Duality for differential games and optimal control
A class of linear differential games is shown to be equivalent to some optimalcontrol problems; the body of available concepts and results for the latter, involving time-optimality, uniqueness of optimal controls, feedback controls, can thus be brought to bear on the former. In this paper, the emphasis is on the reduction rather than on the consequences. In particular, we can include rather general forms of exterior state constraints, even though the interesting results now known treat control systems constrained to coset spaces [1], [5]. The trend of this paper is the exact opposite of Isaacs' natural interpretation of differential games as extension of the optimal control problem. A further implication is that the games treated are valueless, in that problems of value (existence and its value) do not intrude themselves.