Analysis And Control Of Hybrid Dynamical Systems

With the quick development of science and technology,the extensive apply of information handling,computer communicating,robot controlling,and productive process automating,the systems that people meet are large scale,abundant content and complex phenomenon. A lot of man-made systems have appeared which reflect science and technology trend in the area such as communication,manufacture,traffic,military and productive process. It's not convenient to describe these systems with differential equations or difference equations. These systems are different from not only the continuous systems that are described with differential equations but also the discrete systems that are described with difference equations. The used knowledge is not applicable to these new problems. The demand to study these systems prompts the development of theory of discrete event dynamical systems (DEDS). DEDS theory reflects dynamical law of all kinds of man-made systems. With going deep study,people start knows a few important problems which discrete event interacting with continuous variable that so called hybrid system. Unlike the continuous variable dynamical system (CVDS) or discrete event dynamical system (DEDS),hybrid system contains not only continuous dynamical system subject to Newton's law of causation but also discrete event system satisfied the optimal decision logic principle,and both of them accord with the strong interaction condition.The main contents contain the analysis and control of hybrid systems. The controls of hybrid systems mainly deal with state feedback control and neural networks control and analysis of hybrid systems mainly deal with theory of Lyapunov stability on the basis of analyzing and synthesizing current control theory and method. In this dissertation,the main contributions are as follows:1. Hybrid system construction analysis. The concept,property and quality of hybrid system got deep into study from basic construction. Hybrid systems areclassified according the interacting type of discrete event and continuous variable. At last,a classic of hybrid system called parameter hybrid system is analyzed and an algorithm is proposed.2. Stability analysis of hybrid system. Two conditions of hybrid system stability are given and an algorithm that determines stable border is given based on linear matrix inequalities.3. Neural networks control of hybrid systems. Proposed a kind of method that is improved back propagation neural network. A neural network controller is designed. The tracking control of hybrid system is realized by model prediction and feedback correct of neural network control.4. State feedback control of hybrid chaotic system. From analyzing continuous chaotic system,proposed Lyapunov exponent control method of continuous chaotic system based on state feedback control. System stability is realized. The control strategy is extended hybrid chaotic system and a designing controller method of hybrid chaotic system is deduced. From Lyapunov stability theory of nonlinear system,got convergent region of system. This control method is demonstrated effective by the study of a kind of hybrid system.