the
above said protocols is simulated on NS2 and results are shown thereby.
This paper introduces Topic Tracking for Punjabi language. Text mining is a field that automatically
extracts previously unknown and useful information from unstructured textual data. It has strong
connections with natural language processing. NLP has produced technologies that teach computers
natural language so that they may analyze, understand and even generate text. Topic tracking is one of the
technologies that has been developed and can be used in the text mining process. The main purpose of topic
tracking is to identify and follow events presented in multiple news sources, including newswires, radio and
TV broadcasts. It collects dispersed information together and makes it easy for user to get a general
understanding. Not much work has been done in Topic tracking for Indian Languages in general and
Punjabi in particular. First we survey various approaches available for Topic Tracking, then represent our
approach for Punjabi. The experimental results are shown.
EXPLORATORY DATA ANALYSIS AND FEATURE SELECTION FOR SOCIAL MEDIA HACKERS PRED...CSEIJJournal
In machine learning, the intelligence of a developed model is greatly influenced by the dataset used for the
target domain on which the developed model will be deployed. Social media platform has experienced
more of hackers’ attacks on the platform in recent time. To identify a hacker on the platform, there are two
possible ways. The first is to use the activities of the user while the second is to use the supplied details the
user registered the account with. To adequately identify a social media user as hacker proactively, there
are relevant user details called features that can be used to determine whether a social media user is a
hacker or not. In this paper, an exploratory data analysis was carried out to determine the best features
that can be used by a predictive model to proactively identify hackers on the social media platform. A web
crawler was developed to mine the user dataset on which exploratory data analysis was carried out to
select the best features for the dataset which could be used to correctly identify a hacker on a social media
platform.
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)MdTanvirMahtab2
This presentation is about the working procedure of Shahjalal Fertilizer Company Limited (SFCL). A Govt. owned Company of Bangladesh Chemical Industries Corporation under Ministry of Industries.
Courier management system project report.pdfKamal Acharya
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Adaptive Stabilization and Synchronization of Hyperchaotic QI System
1. Computer Science & Engineering: An International Journal (CSEIJ), Vol.1, No.2, June 2011
DOI : 10.5121/cseij.2011.1202 14
ADAPTIVE STABILIZATION AND
SYNCHRONIZATION OF HYPERCHAOTIC QI
SYSTEM
Sundarapandian Vaidyanathan1
1
Research and Development Centre, Vel Tech Dr. RR & Dr. SR Technical University
Avadi, Chennai-600 062, Tamil Nadu, INDIA
sundarvtu@gmail.com
ABSTRACT
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.
KEYWORDS
Adaptive Control, Stabilization, Chaos Synchronization, Hyperchaos, Hyperchaotic Qi System.
1. INTRODUCTION
Chaotic systems are dynamical systems that are highly sensitive to initial conditions. The
sensitive nature of chaotic systems is commonly called as the butterfly effect [1]. Since chaos
phenomenon in weather models was first observed by Lorenz in 1961, a large number of chaos
phenomena and chaos behaviour have been discovered in physical, social, economical,
biological and electrical systems.
The control of chaotic systems is to design state feedback control laws that stabilizes the chaotic
systems around the unstable equilibrium points. Active control technique is used when the
system parameters are known and adaptive control technique is used when the system
parameters are unknown [2-4].
Synchronization of chaotic systems is a phenomenon that may occur when two or more chaotic
oscillators are coupled or when a chaotic oscillator drives another chaotic oscillator. Because of
the butterfly effect, which causes the exponential divergence of the trajectories of two identical
chaotic systems started with nearly the same initial conditions, synchronizing two chaotic
systems is seemingly a very challenging problem in the chaos literature [5-16].
In 1990, Pecora and Carroll [5] introduced a method to synchronize two identical chaotic
systems and showed that it was possible for some chaotic systems to be completely
synchronized. From then on, chaos synchronization has been widely explored in a variety of
fields including physical systems [6], chemical systems [7], ecological systems [8], secure
communications [9-10], etc.
2. Computer Science & Engineering: An International Journal (CSEIJ), Vol.1, No.2, June 2011
15
In most of the chaos synchronization approaches, the master-slave or drive-response formalism
has been used. If a particular chaotic system is called the master or drive system and another
chaotic system is called the slave or response system, then the idea of synchronization is to use
the output of the master system to control the slave system so that the output of the slave system
tracks the output of the master system asymptotically.
Since the seminal work by Pecora and Carroll [5], a variety of impressive approaches have been
proposed for the synchronization of chaotic systems such as the sampled-data feedback
synchronization method [11], OGY method [12], time-delay feedback method [13],
backstepping method [14], adaptive design method [15], sliding mode control method [16], etc.
This paper is organized as follows. In Section 2, we derive results for the adaptive stabilization
of hyperchaotic Qi system (Chen, Yang, Qi and Yuan, [17], 2007) with unknown parameters. In
Section 3, we derive results for the adaptive synchronization of hyperchaotic Qi systems with
unknown parameters. In Section 4, we summarize the main results obtained in this paper.
2. ADAPTIVE STABILIZATION OF HYPERCHAOTIC QI SYSTEM
2.1 Theoretical Results
The hyperchaotic Qi system (Chen, Yang, Qi and Yuan, [17], 2007) is one of the important
models of four-dimensional hyperchaotic systems. It is a novel hyperchaotic system with only
one equilibrium at the origin. The hyperchaotic Qi dynamics is described by
1 2 1 2 3
2 1 1 3 2 4
3 1 2 3
4 2
( )
x a x x x x
x c x d x x x x
x x x b x
x f x
ε
= − +
= − + +
= −
= −
&
&
&
&
(1)
where ( 1,2,3,4)
i
x i = are the state variables and , , , , ,
a b c d f
ε are positive constants.
Figure 1. State Orbits of the Hyperchaotic Qi System
3. Computer Science & Engineering: An International Journal (CSEIJ), Vol.1, No.2, June 2011
16
The system (1) is hyperchaotic when the parameter values are taken as
35, 4.9, 25, 5, 35
a b c d ε
= = = = = and 22.
f = (2)
The hyperchaotic state portrait of the system (1) is described in Figure 1.
When the parameter values are taken as in (2), the system (1) is hyperchaotic and the system
linearization matrix at the equilibrium point 0 (0,0,0,0)
E = is given by
35 35 0 0
25 1 0 1
0 0 4.9 0
0 22 0 0
A
−
=
−
−
which has the eigenvalues
1 2 3
0.8989, 16.6257, 4.9
λ λ λ
= = = − and 4 51.5245
λ = −
Since 1 2
,
λ λ are eigenvalues with positive real part, it is immediate from Lyapunov stability
theory [18] that the system (1) is unstable at the equilibrium point 0 (0,0,0,0).
E =
In this section, we design adaptive control law for globally stabilizing the hyperchaotic system
(1) when the parameter values are unknown.
Thus, we consider the controlled hyperchaotic Qi system as follows.
1 2 1 2 3 1
2 1 1 3 2 4 2
3 1 2 3 3
4 2 4
( )
x a x x x x u
x c x d x x x x u
x x x b x u
x f x u
ε
= − + +
= − + + +
= − +
= − +
&
&
&
&
(3)
where 1 2 3
, ,
u u u and 4
u are feedback controllers to be designed using the states and estimates of
the unknown parameters of the system.
In order to ensure that the controlled system (3) globally converges to the origin asymptotically,
we consider the following adaptive control functions
1 2 1 2 3 1 1
2 1 1 3 2 4 2 2
3 1 2 3 3 3
4 2 4 4
ˆ
ˆ ( )
ˆ
ˆ
ˆ
ˆ
u a x x x x k x
u c x d x x x x k x
u x x b x k x
u f x k x
ε
= − − − −
= − + − − −
= − + −
= − −
(4)
where ˆ ˆ ˆ
ˆ ˆ
, , , ,
a b c d ε and ˆ
f are estimates of the parameters , , , ,
a b c d ε and ,
f respectively, and
,( 1,2,3,4)
i
k i = are positive constants.
4. Computer Science & Engineering: An International Journal (CSEIJ), Vol.1, No.2, June 2011
17
Substituting the control law (4) into the hyperchaotic Qi dynamics (1), we obtain
1 2 1 2 3 1 1
2 1 1 3 2 2
3 3 3 3
4 2 4 4
ˆ
ˆ
( ) ( ) ( )
ˆ
ˆ
( ) ( )
ˆ
( )
ˆ
( )
x a a x x x x k x
x c c x d d x x k x
x b b x k x
x f f x k x
ε ε
= − − + − −
= − − − −
= − − −
= − − −
&
&
&
&
(5)
Let us now define the parameter errors as
ˆ
ˆ ˆ
, ,
ˆ ˆ
ˆ
, ,
a b c
d f
e a a e b b e c c
e d d e e f f
ε ε ε
= − = − = −
= − = − = −
(6)
Using (6), the closed-loop dynamics (5) can be written compactly as
1 2 1 2 3 1 1
2 1 1 3 2 2
3 3 3 3
4 2 4 4
( )
a
c d
b
f
x e x x e x x k x
x e x e x x k x
x e x k x
x e x k x
ε
= − + −
= − −
= − −
= − −
&
&
&
&
(7)
For the derivation of the update law for adjusting the parameter estimates ˆ ˆ ˆ
ˆ
ˆ ˆ
, , , , , ,
a b c d f
ε the
Lyapunov approach is used.
Consider the quadratic Lyapunov function
( )
2 2 2 2 2 2 2 2 2 2
1 2 3 4
1
2
a b c d f
V x x x x e e e e e e
ε
= + + + + + + + + + (8)
which is a positive definite function on 10
.
R
Note also that
ˆ
ˆ ˆ
, ,
ˆ ˆ
ˆ
, ,
a b c
d f
e a e b e c
e d e e f
ε ε
= − = − = −
= − = − = −
&
& &
& & &
& &
&
& & &
(9)
Differentiating V along the trajectories of (7) and using (9), we obtain
2 2 2 2 2
1 1 2 2 3 3 4 4 1 2 1 3
1 2 1 2 3 1 2 3 2 4
ˆ
ˆ
( )
ˆ ˆ
ˆ
ˆ
a b
c d f
V k x k x k x k x e x x x a e x b
e x x c e x x x d e x x x e x x f
ε ε
= − − − − + − − + − −
+ − + − − + − + − −
&
&
&
& &
&
&
(10)
5. Computer Science & Engineering: An International Journal (CSEIJ), Vol.1, No.2, June 2011
18
In view of Eq. (10), the estimated parameters are updated by the following law:
1 2 1 5
2
3 6
1 2 7
1 2 3 8
1 2 3 9
2 4 10
ˆ ( )
ˆ
ˆ
ˆ
ˆ
ˆ
a
b
c
d
f
a x x x k e
b x k e
c x x k e
d x x x k e
x x x k e
f x x k e
ε
ε
= − +
= − +
= +
= − +
= +
= − +
&
&
&
&
&
&
(11)
where ,( 5, ,10)
i
k i = K are positive constants.
Substituting (11) into (10), we get
2 2 2 2 2 2 2 2 2 2
1 1 2 2 3 3 4 4 5 6 7 8 9 10
a b c d f
V k x k x k x k x k e k e k e k e k e k e
ε
= − − − − − − − − − −
& (12)
which is a negative definite function on 10
.
R
Thus, by Lyapunov stability theory [18], we obtain the following result.
Theorem 1. The hyperchaotic Qi system (1) with unknown parameters is globally and
exponentially stabilized for all initial conditions 4
(0)
x R
∈ by the adaptive control law (4),
where the update law for the parameters is given by (11) and , ( 1, ,10)
i
k i = K are positive
constants.
2.2 Numerical Results
For the numerical simulations, the fourth order Runge-Kutta method is used to solve the
hyperchaotic system (1) with the adaptive control law (4) and the parameter update law (11).
The parameters of the hyperchaotic Qi system (1) are selected as
35, 4.9, 25, 5, 35
a b c d ε
= = = = = and 22.
f =
For the adaptive and update laws, we take 2, ( 1,2, ,10).
i
k i
= = K
Suppose that the initial values of the estimated parameters are
ˆ ˆ ˆ
ˆ ˆ
(0) 4, (0) 5, (0) 2, (0) 7, (0) 5
a b c d ε
= = = = = and ˆ(0) 8.
f =
The initial values of the hyperchaotic Qi system (1) are taken as (0) (10,4,8,12).
x =
When the adaptive control law (4) and the parameter update law (11) are used, the controlled
hyperchaotic Qi system converges to the equilibrium 0 (0,0,0,0)
E = exponentially as shown in
Figure 2. The parameter estimates are shown in Figure 3.
6. Computer Science Engineering: An International Journal (CSEIJ), Vol.1, No.2, June 2011
19
Figure 2. Time Responses of the Controlled Hyperchaotic Qi System
Figure 3. Parameter Estimates ˆ ˆ ˆ
ˆ
ˆ ˆ
( ), ( ), ( ), ( ), ( ), ( )
a t b t c t d t t f t
ε
7. Computer Science Engineering: An International Journal (CSEIJ), Vol.1, No.2, June 2011
20
3. ADAPTIVE SYNCHRONIZATION OF IDENTICAL HYPERCHAOTIC QI
SYSTEMS
3.1 Theoretical Results
In this section, we discuss the adaptive synchronization of identical hyperchaotic Qi systems
(Chen, Yang, Qi and Yuan, [17], 2007) with unknown parameters.
As the master system, we consider the hyperchaotic Qi dynamics described by
1 2 1 2 3
2 1 1 3 2 4
3 1 2 3
4 2
( )
x a x x x x
x c x d x x x x
x x x b x
x f x
ε
= − +
= − + +
= −
= −
(13)
where , ( 1,2,3,4)
i
x i = are the state variables and , , , , ,
a b c d f
ε are unknown system
parameters.
The system (13) is hyperchaotic when the parameter values are taken as
35, 4.9, 25, 5, 35
a b c d ε
= = = = = and 22.
f =
As the slave system, we consider the controlled hyperchaotic Qi dynamics described by
1 2 1 2 3 1
2 1 1 3 2 4 2
3 1 2 3 3
4 2 4
( )
y a y y y y u
y c y d y y y y u
y y y b y u
y f y u
ε
= − + +
= − + + +
= − +
= − +
(14)
where , ( 1,2,3,4)
i
y i = are the state variables and , ( 1,2,3,4)
i
u i = are the nonlinear controllers
to be designed.
The synchronization error is defined by
, ( 1,2,3,4)
i i i
e y x i
= − = (15)
Then the error dynamics is obtained as
1 2 1 2 3 2 3 1
2 1 1 3 1 3 2 4 2
3 1 2 1 2 3 3
4 2 4
( ) ( )
( )
e a e e y y x x u
e c e d y y x x e e u
e y y x x be u
e f e u
ε
= − + − +
= − − + + +
= − − +
= − +
(16)
8. Computer Science Engineering: An International Journal (CSEIJ), Vol.1, No.2, June 2011
21
Let us now define the adaptive control functions 1 2 3 4
( ), ( ), ( ), ( )
u t u t u t u t as
1 2 1 2 3 2 3 1 1
2 1 1 3 1 3 2 4 2 2
3 1 2 1 2 3 3 3
4 2 4 4
ˆ
ˆ ( ) ( )
ˆ
ˆ ( )
ˆ
ˆ
u a e e y y x x k e
u c e d y y x x e e k e
u y y x x b e k e
u f e k e
ε
= − − − − −
= − + − − − −
= − + + −
= − −
(17)
where ˆ ˆ ˆ
ˆ ˆ
, , , ,
a b c d ε and ˆ
f are estimates of the parameters , , , ,
a b c d ε and f respectively, and
,( 1,2,3,4)
i
k i = are positive constants.
Substituting the control law (17) into (16), we obtain the error dynamics as
1 2 1 2 3 2 3 1 1
2 1 1 3 1 3 2 2
3 3 3 3
4 2 4 4
ˆ
ˆ
( ) ( ) ( ) ( )
ˆ
ˆ
( ) ( )( )
ˆ
( )
ˆ
( )
e a a e e y y x x k e
e c c e d d y y x x k e
e b b e k e
e f f e k e
ε ε
= − − + − − −
= − − − − −
= − − −
= − − −
(18)
Let us now define the parameter errors as
ˆ ˆ ˆ
ˆ
ˆ ˆ
, , , , ,
a b c d f
e a a e b b e c c e d d e e f f
ε ε ε
= − = − = − = − = − = − (19)
Substituting (19) into (18), the error dynamics simplifies to
1 2 1 2 3 2 3 1 1
2 1 1 3 1 3 2 2
3 3 3 3
4 2 4 4
( ) ( )
( )
a
c d
b
f
e e e e e y y x x k e
e e e e y y x x k e
e e e k e
e e e k e
ε
= − + − −
= − − −
= − −
= − −
(20)
For the derivation of the update law for adjusting the estimates of the parameters, the Lyapunov
approach is used.
Consider the quadratic Lyapunov function
( )
2 2 2 2 2 2 2 2 2 2
1 2 3 4
1
2
a b c d f
V e e e e e e e e e e
ε
= + + + + + + + + + (21)
which is a positive definite function on 10
.
R
Note also that
ˆ
ˆ ˆ
, ,
ˆ ˆ
ˆ
, ,
a b c
d f
e a e b e c
e d e e f
ε ε
= − = − = −
= − = − = −
(22)
9. Computer Science Engineering: An International Journal (CSEIJ), Vol.1, No.2, June 2011
22
Differentiating V along the trajectories of (20) and using (22), we obtain
2 2 2 2 2
1 1 2 2 3 3 4 4 1 2 1 3 1 2
2 1 3 1 3 1 2 3 2 3 2 4
ˆ
ˆ ˆ
( )
ˆ ˆ
ˆ
( ) ( )
a b c
d f
V k e k e k e k e e e e e a e e b e e e c
e e y y x x d e e y y x x e e e f
ε ε
= − − − − + − − + − − + −
+ − − − + − − + − −
(23)
In view of Eq. (23), the estimated parameters are updated by the following law:
1 2 1 5
2
3 6
1 2 7
2 1 3 1 3 8
1 2 3 2 3 9
2 4 10
ˆ ( )
ˆ
ˆ
ˆ ( )
ˆ ( )
ˆ
a
b
c
d
f
a e e e k e
b e k e
c e e k e
d e y y x x k e
e y y x x k e
f e e k e
ε
ε
= − +
= − +
= +
= − − +
= − +
= − +
(24)
where ,( 5, ,10)
i
k i = K are positive constants.
Substituting (24) into (23), we get
2 2 2 2 2 2 2 2 2 2
1 1 2 2 3 3 4 4 5 6 7 8 9 10
a b c d f
V k e k e k e k e k e k e k e k e k e k e
ε
= − − − − − − − − − −
(25)
which is a negative definite function on 10
.
R
Thus, by Lyapunov stability theory [18], it is immediate that the synchronization error and the
parameter error decay to zero exponentially with time for all initial conditions.
Hence, we have proved the following result.
Theorem 2. The identical hyperchaotic Qi systems (13) and (14) with unknown parameters are
globally and exponentially synchronized for all initial conditions by the adaptive control law
(17), where the update law for parameters is given by (24) and ,( 1, ,10)
i
k i = K are positive
constants.
3.2 Numerical Results
For the numerical simulations, the fourth order Runge-Kutta method is used to solve the two
systems of differential equations (13) and (14) with the adaptive control law (17) and the
parameter update law (24).
For the adaptive synchronization of the hyperchaotic Qi systems with parameter values
35, 4.9, 25, 5, 35
a b c d ε
= = = = = and 22,
f =
we apply the adaptive control law (17) and the parameter update law (24).
10. Computer Science Engineering: An International Journal (CSEIJ), Vol.1, No.2, June 2011
23
We take the positive constants , ( 1, ,10)
i
k i = K as 2
i
k = for 1,2, ,10.
i = K
Suppose that the initial values of the estimated parameters are
ˆ ˆ ˆ
ˆ ˆ
(0) 5, (0) 4, (0) 3, (0) 6, (0) 4
a b c d ε
= = = = = and ˆ(0) 2.
f =
We take the initial values of the master system (13) as (0) (5,24,18,20).
x =
We take the initial values of the slave system (14) as (0) (17,20,8,12).
y =
Figure 4 shows the adaptive chaos synchronization of the identical hyperchaotic Qi systems.
Figure 5 shows that the estimated values of the parameters ˆ ˆ ˆ
ˆ
ˆ ˆ
, , , , ,
a b c d f
ε converge to the system
parameters 35, 4.9, 25, 5, 35
a b c d ε
= = = = = and 22.
f =
Figure 4. Adaptive Synchronization of the Identical Hyperchaotic Qi Systems
11. Computer Science Engineering: An International Journal (CSEIJ), Vol.1, No.2, June 2011
24
Figure 5. Parameter Estimates ˆ ˆ ˆ
ˆ
ˆ ˆ
( ), ( ), ( ), ( ), ( ), ( )
a t b t c t d t t f t
ε
4. CONCLUSIONS
In this paper, we applied adaptive control theory for the stabilization and synchronization of the
hyperchaotic Qi system (Chen, Yang, Qi and Yuan, 2007) with unknown system parameters.
First, we designed adaptive control laws to stabilize the hyperchaotic Qi system to its
equilibrium point at the origin based on the adaptive control theory and Lyapunov stability
theory. Then we derived adaptive synchronization scheme and update law for the estimation of
system parameters for identical hyperchaotic Qi systems with unknown parameters. Our
synchronization schemes were established using Lyapunov stability theory. Since the Lyapunov
exponents are not required for these calculations, the proposed adaptive control method is very
effective and convenient to achieve chaos control and synchronization of the hyperchaotic Qi
system. Numerical simulations are shown to demonstrate the effectiveness of the proposed
adaptive stabilization and synchronization schemes.
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Author
Dr. V. Sundarapandian is a Professor
(Systems and Control Engineering), Research
and Development Centre at Vel Tech Dr. RR
Dr. SR Technical University, Chennai, India.
His current research areas are: Linear and
Nonlinear Control Systems, Chaos Theory,
Dynamical Systems and Stability Theory, etc.
He has published over 110 research articles in
international journals and two text-books with
Prentice-Hall of India, New Delhi, India. He has
published over 45 papers in International
Conferences and 90 papers in National
Conferences. He has delivered several Key Note
Lectures on Control Systems, Chaos Theory,
Scientific Computing, SCILAB, etc.