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On Representation Formulas for Long Run Averaging Optimal Control Problem

Buckdahn, R., Quincampoix, Marc and Renault, Jérôme (2015) On Representation Formulas for Long Run Averaging Optimal Control Problem. Journal of Differential Equations, 259. pp. 5554-5581.

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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.

Item Type: Article
Language: English
Date: December 2015
Refereed: Yes
Divisions: TSE-R (Toulouse)
Site: UT1
Date Deposited: 12 Jan 2017 10:12
Last Modified: 25 Jul 2019 11:51
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