A Class Of Switched Linear Systems Optimal Control Strategy

A switched system is a class of hybrid composed of several dynamical subsystems and a switching law that specifies the active subsystem at each instant of time. Switched systems arise in many engineering applications. It is of great practical value and theoretical significance to investigate switched systems. This thesis concerns with some issues related to the optimal control of switched systems, such as the discrete-time switched systems, switched systems with step perturbation, discrete switched systems with time-delay, infinite time switched systems with time-delay. The main contributions are summarized as follows:(1) The quadratic optimal control for a class of discrete linear switched systems with the switched time and switched number fixed is studied in this paper, by means of discrete dynamic programming principle, we disintegrate a multistage decision processes into a series of single decision process which is easy to find solutions, and give the optimal control sequence and the optimal switched sequence.(2) The quadratic optimal control for a class of switching systems with step perturbation is investigated, while the switching sequence and switching frequency is fixed. Based on dynamic programming principle, using multilevel decision, we calculated the optimal switching time and optimal control input. In addition, by making use of the improved genetic algorithm, the optimal searching is accomplished..(3) By transforming the discrete switched systems with time-delay into non-time-delay switched systems, the optimal control of discrete switched systems with time-delay is proposed. The corresponding augmented equation is established, and by the methods of optimal control, the control rule is investigated. Using dynamic programming principle, the method of optimal control is presented.(4) The quadratic optimal control for a class of infinite time switched systems with time-delay is studied. Based on HJB inequalities, the optimal control of infinite time switched systems with time-delay is converted into the problem of seeking upper and lower bounds of the cost function.