The Dynamical Behavior Analysis And Control Of Some Classes Of Nonlinear Dynamical Systems

It is well known that there are a lot of nonlinear issues in many application fields such as project, economy and so on. All of them can be described by the nonlinear dynamical systems. Under a certain parametric condition, the dynamical system will be in the chaotic state, which will generate some unpredictable influence to the system, so it is very necessary and significative to study the nonlinear system's dynamical behavior under a certain parametric condition. By the chaos characteristic and the analysis methods of the chaos theory, the nonlinear system's dynamics behavior can be figured out thoroughly. Because of the sensitivity to the initial value and the unpredictability in a long time, chaos control plays a very important part in the chaos application, has a very high value in research and application. It is need to find ways to restrain chaos if it is harmful and to use it if it is not. In addition, the random disturbance like noise is ubiquitous in the real life. Therefore, the studies on the nonlinear dynamical systems'dynamical behavior and chaos control with the existence of noise is very necessary.In this dissertation, the chaos control of generalized augmentation Lüsystem and Lüsystem is studied and the dynamical behavior and control of the ship power system is also investigated. The main contents of this dissertation are as follows:In chapter one, the history, development process and current research situation of chaos is introduced.In chapter two, chaos control of generalized augmentation Lüsystem is studied. Based on the Lyapunov stability theory, the proportion differential controller and the self-feedback controller is designed separately to control the chaotic system to its 5 balance points. The effectivity of the controllers is confirmed by the numerical simulation. In chapter three, a controller which bases on the state feedback exact linearization method is designed to control the Lüchaotic system. The effectivity of the controller is confirmed by numerical simulation.In chapter four, firstly, a ship electrical power system's dynamical behavior is studied by the numerical method and the marginal value of the system's perturbation parameter is gave out. Secondly, a parameter auto-adaptive controller is designed to control the chaotic system to the expected point and the effectivity of the controller is confirmed by the numerical simulation.In chapter five, firstly, the ship electrical power system's dynamical behavior under the stochastic-parameter-excitation and the stochastic-outside-excitation is studied based on the stochastic Melnikov method. The relationship between the system'perturbation -parameter and the stochastic-excitation-intensity is deduced; The numerical simulation and the theoretical analysis get the consistent conclusion under the two cases that the possibility of the system's generating chaos is increased and the marginal value of the perturbation-parameter at which the system will generate chaos is decreased, in other words, the range of the system's chaos-parameter is expanded; The conclusion under the two kinds of stochastic excitation is compared, it is concluded that the system is easier to be chaotic in the case of stochastic-parameter-excitation than in the case of stochastic-ou- tside-excitation; Based on the condition which is given out in this chapter, the marginal value of the no-stochastic-excitation-system's perturbation-parameter is concluded and improved. Secondly, the case that the stochastic excitation is contained in the system's harmonic excitation is studied. It is concluded that the system's chaos could be restrained when the stochastic-excitation-intensity changed in a proper range.In chapter six, the whole work of this paper is concluded and the further study direction is also pointed out.