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

Denis Pennequin

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

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

Abstract

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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 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.

How to cite

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Pennequin, 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 -

References

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