Maximum principle and second-order conditions for minimax problems of optimal control

In this paper, we study the optimal control problem of minimizing the functional J(x, u)=maxt1≤t≤t2φ{symbol}(x(t), t). We formulate and prove necessary optimality conditions for this problem. We establish the equivalence between the initial minimax problem and a problem involving a terminal functional and phase constraints. © 1992 Plenum Publishing Corporation.