Discrete control problems with phase constraints

Abstract

METHODS of solving discrete control problems with phase constraints are considered. “Direct” optimality conditions are presented in terms of feasible directions. Different variants of the maximum principle are obtained for the class of problems considered. By means of dual methods a connection is established between the “direct” and “dual” optimality conditions, in which Lagrange multipliers are used for the constraints on the variables. A bilateral estimate of the optimal control is obtained. A scheme of the method of feasible directions for the problems considered is given, which is based on the optimality conditions obtained. The majority of the applied problems of discrete optimal control in economics, operational research etc. have constraints on the phase coordinates. Despite the fact that some optimality conditions for such problems are known [1–3], there are essentially no methods for solving them. In the present paper methods of solving discrete optimal control problems with phase constraints are considered. The principal emphasis is on direct methods and the establishment of a connection with mathematical programming methods.