Research Related Problems In Chaos Control And Synchronization

In the recent years, a large number of studies indicate that the relationship between chaos and engineering is more and more close. Chaos has a wide of applications in many fields, such as bioengineering, mechanical engineering, electronic engineering, chemical engineering, information engineering and computer engineering. The main purposes for investigating chaos in theory include uncovering its natures, depicting its basic characters, understanding its dynamical behaviors, controlling and utilizing it to serve people. This paper studies some related problems on chaos control and synchronization, which are important aspects in chaos researching.(1) Control a given chaotic system in order to direct it from chaos to the goal expected. Firstly, the control of chaos for ODE on the generalized approximate inertial manifold of Sine-Gordon equation is investigated. The time-delay feedback control method is applied to introduce the system from the chaos to periodic motion, and Melnikov's method is used to explain the control mechanism. Secondly, the tracking control of Lorenz chaotic system is researched. The adaptive control method is taken, and then the controlled system can track any reference signal.(2) There have been rich theoretical results about chaos complete synchronization (CS). However, many achievements are based on the certain reduced dimensionality systems, and the higher dimensional or uncertain chaotic systems are taken inadequate attention. The paper makes up for this problem. Firstly, based on the Lyapunov stability theory, both the hyperchaotic systems and the systems with unknown parameters realize CS by using the adaptive control. Secondly, the model of two intercoupling uncertain chaotic systems is studied. Based on the Lyapunov-Krasovskii stability theorem and linear matrix inequalities (LMI), a synchronization scheme is proposed by applying the robust control.(3) Due to the theoretical results of chaos generalized synchronization (GS) is very short in present, this paper studies the issue of the linear GS. If the drive system and the GS function are given, the response system can be constructed by using the adaptive control and impulsive control, respectively.The proposed numerical simulations verify the corresponding theoretical results. In addition, a number of them indicate that the chaos synchronization has a good application in the secure communication.