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

ESAIM: Control, Optimisation and Calculus of Variations (2007)

- Volume: 14, Issue: 3, page 590-603
- ISSN: 1292-8119

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topPennequin, Denis. "On some general almost periodic Optimal Control problems: links with periodic problems and necessary conditions." ESAIM: Control, Optimisation and Calculus of Variations 14.3 (2007): 590-603. <http://eudml.org/doc/90885>.

@article{Pennequin2007,

abstract = {
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.
},

author = {Pennequin, Denis},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Almost Periodic Optimal Control; Periodic Optimal Control; Pontryagin theorem; Almost periodicity on groups; almost periodic optimal control; periodic optimal control; almost periodicity on groups},

language = {eng},

month = {12},

number = {3},

pages = {590-603},

publisher = {EDP Sciences},

title = {On some general almost periodic Optimal Control problems: links with periodic problems and necessary conditions},

url = {http://eudml.org/doc/90885},

volume = {14},

year = {2007},

}

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

DA - 2007/12//

PB - EDP Sciences

VL - 14

IS - 3

SP - 590

EP - 603

AB -
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.

LA - eng

KW - Almost Periodic Optimal Control; Periodic Optimal Control; Pontryagin theorem; Almost periodicity on groups; almost periodic optimal control; periodic optimal control; almost periodicity on groups

UR - http://eudml.org/doc/90885

ER -

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