On some general almost periodic Optimal Control problems: links with periodic problems and necessary conditions
Laboratoire Marin MERSENNE, Université Paris 1 Panthéon-Sorbonne, Centre P.M.F., 90 rue de Tolbiac, 75647 Paris cedex 13, France; email@example.com
Revised: 18 January 2007
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 or variable period, q.p. or a.p.) have a constant solution. After that, we give some first order necessary conditions (weak Pontryagin) in the space of Harmonic Synthesis and we also give in this space an existence result.
Mathematics Subject Classification: 43A60 / 49K27 / 49J27
Key words: Almost Periodic Optimal Control / Periodic Optimal Control / Pontryagin theorem / Almost periodicity on groups
© EDP Sciences, SMAI, 2007