In this paper, we study the optimal control problem of minimizing the functionalJ(x, u)=maxt1⩽t⩽t2ϕ(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.
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Communicated by N. V. Banichuk
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Arutyunov, A.V., Silin, D.B. & Zerkalov, L.G. Maximum principle and second-order conditions for minimax problems of optimal control. J Optim Theory Appl 75, 521–533 (1992). https://doi.org/10.1007/BF00940490
- Maximum principle
- optimal control
- controllability conditions