hal-00661833, version 1
A uniform Tauberian theorem in optimal control
Annals of the International Society of Dynamic Games vol 12 : Advances in Dynamic Games Birkhäuser Boston (Ed.) (2013) 199-215
Abstract: 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:
- Université Pierre et Marie Curie [UPMC] - Paris VI – CNRS : FRE3232
- 2:
- CNRS : UMR7534 – Université Paris IX - Paris Dauphine
- Domain : Mathematics/Optimization and Control
- hal-00661833, version 1
- http://hal.archives-ouvertes.fr/hal-00661833
- oai:hal.archives-ouvertes.fr:hal-00661833
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- Submitted on: Friday, 20 January 2012 17:20:24
- Updated on: Wednesday, 23 January 2013 15:44:18
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