GUARANTEED RESULT IN A DIFFERENTIAL GAME WITH A TERMINAL PAYOFF FUNCTION

A method for solving game-type control problems with a terminal payoff function is proposed. It consists of applying the ideas of Fenchel-Mo reau duality [1] to the general scheme of the method of resolvent func tions [2]. The main point of the method is that the resolvent function can be expressed in terms of the conjugate of the payoff function; th en, using the involutive property of the conjugation operator for a co nvex closed function, one obtains a guaranteed estimate for the termin al value of the payoff function, expressed in terms of the initial val ue of the payoff and the integral of the resolvent function.