Research On Control And Synchronization Of Chaos And Their Applications In Secure Communication

In1970s, chaology emerged formally as a novel discipline. For over30years, chaotic science and other sciences have perneated into each other widely. In addition, chaology has been applied to the field of biology, physiology, meteorology, economics, psychology and physics, etc. The control and synchronization of chaotic systems and their applications becomes the hot topic of the research on chaotic theory. This paper focuses on the study of three aspects as follows:(1) The control problem of hyperchaotic systems is investigated. Combining feedback control idea, a new adaptive control method is proposed to suppress a class of hyperchaotic systems with unknown parameters. Based on the second Lyapunov stability method, the asymptotic stability of the zero equilibrium is guaranteed.(2) The fuzzy control problem of a class of hyperchaotic systems is considered. The T-S fuzzy models of the hyperchaotic systems are constructed, and then a fuzzy state feedback controller is designed based on parallel distributed compensation (PDC) method and Exact Linearization (EL) idea. The asymptotic stability of the zero equilibrium of the closed-loop system is proved via linear system theory.(3) The identical synchronization problem of a class of chaotic systems is investigated. The nonlinear state feedback method and the PC approach are employed to synchronize two classes of novel chaotic systems.(4) The generalized synchronization of hyperchaotic systems is studied. Based on the constructed T-S fuzzy models of two classes of hyperchaotc systems, The fuzzy synchronization error system is derived. Based on T-S fuzzy control theory and Exact Linearization (EL) idea, a fuzzy synchronization controller is designed via PDC technique. Then the asymptotic stability of the fuzzy synchronization error system is guaranteed. Consequently, the generalized synchronization of two nonidentical hyperchaotic systems is realized. (5) The applications of chaotic synchronization in secure communication is developed. The secret signals are modulated into the global model of the transmitter. Based on the T-S fuzzy control theory and exact linearization method, an observer-type receiver is designed. By choosing appropriate controller gains, the synchronization error system can be stabilized asymptotically. And then the secret signals can be recovered sucessfully. Simulation results demonstrate the effectiveness of the developed secure communication scheme.