Optimal Control For A Class Of Linear Switched Systems

A switched system is a very important special type of hybrid, which is composed of several continuous or discrete dynamic subsystems and a switching law that specified the active subsystems at each instant of time. Switching control has been applied in many systems and the study of switched systems is significant both in application and theory. The optimal control for switched systems is also significant. This paper is focused on a class of linear switched systems with uncertainty or disturbance. The main contents are following:(1) The quadratic optimal control for a class of linear uncertain switched systems with the switched sequence and switched number fixed is studied in this paper. By means of discrete dynamic programming principle, the optimal control sequence and the optimal switched sequence are given.(2) Practical engineering systems, due to environmental factors, are often subject to various disturbances, this paper further discusses the quadratic optimal control of the linear system with disturbance that satisfies certain conditions. In addition, we get the optimal control input.(3) The quadratic optimal control problem of a class of switched system with disturbance with the subsystems activate order and switched number fixed is studied. With the use of dynamic programming method and two stage optimization, we obtain the optimal switched moment and optimal control input. At last, with the use of the improved genetic algorithm, the optimal searching is accomplished.At the end of the paper, a conclusion of the whole article is given, and the future research is pointed out.