Differential games reducible to optimal control problems

The author studies a linear differential game over a finite horizon and a functional to be minimized by player I and maximized by player II. The author makes assumptions under which the game reduces to a particular control problem and constructs families of ε-optimal policies for both players in the class of so-called step-guided strategies, which are very easy to implement. The author proves that the value of the game equals the value function for the control problem