Study On Control And Parameter Identification Of Chaos Systems

Chaos is a very complex motion with definite stochastic rules and a final bound in nature. In recent years, chaos is widely applied to biology, psychology, mathematics, physics, electronics, information science, astronomy, aerography, economics, and even to music and art. The control and synchronization of chaos become a hot issue of study in nonlinear science. However, the theories of control and synchronization for chaos systems are not perfect enough. The methods for the control and synchronization of chaos systems need to be ulteriorly investigated, so do the designs of simple and effective controllers. Moreover, when the existing methods of control and synchronization are applied in real chaos systems, many problems remain solving. For example, sometimes the parameters of real chaos systems are partially or fully unknown and disturbed. In this thesis, some problems in control and parameter identification of chaos systems are studied thoroughly. The main work and research results are as follows:According to the intrinsic parameter structure of Lorenz system family, by using optimal Lyapunov function, it is strictly proved that the simplest linear feedback control can realize the globally exponentially stable and asymptotically stable of the equilibrium point. It improves and extends the results in existing literature that is merely locally stable. Moreover, the conditions adopted in our theorems are more succinct, less conservative than those of previous results, and more general conclusions are obtained.According to the stability theory of differential equation and the structure of a class of chaos systems, simple sufficient conditions are obtained for PC synchronization and single state-based synchronization. When there are disturbances from parameters and environment, the design of synchronization controllers are discussed and the robust synchronization of a class of chaos systems is realized under two cases whether the parameters of driving system are known or unknown. Moreover, the synchronization of two different chaos systems with the same dimensions in the class is studied and the adaptive law of parameters and controllers are designed.The synchronization of chaos systems based on partial states is studied. According to the stability theory of differential equation and the structure of Liu chaos system, generalized Lorenz chaos system and a novel hyperchaos system, the synchronization of two identical Liu chaos systems, generalized Lorenz systems and novel hyperchaos systems are realized using single state or partial states.Parameter identification of chaos system based on unknown parameter observer is discussed. According to observer idea and stability theory of differential equation, taking unknown parameters of chaotic system as state variables, general methods to choose an appropriate gain function and construct corresponding auxiliary function are proposed based on the work of Guan Xinping et al. The design of unknown parameter observer for any unknown parameter of chaos is achieved and five correlative corollaries are obtained. The application field of unknown parameter observer is extended.According to the idea of adaptive synchronization-based parameter identification, Lyapunov stability theory and LaSalle invariable principle, the synchronization-based parameter observer is proposed and general methods for design of controller and parameter adaptive laws are given. When the model is known, the unknown parameters of chaos system are identified by means of synchronization-based parameter observer. When the model is unknown, the unknown model structure and parameters are identified. The corresponding simulations are given.Parameter identification of continuous chaos system based on extremum point is discussed. When the system model is known, a new parameter estimation approach of continuous chaos system is proposed according to the characteristic that state variables of continuous chaos system present many extremum points, and the values and positions of these extremum points are stochastic, and the derivative of a variable at extremum equals zero. By means of this new method, unknown parameters of Lorenz system and hyperchaotic Chen system are estimated. Finally, anti-disturbance performance of this new method is tested.Finally, a summary is given and some problems are pointed out for further research.