In this paper, we first discuss the stability of linearized error dynamics of the nonlinear ob-server used for time-continuous driving chaos synchronization and give the criteria on it. Then we find by theoretical ana...In this paper, we first discuss the stability of linearized error dynamics of the nonlinear ob-server used for time-continuous driving chaos synchronization and give the criteria on it. Then we find by theoretical analysis and numerical experiments that the observer can still synchronize with the origi-nal system under time-discrete driving provided that some conditions are met. Finally we derive the asymptotical stability criterion of the nonlinear observer used for time-discrete driving chaos synchro-nization . Simulations illustrate the validity of the criterion.展开更多
In this paper, chaos synchronization in the presence of parameter uncertainty, observer gain perturbation and exogenous input disturbance is considered. A nonlinear non-fragile proportional-integral （PI） adaptive ob...In this paper, chaos synchronization in the presence of parameter uncertainty, observer gain perturbation and exogenous input disturbance is considered. A nonlinear non-fragile proportional-integral （PI） adaptive observer is designed for the synchronization of chaotic systems; its stability conditions based on the Lyapunov technique are derived. The observer proportional and integral gains, by converting the conditions into linear matrix inequality （LMI）, are optimally selected from solutions that satisfy the observer stability conditions such that the effect of disturbance on the synchronization error becomes minimized. To show the effectiveness of the proposed method, simulation results for the synchronization of a Lorenz chaotic system with unknown parameters in the presence of an exogenous input disturbance and abrupt gain perturbation are reported.展开更多
Presents the development of a robust and stable sliding observer based design for constructing two chaotic system synchronized system, and the fuzzy sliding observer (FMO) used for synchronization of chaos and to elim...Presents the development of a robust and stable sliding observer based design for constructing two chaotic system synchronized system, and the fuzzy sliding observer (FMO) used for synchronization of chaos and to eliminate chattering caused by switching term K sign ( 1-x 1).展开更多
Chaotic synchronization is a branch of chaotic control. Nowadays, the research and application of chaotic synchronization have become a hot topic and one of the development directions is for the research on chaos. In ...Chaotic synchronization is a branch of chaotic control. Nowadays, the research and application of chaotic synchronization have become a hot topic and one of the development directions is for the research on chaos. In this paper, a universal nonlinear stateobserver is presented for a class of universal chaotic systems to realize the chaotic synchronization, according to the theory of state-observer in the modern control theory. And theoretic analysis and simulation results have illustrated the validity of the approach. Moreover, the approach of synchronization proposed in this paper is very easy, flexible and universal with high synchronization precision.When the approach is applied to secure communication, the results are satisfying.展开更多
In this paper we present the control and synchronization of a coupled Bragg acousto-optic bistable map system using nonlinear feedback technology. This nonlinear feedback technology is useful to control a temporally c...In this paper we present the control and synchronization of a coupled Bragg acousto-optic bistable map system using nonlinear feedback technology. This nonlinear feedback technology is useful to control a temporally chaotic system as well as a spatiotemporally chaotic system. It can be extended to synchronize the spatiotemporal chaos. It can work in a wide range of the controlled and synchronized signals, so it can decrease the sensitivity down to a noise level. The synchronization can be obtained by the analysis of the largest conditional Lyapunov exponent spectrum, and easily implemented in practical systems just by adjusting the coupled strength without any pre-knowledge of the dynamic system required.展开更多
This paper presents chaos synchronization between two different chaotic systems by using a nonlinear controller, in which the nonlinear functions of the system are used as a nonlinear feedback term. The feedback contr...This paper presents chaos synchronization between two different chaotic systems by using a nonlinear controller, in which the nonlinear functions of the system are used as a nonlinear feedback term. The feedback controller is designed on the basis of stability theory, and the area of feedback gain is determined. The artificial simulation results show that this control method is commendably effective and feasible.展开更多
This paper addresses control for the synchronization of Chen chaotic systems via sector nonlinear inputs. Feedback control, adaptive control, fast sliding mode and robust control approaches based on single state feedb...This paper addresses control for the synchronization of Chen chaotic systems via sector nonlinear inputs. Feedback control, adaptive control, fast sliding mode and robust control approaches based on single state feedback controller are investigated. In these cases, sufficient conditions for the synchronization are obtained analytically. Numerical simulations verify the control performances.展开更多
This paper presents chaos synchronization between two different four-dimensional （4D） hyperchaotic Chen systems by nonlinear feedback control laws. A modified 4D hyperchaotic Chen system is obtained by changing the ...This paper presents chaos synchronization between two different four-dimensional （4D） hyperchaotic Chen systems by nonlinear feedback control laws. A modified 4D hyperchaotic Chen system is obtained by changing the nonlinear function of the 4D hyperchaotic Chen system, furthermore, an electronic circuit to realize two different 4D hyperchaotic Chen systems is designed. With nonlinear feedback control method, chaos synchronization between two different 4D hyperchaotic Chen systems is achieved. Based on the stability theory~ the functions of the nonlinear feedback control for synchronization of two different 4D hyperchaotic Chen systems is derived, the range of feedback gains is determined. Numerical simulations are shown to verify the theoretical results.展开更多
In this paper, we propose a robust fractional-order proportional-integral(FOPI) observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient...In this paper, we propose a robust fractional-order proportional-integral(FOPI) observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities(LMIs) approach by using an indirect Lyapunov method. The proposed FOPI observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional(FOP) observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.展开更多
A new fractional-order Lorenz-like system with two stable node-foci has been thoroughly studied in this paper.Some sufficient conditions for the local stability of equilibria considering both commensurate and incommen...A new fractional-order Lorenz-like system with two stable node-foci has been thoroughly studied in this paper.Some sufficient conditions for the local stability of equilibria considering both commensurate and incommensurate cases are given. In addition, with the effective dimension less than three,the minimum effective dimension of the system is approximated as 2.8485 and is verified numerically. It should be affirmed that the linear differential equation in fractional-order Lorenzlike system appears to be less sensitive to the damping, represented by a fractional derivative, than the two other nonlinear equations. Furthermore, combination synchronization of this system is analyzed with the help of nonlinear feedback control method. Theoretical results are verified by performing numerical simulations.展开更多
Synchronization is one of the most important characteristics of dynamic systems.For this paper,the authors obtained results for the nonlinear systems controller for the custom Synchronization of two 4D systems.The fin...Synchronization is one of the most important characteristics of dynamic systems.For this paper,the authors obtained results for the nonlinear systems controller for the custom Synchronization of two 4D systems.The findings have allowed authors to develop two analytical approaches using the second Lyapunov(Lyp)method and the Gardanomethod.Since the Gardano method does not involve the development of special positive Lyp functions,it is very efficient and convenient to achieve excessive systemSYCR phenomena.Error is overcome by using Gardano and overcoming some problems in Lyp.Thus we get a great investigation into the convergence of error dynamics,the authors in this paper are interested in giving numerical simulations of the proposed model to clarify the results and check them,an important aspect that will be studied is Synchronization Complete hybrid SYCR and anti-Synchronization,by making use of the Lyapunov expansion analysis,a proposed control method is developed to determine the actual.The basic idea in the proposed way is to receive the evolution of between two methods.Finally,the present model has been applied and showing in a new attractor,and the obtained results are compared with other approximate results,and the nearly good coincidence was obtained.展开更多
Study of chaotic synchronization as a fundamental phenomenon in the nonlinear dynamical systems theory has been recently raised many interests in science, engineering, and technology. In this paper, we develop a new m...Study of chaotic synchronization as a fundamental phenomenon in the nonlinear dynamical systems theory has been recently raised many interests in science, engineering, and technology. In this paper, we develop a new mathematical framework in study of chaotic synchronization of discrete-time dynamical systems. In the novel drive-response discrete-time dynamical system which has been coupled using convex link function, we introduce a synchronization threshold which passes that makes the drive-response system lose complete coupling and synchronized behaviors. We provide the application of this type of coupling in synchronized cycles of well-known Ricker model. This model displays a rich cascade of complex dynamics from stable fixed point and cascade of period-doubling bifurcation to chaos. We also numerically verify the effectiveness of the proposed scheme and demonstrate how this type of coupling makes this chaotic system and its corresponding coupled system starting from different initial conditions, quickly get synchronized.展开更多
This paper deals with the synchronization of chaotic systems with structure or parameters difference. Nonlinear differential geometry theory was applied to transform the chaotic discrepancy system into canonical form....This paper deals with the synchronization of chaotic systems with structure or parameters difference. Nonlinear differential geometry theory was applied to transform the chaotic discrepancy system into canonical form. A feedback control for synchronizing two chaotic systems is proposed based on sliding mode control design. To make this controller physically realizable, an extended state observer is used to estimate the error between the transmitter and receiver. Two illustrative examples were carried out: (1) The Chua oscillator was used to show that synchronization was achieved and the message signal was recovered in spite of parametric variations; (2) Two second-order driven oscillators were presented to show that the synchronization can be achieved and that the message can be recovered in spite of the strictly different model.展开更多
Relerrlng to contlnuous-Ume claaotlc systems, tills paper presents a new projective syncnromzatlon scheme, wnlcn enables each drive system state to be synchronized with a linear combination of response system states f...Relerrlng to contlnuous-Ume claaotlc systems, tills paper presents a new projective syncnromzatlon scheme, wnlcn enables each drive system state to be synchronized with a linear combination of response system states for any arbitrary scaling matrix. The proposed method, based on a structural condition related to the uncontrollable eigenvalues of the error system, can be applied to a wide class of continuous-time chaotic （hyperchaotic） systems and represents a general framework that includes any type of synchronization defined to date. An example involving a hyperchaotic oscillator is reported, with the aim of showing how a response system attractor is arbitrarily shaped using a scalar synchronizing signal only. Finally, it is shown that the recently introduced dislocated synchronization can be readily achieved using the conceived scheme.展开更多
基金This work was supported in part by the National Natural Science Foundation of China (Grant No. 69872009) the Grant of PhD Programmes in High Education Institutes of Ministry of Education, China (Grant No. 98028630) .
文摘In this paper, we first discuss the stability of linearized error dynamics of the nonlinear ob-server used for time-continuous driving chaos synchronization and give the criteria on it. Then we find by theoretical analysis and numerical experiments that the observer can still synchronize with the origi-nal system under time-discrete driving provided that some conditions are met. Finally we derive the asymptotical stability criterion of the nonlinear observer used for time-discrete driving chaos synchro-nization . Simulations illustrate the validity of the criterion.
文摘In this paper, chaos synchronization in the presence of parameter uncertainty, observer gain perturbation and exogenous input disturbance is considered. A nonlinear non-fragile proportional-integral （PI） adaptive observer is designed for the synchronization of chaotic systems; its stability conditions based on the Lyapunov technique are derived. The observer proportional and integral gains, by converting the conditions into linear matrix inequality （LMI）, are optimally selected from solutions that satisfy the observer stability conditions such that the effect of disturbance on the synchronization error becomes minimized. To show the effectiveness of the proposed method, simulation results for the synchronization of a Lorenz chaotic system with unknown parameters in the presence of an exogenous input disturbance and abrupt gain perturbation are reported.
文摘Presents the development of a robust and stable sliding observer based design for constructing two chaotic system synchronized system, and the fuzzy sliding observer (FMO) used for synchronization of chaos and to eliminate chattering caused by switching term K sign ( 1-x 1).
文摘Chaotic synchronization is a branch of chaotic control. Nowadays, the research and application of chaotic synchronization have become a hot topic and one of the development directions is for the research on chaos. In this paper, a universal nonlinear stateobserver is presented for a class of universal chaotic systems to realize the chaotic synchronization, according to the theory of state-observer in the modern control theory. And theoretic analysis and simulation results have illustrated the validity of the approach. Moreover, the approach of synchronization proposed in this paper is very easy, flexible and universal with high synchronization precision.When the approach is applied to secure communication, the results are satisfying.
文摘In this paper we present the control and synchronization of a coupled Bragg acousto-optic bistable map system using nonlinear feedback technology. This nonlinear feedback technology is useful to control a temporally chaotic system as well as a spatiotemporally chaotic system. It can be extended to synchronize the spatiotemporal chaos. It can work in a wide range of the controlled and synchronized signals, so it can decrease the sensitivity down to a noise level. The synchronization can be obtained by the analysis of the largest conditional Lyapunov exponent spectrum, and easily implemented in practical systems just by adjusting the coupled strength without any pre-knowledge of the dynamic system required.
基金Project Supported by the National Natural Science Foundation of China （Grant No 20373021） and Natural Science Foundation of Liaoning Province, China （Grant No 20052151）.
文摘This paper presents chaos synchronization between two different chaotic systems by using a nonlinear controller, in which the nonlinear functions of the system are used as a nonlinear feedback term. The feedback controller is designed on the basis of stability theory, and the area of feedback gain is determined. The artificial simulation results show that this control method is commendably effective and feasible.
基金This work was partially supported by Nature Science Foundation of China (No. 60374037, 60574036)the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20050055013)the Program for New Century Excellent Talents of China (NCET)
文摘This paper addresses control for the synchronization of Chen chaotic systems via sector nonlinear inputs. Feedback control, adaptive control, fast sliding mode and robust control approaches based on single state feedback controller are investigated. In these cases, sufficient conditions for the synchronization are obtained analytically. Numerical simulations verify the control performances.
基金Project supported by the National Natural Science Foundation of China （Grant No 90405011）, the Natural Science Foundation of Jiangsu Province, China （Grant No 05KJD120083） and the Natural Science Foundation of Nanjing Institute of Technology, China （Grant No KXJ06047）.
文摘This paper presents chaos synchronization between two different four-dimensional （4D） hyperchaotic Chen systems by nonlinear feedback control laws. A modified 4D hyperchaotic Chen system is obtained by changing the nonlinear function of the 4D hyperchaotic Chen system, furthermore, an electronic circuit to realize two different 4D hyperchaotic Chen systems is designed. With nonlinear feedback control method, chaos synchronization between two different 4D hyperchaotic Chen systems is achieved. Based on the stability theory~ the functions of the nonlinear feedback control for synchronization of two different 4D hyperchaotic Chen systems is derived, the range of feedback gains is determined. Numerical simulations are shown to verify the theoretical results.
基金supported by King Abdullah University of Science and Technology (KAUST),KSA
文摘In this paper, we propose a robust fractional-order proportional-integral(FOPI) observer for the synchronization of nonlinear fractional-order chaotic systems. The convergence of the observer is proved, and sufficient conditions are derived in terms of linear matrix inequalities(LMIs) approach by using an indirect Lyapunov method. The proposed FOPI observer is robust against Lipschitz additive nonlinear uncertainty. It is also compared to the fractional-order proportional(FOP) observer and its performance is illustrated through simulations done on the fractional-order chaotic Lorenz system.
基金supported by National Natural Science Foundation of China(11271139)Guangdong Natural Science Foundation(2014A030313256,S2013040016144)+1 种基金Science and Technology Projects of Guangdong Province(2013B010101009)Tianhe Science and Technology Foundation of Guangzhou(201301YG027)
文摘A new fractional-order Lorenz-like system with two stable node-foci has been thoroughly studied in this paper.Some sufficient conditions for the local stability of equilibria considering both commensurate and incommensurate cases are given. In addition, with the effective dimension less than three,the minimum effective dimension of the system is approximated as 2.8485 and is verified numerically. It should be affirmed that the linear differential equation in fractional-order Lorenzlike system appears to be less sensitive to the damping, represented by a fractional derivative, than the two other nonlinear equations. Furthermore, combination synchronization of this system is analyzed with the help of nonlinear feedback control method. Theoretical results are verified by performing numerical simulations.
文摘Synchronization is one of the most important characteristics of dynamic systems.For this paper,the authors obtained results for the nonlinear systems controller for the custom Synchronization of two 4D systems.The findings have allowed authors to develop two analytical approaches using the second Lyapunov(Lyp)method and the Gardanomethod.Since the Gardano method does not involve the development of special positive Lyp functions,it is very efficient and convenient to achieve excessive systemSYCR phenomena.Error is overcome by using Gardano and overcoming some problems in Lyp.Thus we get a great investigation into the convergence of error dynamics,the authors in this paper are interested in giving numerical simulations of the proposed model to clarify the results and check them,an important aspect that will be studied is Synchronization Complete hybrid SYCR and anti-Synchronization,by making use of the Lyapunov expansion analysis,a proposed control method is developed to determine the actual.The basic idea in the proposed way is to receive the evolution of between two methods.Finally,the present model has been applied and showing in a new attractor,and the obtained results are compared with other approximate results,and the nearly good coincidence was obtained.
文摘Study of chaotic synchronization as a fundamental phenomenon in the nonlinear dynamical systems theory has been recently raised many interests in science, engineering, and technology. In this paper, we develop a new mathematical framework in study of chaotic synchronization of discrete-time dynamical systems. In the novel drive-response discrete-time dynamical system which has been coupled using convex link function, we introduce a synchronization threshold which passes that makes the drive-response system lose complete coupling and synchronized behaviors. We provide the application of this type of coupling in synchronized cycles of well-known Ricker model. This model displays a rich cascade of complex dynamics from stable fixed point and cascade of period-doubling bifurcation to chaos. We also numerically verify the effectiveness of the proposed scheme and demonstrate how this type of coupling makes this chaotic system and its corresponding coupled system starting from different initial conditions, quickly get synchronized.
基金Project (No. 20040146) supported by Zhejiang Provincial Edu-cation Department Foundation, China
文摘This paper deals with the synchronization of chaotic systems with structure or parameters difference. Nonlinear differential geometry theory was applied to transform the chaotic discrepancy system into canonical form. A feedback control for synchronizing two chaotic systems is proposed based on sliding mode control design. To make this controller physically realizable, an extended state observer is used to estimate the error between the transmitter and receiver. Two illustrative examples were carried out: (1) The Chua oscillator was used to show that synchronization was achieved and the message signal was recovered in spite of parametric variations; (2) Two second-order driven oscillators were presented to show that the synchronization can be achieved and that the message can be recovered in spite of the strictly different model.
文摘Relerrlng to contlnuous-Ume claaotlc systems, tills paper presents a new projective syncnromzatlon scheme, wnlcn enables each drive system state to be synchronized with a linear combination of response system states for any arbitrary scaling matrix. The proposed method, based on a structural condition related to the uncontrollable eigenvalues of the error system, can be applied to a wide class of continuous-time chaotic （hyperchaotic） systems and represents a general framework that includes any type of synchronization defined to date. An example involving a hyperchaotic oscillator is reported, with the aim of showing how a response system attractor is arbitrarily shaped using a scalar synchronizing signal only. Finally, it is shown that the recently introduced dislocated synchronization can be readily achieved using the conceived scheme.
