CONDITIONS FOR THE EXISTENCE OF A SOLUTION TO A TWO-SWITCHED/HYBRID OPTIMAL CONTROL PROBLEM

摘要

This paper considers a family of two vector fields, f{sub}0(t,x,u) and f{sub}1(t,x,u). There are two controls: the switching function v(t) (taking values in the set {0,1}) and the usual control u(t). Terminal constraints on the state are imposed. The objective is to minimize an integral performance index. We do not make any assumptions about the number of switches nor about the mode sequence - they are determined by the solution of the problem. Under appropriate conditions including convexity constraints, we set forth sufficient conditions as well as necessary conditions for the existence of an optimal solution. The published examples of X. Xu and P. Antsaklis are revisited and a variation considered.