Optimal Control For Several Classes Of Switched Linear Systems

Switched system is a special class of hybrid system which is consist of severalcontinuous or discrete subsystems and a switching sequence and has been widelyapplied in actual systems. The problem of optimal control is a significant topic forswitched system. It has very essential values both in theoretical research and practicalapplication. Based on it，the paper focuses on the optimal control problem of a classof switched linear systems with unstable subsystems and a class of multiple timedelay switched linear systems. The main contents are summarized as:Firstly，the optimal control problem for a class of switched linear systems isinvestigated in the paper. Under the assume that every subsystem is unstable but canbe stabilized. First，a state feedback control law is designed to stabilize everysubsystem and make the switched system stable. Then assume that the switchingsequence is fixed and find out the optimal switching times by using dynamicprogramming method.Secondly，the optimal control problem for a class of multiple time delaysswitched linear system is investigated in the paper. By using HJB equation which is indynamic programming method，the optimal control problem is changed into theproblem of how to obtain the upper and lower bound of the cost function successfully.Thus the extreme value of the cost function is obtained.Finally， a conclusion of the paper and the future research are proposed.