Dual control theory problems

Abstract

Control in closed systems, with incomplete a priori information about the plant, should, in the general case, include two types of action on the plant: (a) tentative actions, ‘experiments’, with the controlled plant, whose problem consists in studying it; (b) directing actions, whose task consists in adjusting the plant to the required operating conditions. The controlling action in optimum control, should, generally speaking, realize both of the above-mentioned tasks simultaneously, and because of this, has a dual character. Dual control problems are considered in this paper. The problem is set up, and its general solution given, for discrete-time systems, when a change in the plant's characteristics represents a discrete Markov process. Various examples are considered.