Nonlinear Observer-based Theory Of Chaotic Systems, Control And Synchronization Of Research

The control and synchronization of chaotic systems have been the research hotspots of nonlinear science for recent years. The subject of control and synchronization of chaotic systems has received a large amount of attentions due to its particularity s complexity and outlook for applications. In this thesis, based on the observer theory, we study the control and synchronization of chaotic systems in which the state variables cannot be all measured. The work of the thesis is presented as follows:1. nonlinear observer and the design of a class of chaotic systemsAn observer, driven by the inputs and outputs of the observered system is a physically realizable dynamic system. It can produce a group of outputs with which approximate the state ouputs of the observed system properly. If a nonlinear system satisfys the obsevervation condition, the observer of the nonlinear system can be designed. Observer research of linear system has developed more maturely than that of nonlinear system. Due to the complexity of the nonlinear system itself, the nonlinear observer design is more complex and challenged.Observer design for a class of nonlinear systems which satisfy certain conditions is considered, and the convergent condition of the observation error is developed.Based on the eigenstructure assignment theory and optimization theory, a convenient and practicable method is presented to demonstrate the results.2. The control for a class of chaotic systems using observer theoryUnder certain assumptions, input-state linearization method in nonlinear control theory can convert a nonlinear system into a linear system via change of state, then it realize the control goal of chaotic systems by using control methods in linear system theory. The key to realizing thecontrol of chaotic systems is that all the states can be measured as feedback state variables. But in fact, not all of the states of nonlinear systems can be measured.By combining the input-state linearization method and observation of the states in chaotic systems, the control goal of a class of chaotic systems in which state variables cannot be all measured is realized. The design procedure is as follows:a. The control law of a class of chaotic systems is designed by using input-state linearization method. Generally, the control law includes all the states of the system.b. As the states of the chaotic system cannot be all measured , we design the observer of the system and attain the state estimation of the system.c. The estimation states take place of the states in the control input u as state feedback, then we attain the observed-based control law.The simulation results of the Rossler system illustrate the validity of this method3. The control for a class of chaotic systems using parameter identificationMost methods of control chaos are givn on the condition that the states of the chaotic system with known parameters can be all measured. The case that the states of the system with unknown parameters cannot be all measured is seldom involved , even if involved , it will usually require large energies and complex methods.A parameter identification method is presented by identifying the unknown parameters of the Rossler system. The main idea is as follows: First we take unknown parameters of chaotic systems as unknown states, then the parameter identification problem can be converted to the identification of states of the system. Second , wedesign the parameter identification law via the states observed. With the parameters identified,-u-the control law is designed for a class of chaotic systems. Generally, the control law u contains all the states and some parameters of the system. Finally, we design the observer of the chaotic system by using our observer design method in order to achieve the state estimation of the system. The parameter in the control law u is replaced by the identification parmeter, and the unknown state in the control law u is replaced by the estimation state of the system, then we...