Application of theory of games to some problems of automatic control. I

Problems connected with application of the theory of games to some problems of the automatic control are discussed. In the first part of the work the necessary and sufficient conditions of the existence of a game pure strategy solution are formulated and the solution is found. In the second part of the work main equations known in the literature are considered which determine the mixed strategy solution of the game connected with the control problems. Some examples described in the paper illustrate the theoretical propositions.