On some general almost periodic optimal control problems : links with periodic problems and necessary conditions

Denis Pennequin

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On some general almost periodic Optimal Control problems: links with periodic problems and necessary conditions

Denis Pennequin (2007)

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In this paper, we are concerned with periodic, quasi-periodic (q.p.) and almost periodic (a.p.) Optimal Control problems. After defining these problems and setting them in an abstract setting by using Abstract Harmonic Analysis, we give some structure results of the set of solutions, and study the relations between periodic and a.p. problems. We prove for instance that for an autonomous concave problem, the a.p. problem has a solution if and only if all problems (periodic with fixed...

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The existence of a continuous periodic and almost periodic solutions of the nonlinear integral inclusion is established by means of the generalized Schauder fixed point theorem.