Control And Synchronization Of The Chaotic System With Uncertain Parameters

Control and synchronization of the chaotic systems are always the focuses and forefront projects in academic research. In the past, most researches are based on determinate parameters and seldom involved the control and synchronization of the chaotic system with uncertain parameters. Under this situation, this paper proposes new approaches to solve these problems.First, according to the actuality and development tide of domestic and foreign research, systematic review is presented the development history of chaos control and synchronization, chaos definition and its characters. The introduction illustrates some common approaches related with the research of the chaotic system.For solving the control of the discrete chaotic system with uncertain parameter, the discrete chaotic system can also be controlled by the open-plus-closed-loop control if parameters satisfy a given assumption. When parameters are uncertain and unknown, the open-plus-closed-loop control will not be available. In this paper, the new approach, the parametric adaptive open-plus-closed-loop control, is proposed to deal with this kind of problem and the robustness is proved.Synchronization of chaotic systems is not easily solved till now and become more difficult if parameters are uncertain. Synchronization rule is based on two states x(t)andy(t), which are‖x(t)-y(t)‖→0,when t→∞. Because this rule prevents theengineering applications of synchronization theory, the engineering synchronization is defined in this paper and the rule of the parametric adaptive synchronization in engineering synchronization is studied. In chapter 4, the new synchronization approaches, the parametric adaptive lag synchronization, is proposed to deal with the chaotic synchronization when the chaos systems have uncertain parameters. The parametric adaptive lag synchronization shows the character against vibration of parameters through the encryption of sound signal.