Study On Some Synchronization Methods Of Chaotic Systems

Chaos is a kind of special complicated nonlinear system, which is ubiquitous innature. Since it has the characteristics of sensitivity to initial values, high randomicityand certainty to nonlinear equations, chaos attracts great attentions from investigators.Chaotic synchronization is an important research aspect in chaotic science. Since1990, chaotic synchronization has achieved rapid development, its application insecure communications and image processing progress remarkably as well.Based on control theories of nonlinear systems, this dissertation studies thesynchronization control methods of continuous-time and piecewise linear chaoticsystems. The main contributions are listed as follows:(1) Three synchronization methods, including generalized synchronization,impulsive delay feedback synchronization and SDRE synchronization, are proposedfor unified chaotic system.Firstly, the generalized synchronization method of unified system is proposed. Bychoosing different control parameters, the state completed synchronization (CS) andgeneralized synchronization (GS) of unified system are achieved. This method hashigher security in secure communications. Secondly, the impulsive delay feedbacksynchronization method is presented. It makes the synchronization speed quicker atthe same intensity of impulsive signals. Finally, the SDRE synchronization method ofunified system is brought forward. The state adjustors with given stability improve thesynchronization dynamic performance.(2) Adaptive synchronization and variable structure Backstepping synchronizationmethods are proposed for Liu chaotic system with uncertain parameters.After investigating the single variable driving synchronization and state observersynchronization methods, the structure characteristics of Liu chaotic system aredeeply analyzed. Based on it, the adaptive synchronization approach is presented.Two kinds of controllers are designed for identifying unknown linear or nonlinearparameters. Then the variable structure Backstepping synchronization method is putforward, which has strong systematization, easily constructs global Lyapunovfunctions and quickly realizes unknown parameters identification andsynchronization.(3) To study the universal synchronization control method, the robust H_∞fuzzysynchronization method is proposed for generalized Lorenz systems.With the noise disturbance and uncertain parameters, the robust H_∞fuzzy synchronization method for generalized Lorenz systems keep satisfiedsynchronization performance. The synchronization strategy and control models are fitfor all continuous chaotic systems which satisfy GLCF format.(4) Backstepping synchronization and Active synchronization methods are proposedfor different structure chaotic systems: Liu-Genesio systems and hyperchaotic Liu-R(?)ssler systems.Firstly, the Backstepping method is put forward to synchronize Liu system andGenesio system, which designs the single driving and multi-driving controllers aredesigned, receives Q-S synchronization format and simplifies the structures ofcontrollers. Secondly, the active synchronization method is presented for hyperchaoticLiu system and hyperchaotic R(?)ssler system. Moreover this method establishes theunified control models for completed synchronization, generalized synchronizationand delayed synchronization.(5) Feedback synchronization method based on LMI is proposed for a new piecewiselinear chaotic system.After analyzing the structure characteristics of the new piecewise linear chaoticsystem, studying linear feedback synchronization method and investigating stateobserver synchronization method, the feedback synchronization method based onLMI is proposed. The global format of transformed piecewise chaotic systems onlyneeds seek feasible solutions by LMI. So the method provides a new thought forsynchronizing a class piecewise chaotic systems.Finally, some open issues on synchronization control of chaotic systems as wellas the future work are pointed out.