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.
Classification : 43A60, 49K27, 49J27
Mots clés : almost periodic optimal control, periodic optimal control, Pontryagin theorem, almost periodicity on groups
@article{COCV_2008__14_3_590_0,
author = {Pennequin, Denis},
title = {On some general almost periodic optimal control problems : links with periodic problems and necessary conditions},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {590--603},
publisher = {EDP-Sciences},
volume = {14},
number = {3},
year = {2008},
doi = {10.1051/cocv:2007065},
zbl = {1142.49012},
mrnumber = {2434068},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv:2007065/}
}
TY - JOUR AU - Pennequin, Denis TI - On some general almost periodic optimal control problems : links with periodic problems and necessary conditions JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2008 DA - 2008/// SP - 590 EP - 603 VL - 14 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2007065/ UR - https://zbmath.org/?q=an%3A1142.49012 UR - https://www.ams.org/mathscinet-getitem?mr=2434068 UR - https://doi.org/10.1051/cocv:2007065 DO - 10.1051/cocv:2007065 LA - en ID - COCV_2008__14_3_590_0 ER -
Pennequin, Denis. On some general almost periodic optimal control problems : links with periodic problems and necessary conditions. ESAIM: Control, Optimisation and Calculus of Variations, Tome 14 (2008) no. 3, pp. 590-603. doi : 10.1051/cocv:2007065. http://www.numdam.org/articles/10.1051/cocv:2007065/
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