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Annals of the International Society of Dynamic Games vol 12 : Advances in Dynamic Games, P.Cardaliaguet and R.Cressman (Ed.) (2013) 199-215

A uniform Tauberian theorem in optimal control

Miquel Oliu-Barton 1, Guillaume Vigeral 2

(2013)

In an optimal control framework, we consider the value $V_T(x)$ of the problem starting from state $x$ with finite horizon $T$, as well as the value $W_\lambda(x)$ of the $\lambda$-discounted problem starting from $x$. We prove that uniform convergence (on the set of states) of the values $V_T(\cdot)$ as $T$ tends to infinity is equivalent to uniform convergence of the values $W_\lambda(\cdot)$ as $\lambda$ tends to 0, and that the limits are identical. An example is also provided to show that the result does not hold for pointwise convergence. This work is an extension, using similar techniques, of a related result by Lehrer and Sorin in a discrete-time framework.

1 :	Equipe combinatoire et optimisation (C&O)
	Université Pierre et Marie Curie (UPMC) - Paris VI – CNRS : FRE3232
2 :	CEntre de REcherches en MAthématiques de la DEcision (CEREMADE)
	CNRS : UMR7534 – Université Paris IX - Paris Dauphine

Domaine

:

Mathématiques/Optimisation et contrôle

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Contributeur : Guillaume Vigeral <>

Soumis le : Vendredi 20 Janvier 2012, 17:20:24

Dernière modification le : Mercredi 23 Janvier 2013, 15:44:18