The paper is concerned with adaptive tracking problem for a class of chaotic system with time-varying uncertainty, but bounded by norm polynomial. Based on adaptive technique, it proposes a novel controller to asympto...The paper is concerned with adaptive tracking problem for a class of chaotic system with time-varying uncertainty, but bounded by norm polynomial. Based on adaptive technique, it proposes a novel controller to asymptotically track the arbitrary desired bounded trajectory. Simulation on the Rossler chaotic system is performed and the result verifies the effectiveness of the proposed method.展开更多
This work investigates adaptive control of a large class of uncertain time-delay chaotic systems （UTCSs） with unknown general perturbation terms bounded by a polynomial （unknown gains）, Associated with the differe...This work investigates adaptive control of a large class of uncertain time-delay chaotic systems （UTCSs） with unknown general perturbation terms bounded by a polynomial （unknown gains）, Associated with the different cases of known and unknowl system matrices, two corresponding adaptive controllers are proposed to stabilize unstable fixed points of the systems by means of Lyapunov stability theory and linear matrix inequafities （LMI） which can be solved easily by convex optimization algorithms, Two examples are used for examining the effectiveness of the proposed methods.展开更多
A more general form of projective synchronization, so called linear generalized synchronization （LGS） is proposed, which includes the generalized projective synchronization （GPS） and the hybrid projective synchron...A more general form of projective synchronization, so called linear generalized synchronization （LGS） is proposed, which includes the generalized projective synchronization （GPS） and the hybrid projective synchronization （HPS） as its special cases, Based on the adaptive technique and Lyapunov stability theory, a general method for achieving the LGS between two chaotic or hyperehaotic systems with uncertain parameters in any scaling matrix is presented. Some numerical simulations are provided to show the effectiveness and feasibility of the proposed synchronization method.展开更多
The paper discusses lag synchronization of Lorenz chaotic system with three uncertain parameters. Based on adaptive technique, the lag synchronization of Lorenz chaotic system is achieved by designing a novel nonlinea...The paper discusses lag synchronization of Lorenz chaotic system with three uncertain parameters. Based on adaptive technique, the lag synchronization of Lorenz chaotic system is achieved by designing a novel nonlinear controller. Furthermore, the parameters identification is realized simultaneously. A sufficient condition is given and proved theoreticcally by Lyapunov stability theory and LaSalle’s invariance principle. Finally, the numerical simulations are provided to show the effectiveness and feasibility of the proposed method.展开更多
This paper deals with the finite-time stabilization of unified chaotic complex systems with known and unknown parameters. Based on the finite-time stability theory, nonlinear control laws are presented to achieve fini...This paper deals with the finite-time stabilization of unified chaotic complex systems with known and unknown parameters. Based on the finite-time stability theory, nonlinear control laws are presented to achieve finite-time chaos control of the determined and uncertain unified chaotic complex systems, respectively. The two controllers are simple, and one of the uncertain unified chaotic complex systems is robust. For the design of a finite-time controller on uncertain unified chaotic complex systems, only some of the unknown parameters need to be bounded. Simulation results for the chaotic complex Lorenz, Lu¨ and Chen systems are presented to validate the design and analysis.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
Chaos synchronization has been applied in secure communication, chemicalreaction, biological systems, and information processing. A new theorem to synchronization ofunified chaotic systems via adaptive control is prop...Chaos synchronization has been applied in secure communication, chemicalreaction, biological systems, and information processing. A new theorem to synchronization ofunified chaotic systems via adaptive control is proposed. The constructive theorem provides thedesign scheme for adaptive controller such that a respond system can synchronize with respect to anuncertain drive system. One example for discontinuous chaotic system is proposed to illustrate theeffectiveness and feasibility.展开更多
A parameter adaptive control approach was applied to a kind of financial chaotic systems.According to Lyapunov stability theorem,synchronization of two financial chaotic systems with different certain parameters or th...A parameter adaptive control approach was applied to a kind of financial chaotic systems.According to Lyapunov stability theorem,synchronization of two financial chaotic systems with different certain parameters or the same uncertain parameters were implemented through designing proper control functions and using parameters self-adaptive control principle.The sufficient synchronization conditions of the two financial systems were obtained.Under the situation of the same uncertain parameters,the synchronization system has simpler controller and better performance.Numerical simulations show the effectiveness of the method.展开更多
In order to eliminate chaotic oscillation of electromechanical characteristics of seismograph system, the complex dynamic the four-dimensional nonlinear equations of seismograph system were analyzed. Sliding mode meth...In order to eliminate chaotic oscillation of electromechanical characteristics of seismograph system, the complex dynamic the four-dimensional nonlinear equations of seismograph system were analyzed. Sliding mode method was applied to stabilize the chaotic orbits of the eleetromechanieal seismograph system to arbitrary chosen fixed points and periodic orbits precisely, and MATLAB simulations were presented to confirm the validity of the controller. The results show that using sliding mode method can make the system track target orbit strictly and smoothly with short transition time, and its insensitivity to noise disturbances is shown. It also provides reference for relevant chaos control in relevant system.展开更多
By the control method independent of system parameters, synchronization of two Chen chaotic systems with identical, but uncertain parameters is discussed in this article. Based on Lyapunov＇s theorem, an adaptive cont...By the control method independent of system parameters, synchronization of two Chen chaotic systems with identical, but uncertain parameters is discussed in this article. Based on Lyapunov＇s theorem, an adaptive controller and the parameters estimate update law are derived to make the solution of the error dynamical equation converge at the point E（0, 0,0） with a quick speed, that is, the states of two Chen chaotic systems can be asymptotically synchronized. Numerical simulations verify the effectiveness and the adaptivity to the variation of Chen system parameters.展开更多
基金Project supported by National Natural Science Foundation of China （Grant No 60274032）, and Science and Technology Rising-Star Program of Shanghai, China （Grant No 04QMH1405）.
文摘The paper is concerned with adaptive tracking problem for a class of chaotic system with time-varying uncertainty, but bounded by norm polynomial. Based on adaptive technique, it proposes a novel controller to asymptotically track the arbitrary desired bounded trajectory. Simulation on the Rossler chaotic system is performed and the result verifies the effectiveness of the proposed method.
文摘This work investigates adaptive control of a large class of uncertain time-delay chaotic systems （UTCSs） with unknown general perturbation terms bounded by a polynomial （unknown gains）, Associated with the different cases of known and unknowl system matrices, two corresponding adaptive controllers are proposed to stabilize unstable fixed points of the systems by means of Lyapunov stability theory and linear matrix inequafities （LMI） which can be solved easily by convex optimization algorithms, Two examples are used for examining the effectiveness of the proposed methods.
基金the National Natural Science Foundation of China (60574045 10661006).
文摘A more general form of projective synchronization, so called linear generalized synchronization （LGS） is proposed, which includes the generalized projective synchronization （GPS） and the hybrid projective synchronization （HPS） as its special cases, Based on the adaptive technique and Lyapunov stability theory, a general method for achieving the LGS between two chaotic or hyperehaotic systems with uncertain parameters in any scaling matrix is presented. Some numerical simulations are provided to show the effectiveness and feasibility of the proposed synchronization method.
文摘The paper discusses lag synchronization of Lorenz chaotic system with three uncertain parameters. Based on adaptive technique, the lag synchronization of Lorenz chaotic system is achieved by designing a novel nonlinear controller. Furthermore, the parameters identification is realized simultaneously. A sufficient condition is given and proved theoreticcally by Lyapunov stability theory and LaSalle’s invariance principle. Finally, the numerical simulations are provided to show the effectiveness and feasibility of the proposed method.
基金the National Natural Science Foundation of China(Grant Nos.60874009 and 10971120)the Natural Science Foundation of Shandong Province,China(Grant No.ZR2010FM010)
文摘This paper deals with the finite-time stabilization of unified chaotic complex systems with known and unknown parameters. Based on the finite-time stability theory, nonlinear control laws are presented to achieve finite-time chaos control of the determined and uncertain unified chaotic complex systems, respectively. The two controllers are simple, and one of the uncertain unified chaotic complex systems is robust. For the design of a finite-time controller on uncertain unified chaotic complex systems, only some of the unknown parameters need to be bounded. Simulation results for the chaotic complex Lorenz, Lu¨ and Chen systems are presented to validate the design and analysis.
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This project is jointly supported by the National Natural Science Foundation of China(No.60074034,No.70271068),the Research Fund for the Doctoral Program of Higher Education(No.200020008004)and the Foundation for University Key Teacher by the Ministry of
文摘Chaos synchronization has been applied in secure communication, chemicalreaction, biological systems, and information processing. A new theorem to synchronization ofunified chaotic systems via adaptive control is proposed. The constructive theorem provides thedesign scheme for adaptive controller such that a respond system can synchronize with respect to anuncertain drive system. One example for discontinuous chaotic system is proposed to illustrate theeffectiveness and feasibility.
基金supported by Doctor Fund Item of Chongqing University of Posts and Telecommunications granted A2006-85 and Science Fund Item of Chongqing teaching committee granted KJ060506the scienceand technology research program of the municipal education committee of chongqing of granted KJ080524
文摘A parameter adaptive control approach was applied to a kind of financial chaotic systems.According to Lyapunov stability theorem,synchronization of two financial chaotic systems with different certain parameters or the same uncertain parameters were implemented through designing proper control functions and using parameters self-adaptive control principle.The sufficient synchronization conditions of the two financial systems were obtained.Under the situation of the same uncertain parameters,the synchronization system has simpler controller and better performance.Numerical simulations show the effectiveness of the method.
基金the Independent Research Project of State Key Laboratory of Power Transmission Equipment & System Security and New Technology,China ( No. 2007DA10512711205)
文摘In order to eliminate chaotic oscillation of electromechanical characteristics of seismograph system, the complex dynamic the four-dimensional nonlinear equations of seismograph system were analyzed. Sliding mode method was applied to stabilize the chaotic orbits of the eleetromechanieal seismograph system to arbitrary chosen fixed points and periodic orbits precisely, and MATLAB simulations were presented to confirm the validity of the controller. The results show that using sliding mode method can make the system track target orbit strictly and smoothly with short transition time, and its insensitivity to noise disturbances is shown. It also provides reference for relevant chaos control in relevant system.
基金the National Natural Science Foundation of Zhejiang Province （Y105320）.
文摘By the control method independent of system parameters, synchronization of two Chen chaotic systems with identical, but uncertain parameters is discussed in this article. Based on Lyapunov＇s theorem, an adaptive controller and the parameters estimate update law are derived to make the solution of the error dynamical equation converge at the point E（0, 0,0） with a quick speed, that is, the states of two Chen chaotic systems can be asymptotically synchronized. Numerical simulations verify the effectiveness and the adaptivity to the variation of Chen system parameters.
基金Supported by National Natural Science Foundation of China(60574045)the Natural Science Foundation of Guangxi(0991244)the Science Foundation of Education Commission of Guangxi(200807MS043)
