2020-08-15T10:57:07Zhttp://tse.rima1.fr/academ-xoai/oai2/puboai:tse-fr.eu:313202019-07-24T08:26:51Zut1tse:publicationtse:group:mad
On Representation Formulas for Long Run Averaging Optimal Control Problem
text
info:eu-repo/semantics/article
refereedJournalArticle
Buckdahn
R.
aut
Author
Auteur
Quincampoix
Marc
aut
Author
Auteur
Renault
Jérôme
aut
Author
Auteur
2015-12
eng
English
anglais
application/pdf
born digital
Journal of Differential Equations
text
refereedJournal
http://tse-fr.eu/pub/30534
0022-0396
259
5554
5581
10.1016/j.jde.2015.06.039
http://tse-fr.eu/pub/31320
We investigate an optimal control problem with an averaging cost. The asymptotic behaviour of the values is a classical problem in ergodic control. To study the long run averaging we consider both Cesàro and Abel means. A main result of the paper says that there is at most one possible accumulation point – in the uniform convergence topology – of the values, when the time horizon of the Cesàro means converges to infinity or the discount factor of the Abel means converges to zero. This unique accumulation point is explicitly described by representation formulas involving probability measures on the state and control spaces. As a byproduct we obtain the existence of a limit value whenever the Cesàro or Abel values are equicontinuous. Our approach allows to generalise several results in ergodic control, and in particular it allows to cope with cases where the limit value is not constant with respect to the initial condition.
http://tse-fr.eu/pub/31320
http://www.sciencedirect.com/science/article/pii/S0022039615003514
https://www.tse-fr.eu/sites/default/files/TSE/documents/doc/by/renault/representation_formula.pdf
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Toulouse School of Economics
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eng
English
anglais