Hybrid Dynamic System Modeling, Stability And Optimal Control Problem Research

Modeling methods, stability, optimal control and maximum principle of hybrid dynamical systems (HDS) are studied in this dissertation. This dissertation is divided into five chapters totally.At first, we analyze and summarize the domestic and overseas status about the study of HDS and the sense of work related to the later four chapters. Chapter II summarizes the present research to HDS stability, and study the pulse-width-modulated sampling control system. Under the HDS model put forward by A. N. Michel, we introduce the pulse-width-modulated sampling control system's HDS stability that is the steady-state stability. We prove the system's steady-state stability when the sampling timelike intervals are variable.In chapter III, based on the present modeling methods of HDS we propose an improved HDS fiamework, which can simply cover the real world example of HDS. Under this HDS model, new definition of invariant sets and stability are given; additionally we introduce the HDS optimal control problems to this model. To determinative jumping systems, a special kind of HDS, the optimal control problem is studied in this chapter. In order to clearly realize the effect of jumps, under the strong assumptions we discuss the deterministic jumping systems' optimal control problems making use of variation methods, and we obtain that the optimal conditions equal to continuous dynamical systems at continuous parts; at the jumping times, costates, jumping law and jumping cost satisfy certain conditions, which is the jumps'effect. We also obtain the optimal control's necessary conditions, when the jumping times are unknown and subsystems' final slates are controlled.In the following, making use of the continuous dynamical systems' methods, maximum principle of determinate jumping systems' is proved in chapter IV. The control function of every subsystem is bounded and measurable, which belongs to bounded, convex and closed set. At first we introduce the system's variation equations, and obtain a lemma based on the property of optimal controls'. By this lemma, we prove that the maximum principle is right and the conditions costates, which are absolutely continuous, satis fy equal to the case of chapter III.At last, this dissertation discusses more general jumping systems —impulsive...