Width-modulated Sampled-data System Of Hds Boundedness Analysis And Hds Optimal Control Problem

Hybrid Dynamical Systems (HDS), also named Hybrid Systems, is constituted by Continuous Variable Dynamical Systems (CVDS) and Discrete Event Dynamical Systems (DEDS).Because most systems are not pure continuous and computers are used widely in practice, the running models of all control systems have changed. So the models similar to HDS is common in the world .In addition, because the number of the cosmically and complex systems become more and more, the control request is more and more strict. But the methods transforming the systems to pure continuous or pure discrete systems for modeling, analyzing and designing cannot be satisfied. Then it is necessary to study HDS.This paper is mainly studying the system modeling, boundedness and optimal control problems of Hybrid Dynamical Systems. The following is included:Chapter 1 is the introduction of Hybrid Dynamical Systems. First, it tells the research background and reaearch progress of Hybrid Dynamical Systems.Then the paper introduces the application and research content of Hybrid Dynamical Systems. At last, we present the problems that need to be solved.Chapter 2 is the defination characteristics and model of Hybrid Dynamical Systems.Chapter 3 is the model describe and stability analysis of Hybrid Dynamical Systems. There are many kinds of models about the model of Hybrid Dynamical Systems.Generally, people use ordinary differential equations (ODEs) to describe the continous characteristics of the system and describe the discrete characteristics with discrete events model. In this paper, we will use 5-tuple HDS model and its related defination of invariability and stability that were putted out by American scholar A.N.Michel in his article. For a concrete kind of pulse width modulation system, we model and describe it in HDS, that is 5-tuple HDS model. As researchers have studied intensively the Lyapunov stability, But under someconditions, if only considering the system state boundedness, obviously it can be satisfied by weak restrictive conditions, so the research of Lagrange stability is reasonable. In a sense, it is valuable to study Lagrange stability. In this paper, we will discuss Lagrange stability-that is boundedness and put forward and prove corresponding sufficient conditions.Chapter 4 is the optimal control problem of Hybrid Dynamical Systems.The optimal control problems of Hybrid Dynamical Systems under free terminal state are studied. According to the existing local minimum principles under free terminal state of Hybrid Dynamical Systems, we can prove that if all local are iterated, then during whole movement time, for Hybrid Dynamical Systems, minimum principles will be satisfied.Two aspects are mainly included in this paper:First, Pulse-Width Modulated Control Systems with a sampler (PWM system) are modeled and analyzed by HDS methods. The Lyapunov stability, that is boundedness, is discussed and sufficient conditions are putted forward.Second, we study the optimal control problems of HDS under terminal free state. Researchers have studied intensively the local optimal control problems of HDS, we will extend it to whole movement time of HDS using iteration methods of local optimal control.