In this paper we present a new projective synchronization scheme, where two chaotic （hyperchaotic） discrete-time systems synchronize for any arbitrary scaling matrix. Specifically, each drive system state synchroniz...In this paper we present a new projective synchronization scheme, where two chaotic （hyperchaotic） discrete-time systems synchronize for any arbitrary scaling matrix. Specifically, each drive system state synchronizes with a linear combination of response system states. The proposed observer-based approach presents some useful features： i） it enables exact synchronization to be achieved in finite time （i.e., dead-beat synchronization）; ii） it exploits a scalar synchronizing signal; iii） it can be applied to a wide class of discrete-time chaotic （hyperchaotic） systems; iv） it includes, as a particular case, most of the synchronization types defined so far. An example is reported, which shows in detail that exact synchronization is effectively achieved in finite time, using a scalar synchronizing signal only, for any arbitrary scaling matrix.展开更多
Leader-following consensus of fractional order multi-agent systems is investigated. The agents are considered as discrete-time fractional order integrators or fractional order double-integrators. Moreover, the interac...Leader-following consensus of fractional order multi-agent systems is investigated. The agents are considered as discrete-time fractional order integrators or fractional order double-integrators. Moreover, the interaction between the agents is described with an undirected communication graph with a fixed topology. It is shown that the leader-following consensus problem for the considered agents could be converted to the asymptotic stability analysis of a discrete-time fractional order system. Based on this idea, sufficient conditions to reach the leader-following consensus in terms of the controller parameters are extracted. This leads to an appropriate region in the controller parameters space. Numerical simulations are provided to show the performance of the proposed leader-following consensus approach.展开更多
An uncertain nonlinear discrete-time system model with time-varying input delays for networked control systems (NCSs) is presented. The problem of exponential stability for the system is considered and some new criter...An uncertain nonlinear discrete-time system model with time-varying input delays for networked control systems (NCSs) is presented. The problem of exponential stability for the system is considered and some new criteria of exponential stability are obtained based on norm inequality methods. A numerical example is given todemonstrate that those criteria are useful to analyzing the stability of nonlinear NCSs.展开更多
This paper concerns the absolute stability problem of discrete-time descriptor systems with feedback connected ferromagnetic hysteresis nonlinearities. The ferromagnetic hysteresis model satisfies the passivity condit...This paper concerns the absolute stability problem of discrete-time descriptor systems with feedback connected ferromagnetic hysteresis nonlinearities. The ferromagnetic hysteresis model satisfies the passivity conditions of hysteresis operator, that is the input-output relation of the transformed operator is passive. The bound condition of the solution of the ferromagnetic hysteresis model is given. Through the framework of loop transformation, an augmented discrete-time descriptor system model is established for the stability analysis. A new extended Tsypkin criterion for the absolute stability of discrete-time descriptor systems with hysteresis is presented based on the linear matrix inequalities technique. A numerical example is given to illustrate the effectiveness of the extended criterion.展开更多
This paper gives a mathematical definition for the "caution" and "probing", and presents a decomposition theorem for nonlinear discrete-time stochastic systems. Under some assumptions, the problem ...This paper gives a mathematical definition for the "caution" and "probing", and presents a decomposition theorem for nonlinear discrete-time stochastic systems. Under some assumptions, the problem of finding the closed-loop optimal control can be decomposed into three problems: the deterministic optimal feedback, cautious optimal and probing optimal control problems.展开更多
This paper considers the stability analysis of uncertain discrete-time piecewise linear systems with time delays based on piecewise Lyapunov-Krasovskii functionals. It is shown that the stability can be established fo...This paper considers the stability analysis of uncertain discrete-time piecewise linear systems with time delays based on piecewise Lyapunov-Krasovskii functionals. It is shown that the stability can be established for the control systems if there is a piecewise Lyapunov-Krasovskii functional, and moreover, the functional can be obtained by solving a set of linear matrix inequalities （LMIs） that are numerically feasible. A numerical example is given to demonstrate the efficiency and advantage of the proposed method.展开更多
In this paper, a learning control approach is applied to the generalized projective synchronisation （GPS） of different chaotic systems with unknown periodically time-varying parameters. Using the Lyapunov--Krasovski...In this paper, a learning control approach is applied to the generalized projective synchronisation （GPS） of different chaotic systems with unknown periodically time-varying parameters. Using the Lyapunov--Krasovskii functional stability theory, a differential-difference mixed parametric learning law and an adaptive learning control law are constructed to make the states of two different chaotic systems asymptotically synchronised. The scheme is successfully applied to the generalized projective synchronisation between the Lorenz system and Chen system. Moreover, numerical simulations results are used to verify the effectiveness of the proposed scheme.展开更多
In this paper, a very simple synchronization method is presented for a class of fractional-order chaotic systems only via feedback control. The synchronization technique, based on the stability theory of fractional-or...In this paper, a very simple synchronization method is presented for a class of fractional-order chaotic systems only via feedback control. The synchronization technique, based on the stability theory of fractional-order systems, is simple and theoretically rigorous.展开更多
A controller is designed to realize the synchronization between chaotic systems with different orders. The structure of the controller, the error equations and the Lyapunov functions are determined based on stability ...A controller is designed to realize the synchronization between chaotic systems with different orders. The structure of the controller, the error equations and the Lyapunov functions are determined based on stability theory. Hyperchaotic Chen system and Rossler system are taken for example to demonstrate the method to be effective and feasible. Simulation results show that all the state wriables of Rossler system can be synchronized with those of hyperchaotic Chen system by using only one controller, and the error signals approach zero smoothly and quickly.展开更多
This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projectiv...This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projective synchronization between three-dimensional （3D） integer-order Lorenz chaotic system and 3D fractional-order Chen chaotic system are presented to demonstrate the effectiveness of the proposed scheme.展开更多
In this paper, some novel sufficient conditions for asymptotic stability of impulsive control systems are presented by comparison systems. The results are used to obtain the conditions under which the chaotic systems ...In this paper, some novel sufficient conditions for asymptotic stability of impulsive control systems are presented by comparison systems. The results are used to obtain the conditions under which the chaotic systems can be asymptotically controlled to the origin via impulsive control. Compared with some existing results, our results are more relaxed in the sense that the Lyapunov function is required to be nonincreasing only along a subsequence of switchings. Moreover, a larger upper bound of impulsive intervals for stabilization and synchronization is obtained.展开更多
In this paper, a modified impulsive control scheme is proposed to realize the complete synchronization of fractional order hyperchaotic systems. By constructing a suitable response system, an integral order synchroniz...In this paper, a modified impulsive control scheme is proposed to realize the complete synchronization of fractional order hyperchaotic systems. By constructing a suitable response system, an integral order synchronization error system is obtained. Based on the theory of Lyapunov stability and the impulsive differential equations, some effective sufficient conditions are derived to guarantee the asymptotical stability of the synchronization error system. In particular, some simpler and more convenient conditions are derived by taking the fixed impulsive distances and control gains. Compared with the existing results, the main results in this paper are practical and rigorous. Simulation results show the effectiveness and the feasibility of the proposed impulsive control method.展开更多
In this paper, we propose a multidimensional version of recurrent least squares support vector machines （MDRLS- SVM） to solve the problem about the prediction of chaotic system. To acquire better prediction performa...In this paper, we propose a multidimensional version of recurrent least squares support vector machines （MDRLS- SVM） to solve the problem about the prediction of chaotic system. To acquire better prediction performance, the high-dimensional space, which provides more information on the system than the scalar time series, is first reconstructed utilizing Takens＇s embedding theorem. Then the MDRLS-SVM instead of traditional RLS-SVM is used in the high- dimensional space, and the prediction performance can be improved from the point of view of reconstructed embedding phase space. In addition, the MDRLS-SVM algorithm is analysed in the context of noise, and we also find that the MDRLS-SVM has lower sensitivity to noise than the RLS-SVM.展开更多
A no-chattering sliding mode control strategy for a class of fractional-order chaotic systems is proposed in this paper. First, the sliding mode control law is derived to stabilize the states of the commensurate fract...A no-chattering sliding mode control strategy for a class of fractional-order chaotic systems is proposed in this paper. First, the sliding mode control law is derived to stabilize the states of the commensurate fractional-order chaotic system and the non-commensurate fractional-order chaotic system, respectively. The designed control scheme guarantees the asymptotical stability of an uncertain fractional-order chaotic system. Simulation results are given for several fractional-order chaotic examples to illustrate the effectiveness of the proposed scheme.展开更多
In this paper, a practical impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. By virtue of the new definition of synchronization and the theory of impulsive d...In this paper, a practical impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. By virtue of the new definition of synchronization and the theory of impulsive differential equations, some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level. The idea and approach developed in this paper can provide a more practical framework for the synchronization between identical and different chaotic systems in parameter perturbation circumstances. Simulation results finally demonstrate the effectiveness of the method.展开更多
The stability of impulsive fractional-order systems is discussed. A new synchronization criterion of fractional-order chaotic systems is proposed based on the stability theory of impulsive fractional-order systems. Th...The stability of impulsive fractional-order systems is discussed. A new synchronization criterion of fractional-order chaotic systems is proposed based on the stability theory of impulsive fractional-order systems. The synchronization criterion is suitable for the case of the order 0 〈 q ≤ 1. It is more general than those of the known results. Simulation results are given to show the effectiveness of the proposed synchronization criterion.展开更多
This paper presents the problem of generating four-wing （eight-wing） chaotic attractors. The adopted method consists in suitably coupling two （three） identical Lorenz systems. In analogy with the original Lorenz s...This paper presents the problem of generating four-wing （eight-wing） chaotic attractors. The adopted method consists in suitably coupling two （three） identical Lorenz systems. In analogy with the original Lorenz system, where the two wings of the butterfly attractor are located around the two equilibria with the unstable pair of complex-conjugate eigenvalues, this paper shows that the four wings （eight wings） of these novel attractors axe located around the four （eight） equilibria with two （three） pairs of unstable complex-conjugate eigenvalues.展开更多
In this paper, an improved impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the new definition of synchronization with error bound and a novel impu...In this paper, an improved impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the new definition of synchronization with error bound and a novel impulsive control scheme （the so-called dual-stage impulsive control）, some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level, which is more reasonable and rigorous than the existing results. In particular, some simpler and more convenient conditions are derived by taking the same impulsive distances and control gains. Finally, some numerical simulations for the Lorenz system and the Chen system are given to demonstrate the effectiveness and feasibility of the proposed method.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
This paper presents a general method of the generalized projective synchronization and the parameter identification between two different chaotic systems with unknown parameters. This approach is based on Lyapunov sta...This paper presents a general method of the generalized projective synchronization and the parameter identification between two different chaotic systems with unknown parameters. This approach is based on Lyapunov stability theory, and employs a combination of feedback control and adaptive control. With this method one can achieve the generalized projective synchronization and realize the parameter identifications between almost all chaotic （hyperchaotic） systems with unknown parameters. Numerical simulations results are presented to demonstrate the effectiveness of the method.展开更多
文摘In this paper we present a new projective synchronization scheme, where two chaotic （hyperchaotic） discrete-time systems synchronize for any arbitrary scaling matrix. Specifically, each drive system state synchronizes with a linear combination of response system states. The proposed observer-based approach presents some useful features： i） it enables exact synchronization to be achieved in finite time （i.e., dead-beat synchronization）; ii） it exploits a scalar synchronizing signal; iii） it can be applied to a wide class of discrete-time chaotic （hyperchaotic） systems; iv） it includes, as a particular case, most of the synchronization types defined so far. An example is reported, which shows in detail that exact synchronization is effectively achieved in finite time, using a scalar synchronizing signal only, for any arbitrary scaling matrix.
文摘Leader-following consensus of fractional order multi-agent systems is investigated. The agents are considered as discrete-time fractional order integrators or fractional order double-integrators. Moreover, the interaction between the agents is described with an undirected communication graph with a fixed topology. It is shown that the leader-following consensus problem for the considered agents could be converted to the asymptotic stability analysis of a discrete-time fractional order system. Based on this idea, sufficient conditions to reach the leader-following consensus in terms of the controller parameters are extracted. This leads to an appropriate region in the controller parameters space. Numerical simulations are provided to show the performance of the proposed leader-following consensus approach.
文摘An uncertain nonlinear discrete-time system model with time-varying input delays for networked control systems (NCSs) is presented. The problem of exponential stability for the system is considered and some new criteria of exponential stability are obtained based on norm inequality methods. A numerical example is given todemonstrate that those criteria are useful to analyzing the stability of nonlinear NCSs.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 50977008,60821063 and 61034005)National Basic Research Program of China (Grant No. 2009CB32060)
文摘This paper concerns the absolute stability problem of discrete-time descriptor systems with feedback connected ferromagnetic hysteresis nonlinearities. The ferromagnetic hysteresis model satisfies the passivity conditions of hysteresis operator, that is the input-output relation of the transformed operator is passive. The bound condition of the solution of the ferromagnetic hysteresis model is given. Through the framework of loop transformation, an augmented discrete-time descriptor system model is established for the stability analysis. A new extended Tsypkin criterion for the absolute stability of discrete-time descriptor systems with hysteresis is presented based on the linear matrix inequalities technique. A numerical example is given to illustrate the effectiveness of the extended criterion.
文摘This paper gives a mathematical definition for the "caution" and "probing", and presents a decomposition theorem for nonlinear discrete-time stochastic systems. Under some assumptions, the problem of finding the closed-loop optimal control can be decomposed into three problems: the deterministic optimal feedback, cautious optimal and probing optimal control problems.
文摘This paper considers the stability analysis of uncertain discrete-time piecewise linear systems with time delays based on piecewise Lyapunov-Krasovskii functionals. It is shown that the stability can be established for the control systems if there is a piecewise Lyapunov-Krasovskii functional, and moreover, the functional can be obtained by solving a set of linear matrix inequalities （LMIs） that are numerically feasible. A numerical example is given to demonstrate the efficiency and advantage of the proposed method.
基金supported by the National Natural Science Foundation of China (Grant No. 60374015)
文摘In this paper, a learning control approach is applied to the generalized projective synchronisation （GPS） of different chaotic systems with unknown periodically time-varying parameters. Using the Lyapunov--Krasovskii functional stability theory, a differential-difference mixed parametric learning law and an adaptive learning control law are constructed to make the states of two different chaotic systems asymptotically synchronised. The scheme is successfully applied to the generalized projective synchronisation between the Lorenz system and Chen system. Moreover, numerical simulations results are used to verify the effectiveness of the proposed scheme.
文摘In this paper, a very simple synchronization method is presented for a class of fractional-order chaotic systems only via feedback control. The synchronization technique, based on the stability theory of fractional-order systems, is simple and theoretically rigorous.
基金Project supported by the National Natural Science Foundation of China （Grant No 20373021） and Natural Science Foundation of Liaoning Province （Grant No 20052151）.
文摘A controller is designed to realize the synchronization between chaotic systems with different orders. The structure of the controller, the error equations and the Lyapunov functions are determined based on stability theory. Hyperchaotic Chen system and Rossler system are taken for example to demonstrate the method to be effective and feasible. Simulation results show that all the state wriables of Rossler system can be synchronized with those of hyperchaotic Chen system by using only one controller, and the error signals approach zero smoothly and quickly.
文摘This paper investigates the function projective synchronization between fractional-order chaotic systems and integer-order chaotic systems using the stability theory of fractional-order systems. The function projective synchronization between three-dimensional （3D） integer-order Lorenz chaotic system and 3D fractional-order Chen chaotic system are presented to demonstrate the effectiveness of the proposed scheme.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.10926066 and 11026182)the Natural Science Foundation of Zhejiang Province,China(Grant No.Y6100007)+3 种基金the Zhejiang Educational Committee,China(Grant No.Y200805720)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK2010408)the Innovation Fund of Basic Scientific Research Operating Expenses,China(Grant No.3207010501)the Alexander von Humboldt Foundation of Germany
文摘In this paper, some novel sufficient conditions for asymptotic stability of impulsive control systems are presented by comparison systems. The results are used to obtain the conditions under which the chaotic systems can be asymptotically controlled to the origin via impulsive control. Compared with some existing results, our results are more relaxed in the sense that the Lyapunov function is required to be nonincreasing only along a subsequence of switchings. Moreover, a larger upper bound of impulsive intervals for stabilization and synchronization is obtained.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 50830202 and 51073179)the Natural Science Foundation of Chongqing,China (Grant No. CSTC 2010BB2238)+2 种基金the Doctoral Program of Higher Education Foundation of Institutions of China (Grant Nos. 20090191110011 and 20100191120025)the Natural Science Foundation for Postdoctoral Scientists of China (Grant Nos. 20100470813 and 20100480043)the Fundamental Research Funds for the Central Universities(Grant Nos. CDJZR11 12 00 03 and CDJZR11 12 88 01)
文摘In this paper, a modified impulsive control scheme is proposed to realize the complete synchronization of fractional order hyperchaotic systems. By constructing a suitable response system, an integral order synchronization error system is obtained. Based on the theory of Lyapunov stability and the impulsive differential equations, some effective sufficient conditions are derived to guarantee the asymptotical stability of the synchronization error system. In particular, some simpler and more convenient conditions are derived by taking the fixed impulsive distances and control gains. Compared with the existing results, the main results in this paper are practical and rigorous. Simulation results show the effectiveness and the feasibility of the proposed impulsive control method.
基金Project supported by the National Natural Science Foundation of China （Grant No 90207012）.
文摘In this paper, we propose a multidimensional version of recurrent least squares support vector machines （MDRLS- SVM） to solve the problem about the prediction of chaotic system. To acquire better prediction performance, the high-dimensional space, which provides more information on the system than the scalar time series, is first reconstructed utilizing Takens＇s embedding theorem. Then the MDRLS-SVM instead of traditional RLS-SVM is used in the high- dimensional space, and the prediction performance can be improved from the point of view of reconstructed embedding phase space. In addition, the MDRLS-SVM algorithm is analysed in the context of noise, and we also find that the MDRLS-SVM has lower sensitivity to noise than the RLS-SVM.
基金supported by the National Natural Science Foundation of China (Grant No. 51109180)the Personal Special Fund of Northwest Agriculture and Forestry University,China (Grant No. RCZX-2009-01)
文摘A no-chattering sliding mode control strategy for a class of fractional-order chaotic systems is proposed in this paper. First, the sliding mode control law is derived to stabilize the states of the commensurate fractional-order chaotic system and the non-commensurate fractional-order chaotic system, respectively. The designed control scheme guarantees the asymptotical stability of an uncertain fractional-order chaotic system. Simulation results are given for several fractional-order chaotic examples to illustrate the effectiveness of the proposed scheme.
基金Project supported by the National Natural Science foundation of China (Grant Nos 60534010, 60572070, 60774048 and 60728307)the Program for Changjiang Scholars and Innovative Research Team in University (Grant No 60521003) the National High Technology Research and Development Program of China (Grant No 2006AA04Z183)
文摘In this paper, a practical impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. By virtue of the new definition of synchronization and the theory of impulsive differential equations, some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level. The idea and approach developed in this paper can provide a more practical framework for the synchronization between identical and different chaotic systems in parameter perturbation circumstances. Simulation results finally demonstrate the effectiveness of the method.
基金supported by Scientific Research Foundation of Huaiyin Institute of Technology (Grant No. HGA1102)
文摘The stability of impulsive fractional-order systems is discussed. A new synchronization criterion of fractional-order chaotic systems is proposed based on the stability theory of impulsive fractional-order systems. The synchronization criterion is suitable for the case of the order 0 〈 q ≤ 1. It is more general than those of the known results. Simulation results are given to show the effectiveness of the proposed synchronization criterion.
文摘This paper presents the problem of generating four-wing （eight-wing） chaotic attractors. The adopted method consists in suitably coupling two （three） identical Lorenz systems. In analogy with the original Lorenz system, where the two wings of the butterfly attractor are located around the two equilibria with the unstable pair of complex-conjugate eigenvalues, this paper shows that the four wings （eight wings） of these novel attractors axe located around the four （eight） equilibria with two （three） pairs of unstable complex-conjugate eigenvalues.
基金supported by the National Natural Science Foundation of China (Grant Nos 60534010,60774048,60728307,60804006 and 60521003)the National High Technology Research and Development Program of China (Grant No 2006AA04Z183)+2 种基金Liaoning Provincial Natural Science Foundation of China (Grant No 20062018)State Key Development Program for Basic research of China (Grant No 2009CB320601)111 Project,China (Grant No B08015)
文摘In this paper, an improved impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the new definition of synchronization with error bound and a novel impulsive control scheme （the so-called dual-stage impulsive control）, some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level, which is more reasonable and rigorous than the existing results. In particular, some simpler and more convenient conditions are derived by taking the same impulsive distances and control gains. Finally, some numerical simulations for the Lorenz system and the Chen system are given to demonstrate the effectiveness and feasibility of the proposed method.
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.
基金Project supported by the Natural Science Foundation of Hebei Province, China (Grant No A2006000128)
文摘This paper presents a general method of the generalized projective synchronization and the parameter identification between two different chaotic systems with unknown parameters. This approach is based on Lyapunov stability theory, and employs a combination of feedback control and adaptive control. With this method one can achieve the generalized projective synchronization and realize the parameter identifications between almost all chaotic （hyperchaotic） systems with unknown parameters. Numerical simulations results are presented to demonstrate the effectiveness of the method.
