The Stabiliaty Analysis And Optimal Control Of Multi-model Hybrid System

Hybrid dynamic system is called hybrid system for shortens. Hybrid systems are generally understood as reactive systems that inter-mix discrete and continuous components. It contains two distinct types of systems, continuous variable dynamic system and discrete event dynamic system, which interact with each other, which is different from traditional continuous dynamic system and discrete event dynamic. Hybrid system has been widely considered in control engineering and computer science in the latest twenty years. The hybrid characters of mixing continuous and discrete variables in the hybrid system are becoming more and more pervasive in the control system. The occurrence and the research of hybrid system theory are both the demand of modern industry and the inevitable result of the development of control theory and computer technology. In order to describe the behavior of the complex dynamic system accurately, a new class system named multi-model hybrid system was introduced in this dissertation, which based on the theory of hybrid system and switched system and the development of multiple models. Furthermore, Markov hybrid system was also introduced, of which the discrete state was a Markov chain. Multi-model hybrid system can be looked as a type complex nonlinear system, the dynamic character of which is consisted of two parts: continuous variable and discrete event. The dynamic behavior of the multi-model hybrid system is depicted as flowing: the continuous dynamic of the system is a set of nonlinear dynamic equations, and with the changer of the discrete state, the continuous states would have a discontinuous jump. According to the structure of the multi-model hybrid system, the properties of the system were determined by the subsystems and the switching logic. In the dissertation, the model, stability analysis and the optimal control of this class system were studied. In the latter part of this dissertation, Markov hybrid system was introduced. With the properties of the Markov chain, some characters of this kind system, including stability, stochastic stability and optimal control, were discussed. The main contributions of the dissertation are as follows: 1. The model of the multi-model hybrid system In the model of the multi-model hybrid system, it was considered that the sate space of the subsystem is different, and the changer of the sate including continuous and discrete when the transformation of the subsystem. It was also emphasized that the continuous variable would have discontinuous jump when the discrete state changed. The state space of the multi-model hybrid system was analyzed, on which the definition of hybrid distance was given. In the multi-model hybrid system, the continuous dynamic consist of a group of continuous subsystems, which were defined on different state space. And the discrete event dynamic was depicted by a simple directed graph. The node and the arc of the graph denoted the discrete state and the discrete event of the multi-model hybrid system respectively. If a discrete event takes place, it shows that the hybrid system switches from a subsystem to anther.The state space of the multi-model hybrid system is consisting of several subsets with different dimensions. That brings much difficulty in analyzing the system. The definition of hybrid distance was defined on the state space of the multi-model hybrid system with the theory of the directed path of the graph. 2. The stability of the multi-model hybrid system According to the complicated architecture of the multi-model hybrid system and the aforementioned hybrid distance, the definition of invariant subset was given. And the stability and asymptotic stability of the invariant subset were studied, respectively. Sufficient conditions for the stability and asymptotic stability of the invariant subset were given. 3. The optimal control of the multi-model hybrid system Compared with the traditional continuous variable system, there has been a problem of model transformation in the analysis of multi-model hybrid system optimal control. When the model transformation occurred, there would be some costing for the phenomenon. That was considered in the analysis of the optimal problem. With the theories of the dynamic programming and the Hamilton-Jocbi-Bellman equation, the existing problem of the optimal control was studied. The value function of the optimal was given, by which the optimum solution was constructed. The value function of the optimal was given first. And the properties of the value function were analyzed. If the value function is continuously differentiable almost everywhere, them we have the conclusion that the value function satisfy a Hamilton-Jocbi-Bellman equation. The optimum solution was constructed through the Hamilton-Jocbi-Bellman equation. However, ordinarily the value function is not continuously differentiable. And there is not a unique smooth solution for the aforementioned Hamilton-Jocbi-Bellman equation. With the theory of...