A Class Of Hybrid System Optimal Control And Stability Analysis

Hybrid system is a unified dynamic system which includes discrete event dynamic systems and continuous variable dynamic system, they interaction between the dynamic system. System includes changes in continuous time and discrete event-driven, it is mainly product of combination of computer science and control theory. Switched system is a hybrid system consists of a series of continuous or discrete sub-system and the harmonization of rules among these subsystems consisting of switching. Results of its research and engineering application closely related to the switched system has been used in many practical engineering, and attracted wide attention of scholars home and abroad. Although it has been made a lot of results, but it still has the complexity of the research, it needs further improvement and development.Based on previous research of hybrid systems, we analyze and study the optimal control and stability of hybrid systems both in-depth, specific content and major innovations summarized as the following sections:(1) In this article, we first analyze the sources and background of hybrid systems on automatic control and introducts the basic structure, characteristics and classification of hybrid systems, and we analyzed the contents of the current research and future trends of hybrid system.(2) This article describes the concept, classification, characteristics and status of switched systems, we analyze two types of switched system models and give a class of switched systems which are often used in real life, we analyze this switched system and study of its switching logic.(3) We study a class of continuous switched systems and use maximum principle to analyze the optimal control of it. First, we give some necessary conditions, which make the switched system to achieve the minimum objective function, and use the necessary conditions for the maximum principle to improve the algorithm, it does not need to calculate the partial derivatives of the objective function directly, so it avoids a lot of mathematical calculations. At last, the continuous optimal control of switched systems is calculated.(4) First, we give a theorem, which make the discrete switched system to achieve the minimum objective function, respectively, we use the discrete maximum principle and dynamic programming methods to prove this theory is correct, and draw recurrence formula of optimal control, in this article, because the switching frequency of the switched system is limited, so we can use discrete dynamic programming method, which caculated from the last one of the system to move front, the advantages of this method is that we set an arbitrary initial state of any time, the resulting optimal control sequence unchanged.(5) we analyze the stability of a class of continuous switched systems. Avoiding the complex structure of the Lyapunov function, we use the monotonicity of the state variables square functions to determine the stability of the continuous switched system, and it reduces the complex mathematical calculations.