Control And Synchronization Of A Class Of Uncertain Chaotic Systems

In recent years, chaos control and synchronization have been an active area of research and development. The development of chaos synchrozization and control not only brings satisfied solutions for the old problems of nonlinear dynamics, control and synchronization, but also brings new ideas and new techniques. Some correlative problems in this area are studied in this paper.Firstly, Based on Gerschgorin's theorem in matrix theory and differential equation theory, two design scheme are proposed for a class of chaotic systems with parameters perturbation. In the first way, when the bounds of perturbation are known, then using the adaptive compensation term and Gerschgorin's theorem, some simple generic criterions of global synchronization between two chaotic systems are established, by the Lyapunov method, the tracking errors are proved to converging to zero. In the second way, with the differential equation, the upper bound of the perturbation need not to be known, then based on Gerschgorin's theorem, some simple generic criterions of global synchronization between two chaotic systems are established, by using a high gain of the controller,the tracking errors can converging to a arbitrary small neighborhood of zero.Secondly, an extended state observer and a reduced order observer are presented in this charter, with the two observers, a class of uncertain chaotic systems can be controlled. In the first way, a class of uncertain chaotic systems with input nonlinearities is considered, with the nonlinearities in the controller, the disadvantage can be canceled, to make this controller physically realizable, an extended state observer is used to estimate the unknown information. By theoretical analysis, the tracking error converging to zero. In the second way, based on reduced-order observer, the synchronization of a class of uncertain chaotic system is considered, if the chaotic drive system has a special structure then without any premise on the nature of the perturbation, a reduced-order response system can be designed to estimate the unmeasured states. The state error is proved to converging to zero.Thirdly, synchronization of a class of time-delay chaotic systems with parameters perturbation is discussed in this charter. The knowledge of the delay time is unknown, and the uncertain structure satisfied matching condition. Through adaptive control term, we design a new time-delay response chaotic system, an appended term in the response chaotic system is introduced to cancel the uncertainties in the driven system, then based on Lyapunov-Krasovskii functional, it is shown that the response chaotic system can synchronization the driven system.Finally, the tracking problem for a class of uncertain chaotic systems with dead-zone nonlinearity in the input function is considered in this paper. With the dead-zone nonlinearity in the controller, the disadvantage can be canceled. The knowledge of the dead-zone nonlinearity in the input is not to be known. To make this...