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Well posedness of optimal control problems. (English) Zbl 0810.49010
A notion of well posedness for optimal control problems requires existence and uniqueness of the optimal control, and strong convergence of every asymptotically minimizing sequence of control laws. Some abstract results given by the same author in a previous paper related with the differentiability properties of the value function are used. Well posedness criteria for optimal control problems monitored by ordinary differential equations with unconstrained terminal point are obtained. The well posedness criteria, given in the paper, are compared with some known results. Some examples are given.

49J35 Existence of solutions for minimax problems
49J15 Existence theories for optimal control problems involving ordinary differential equations