Chaos as a very special type of complex dynamical behaviors has been studied for about four decades. Yet the traditional trend of analyzing and understanding chaos has evolved to controlling and utilizing chaos today....Chaos as a very special type of complex dynamical behaviors has been studied for about four decades. Yet the traditional trend of analyzing and understanding chaos has evolved to controlling and utilizing chaos today. Research in the field of chaos modeling, control, and synchronization includes not only ordering chaos, which means to weaken or completely suppress chaos when it is harmful, but also chaotification, which refers to enhancing existing Chaos or creating chaos purposely when it is useful, by any means of control technology. This article offers a brief overview about the potential impact of controlled chaos on beneficial applications in science and engineering, and introduces some recent progress in chaotification via feedback control methods.展开更多
The chaotification problem of discrete Hamilton systems in one dimensional space is investigated and corresponding chaotification theorem is established. Feedback control techniques is used to make arbitrary discrete ...The chaotification problem of discrete Hamilton systems in one dimensional space is investigated and corresponding chaotification theorem is established. Feedback control techniques is used to make arbitrary discrete Hamilton systems chaotic, or enhance its existing chaotic behaviors. By designing a universal controller and combining anti-integrable limit it is proved that chaos of the controlled systems is in the sense of Devaney. In particular, the systems corresponding to the original systems and designed controllers are only required to satisfy some mild assumptions. Moreover, the range of the coefficient of the controller is given.展开更多
This paper investigates the chaotification problem of a stable continuous-time T S fuzzy system. A simple nonlinear state time-delay feedback controller is designed by parallel distributed compensation technique. Then...This paper investigates the chaotification problem of a stable continuous-time T S fuzzy system. A simple nonlinear state time-delay feedback controller is designed by parallel distributed compensation technique. Then, the asymptotically approximate relationship between the controlled continuous-time T-S fuzzy system with time-delay and a discrete-time T-S fuzzy system is established. Based on the discrete-time T-S fuzzy system, it proves that the chaos in the discrete- time T-S fuzzy system satisfies the Li-Yorke definition by choosing appropriate controller parameters via the revised Marotto theorem. Finally, the effectiveness of the proposed chaotic anticontrol method is verified by a practical example.展开更多
This paper shows that two or more switched linear systems can generate chaotic dynamical behaviors by an appropriate switching rule as they at least consist of a controllable system and an unstable system with the exp...This paper shows that two or more switched linear systems can generate chaotic dynamical behaviors by an appropriate switching rule as they at least consist of a controllable system and an unstable system with the expanding property. According to the results in the reference （Xie, L. L., Zhou, Y., and Zhao, Y. Criterion of chaos for switched linear systems with antrollers. International Journal of Bifurcation and Chaos, 20（12）, 4105-4109 （2010））, a nonlinear feedback gain is needed to generate chaotic dy- namics. A linear feedback control is usually used to approximate the nonlinear one for simulation. In order to obtain the exact control, as a main result of this paper, the con- troller is constructed by Russell＇s result, and a block diagram is included to interpret the realization of the controller. Numerical simulations are given to illustrate the generated chaotic dynamical behavior of the switched linear systems with some parameters and show the effects of the constructed controller.展开更多
In this paper, an approach for chaotifying a stable controllable linear system via single input state-feedback is presented. The overflow function of the system states is designed as the feedback controller, which can...In this paper, an approach for chaotifying a stable controllable linear system via single input state-feedback is presented. The overflow function of the system states is designed as the feedback controller, which can make the fixed point of the closed-loop system to be a snap-back repeller, thereby yields chaotic dynamics. Based on the Marotto theorem, it proves theoretically that the closed-loop system is chaotic in the sense of Li and Yorke. Finally, the simulation results are used to illustrate the effectiveness of the proposed method.展开更多
This paper is concerned with chaotification of discrete Lagrange systems in one dimension, via feedback control techniques. A chaotification theorem for discrete Lagrange systems is established. The controlled systems...This paper is concerned with chaotification of discrete Lagrange systems in one dimension, via feedback control techniques. A chaotification theorem for discrete Lagrange systems is established. The controlled systems are proved to be chaotic in the sense of Devaney. In particular, the systems corresponding to the original systems and designed controllers are only required to satisfy, some mild assumptions.展开更多
This paper studies the problem of making an arbitrary discrete system chaotic, or enhancing its existing chaotic behaviors, by designing a universal controller. The only assumption is that the arbitrarily given system...This paper studies the problem of making an arbitrary discrete system chaotic, or enhancing its existing chaotic behaviors, by designing a universal controller. The only assumption is that the arbitrarily given system has a bounded first derivative in a (small) region of interest.展开更多
基金the US Army Research Office under the Grant DAAG55-98-1-0198 and the Hong Kong Research Grants Council under the CERG Grant No
文摘Chaos as a very special type of complex dynamical behaviors has been studied for about four decades. Yet the traditional trend of analyzing and understanding chaos has evolved to controlling and utilizing chaos today. Research in the field of chaos modeling, control, and synchronization includes not only ordering chaos, which means to weaken or completely suppress chaos when it is harmful, but also chaotification, which refers to enhancing existing Chaos or creating chaos purposely when it is useful, by any means of control technology. This article offers a brief overview about the potential impact of controlled chaos on beneficial applications in science and engineering, and introduces some recent progress in chaotification via feedback control methods.
基金the National Natural Science Foundation of China(10272022)
文摘The chaotification problem of discrete Hamilton systems in one dimensional space is investigated and corresponding chaotification theorem is established. Feedback control techniques is used to make arbitrary discrete Hamilton systems chaotic, or enhance its existing chaotic behaviors. By designing a universal controller and combining anti-integrable limit it is proved that chaos of the controlled systems is in the sense of Devaney. In particular, the systems corresponding to the original systems and designed controllers are only required to satisfy some mild assumptions. Moreover, the range of the coefficient of the controller is given.
基金supported by the National Natural Science Foundation of China (Grant Nos. 60904101,60972164 and 60904046)the Fundamental Research Funds for the Central Universities (Grant No. N090404009)the Research Foundation of Education Bureau of Liaoning Province,China (Grant No. 2009A544)
文摘This paper investigates the chaotification problem of a stable continuous-time T S fuzzy system. A simple nonlinear state time-delay feedback controller is designed by parallel distributed compensation technique. Then, the asymptotically approximate relationship between the controlled continuous-time T-S fuzzy system with time-delay and a discrete-time T-S fuzzy system is established. Based on the discrete-time T-S fuzzy system, it proves that the chaos in the discrete- time T-S fuzzy system satisfies the Li-Yorke definition by choosing appropriate controller parameters via the revised Marotto theorem. Finally, the effectiveness of the proposed chaotic anticontrol method is verified by a practical example.
基金supported by the National Natural Science Foundation of China(Nos.11071262,11101440,and 61263011)
文摘This paper shows that two or more switched linear systems can generate chaotic dynamical behaviors by an appropriate switching rule as they at least consist of a controllable system and an unstable system with the expanding property. According to the results in the reference （Xie, L. L., Zhou, Y., and Zhao, Y. Criterion of chaos for switched linear systems with antrollers. International Journal of Bifurcation and Chaos, 20（12）, 4105-4109 （2010））, a nonlinear feedback gain is needed to generate chaotic dy- namics. A linear feedback control is usually used to approximate the nonlinear one for simulation. In order to obtain the exact control, as a main result of this paper, the con- troller is constructed by Russell＇s result, and a block diagram is included to interpret the realization of the controller. Numerical simulations are given to illustrate the generated chaotic dynamical behavior of the switched linear systems with some parameters and show the effects of the constructed controller.
文摘In this paper, an approach for chaotifying a stable controllable linear system via single input state-feedback is presented. The overflow function of the system states is designed as the feedback controller, which can make the fixed point of the closed-loop system to be a snap-back repeller, thereby yields chaotic dynamics. Based on the Marotto theorem, it proves theoretically that the closed-loop system is chaotic in the sense of Li and Yorke. Finally, the simulation results are used to illustrate the effectiveness of the proposed method.
基金The project supported by National Natural Science Foundation of China under Grant No. 10272021
文摘This paper is concerned with chaotification of discrete Lagrange systems in one dimension, via feedback control techniques. A chaotification theorem for discrete Lagrange systems is established. The controlled systems are proved to be chaotic in the sense of Devaney. In particular, the systems corresponding to the original systems and designed controllers are only required to satisfy, some mild assumptions.
基金This research is partially supported by the National Natural Science Foundation (Grant No. 19971057)the Hong Kong RGC (Grant No. CERG 9040579).
文摘This paper studies the problem of making an arbitrary discrete system chaotic, or enhancing its existing chaotic behaviors, by designing a universal controller. The only assumption is that the arbitrarily given system has a bounded first derivative in a (small) region of interest.
