MEAN-FIELD LIMIT FOR A CLASS OF STOCHASTIC ERGODIC CONTROL PROBLEMS

Albeverio Sergio,De Vecchi Francesco C.,Romano Andrea,Ugolini Stefania

SIAM JOURNAL ON CONTROL AND OPTIMIZATION（2022）

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摘要

We establish existence and uniqueness of an optimal control for a family of McKeanVlasov (mean-field) type ergodic optimal control problems with linear control and quadratic dependence on control of the cost function. We propose an N-particle Markovian optimal control problem approximating the McKean-Vlasov one and prove the convergence in relative entropy and total variation of the law of the former to the law of the latter when N goes to infinity.

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关键词

&nbsp, mean-field control, ergodic optimal control, McKean-Vlasov limit, de Finetti's theorem, strong Kac's chaos, convergence of probability measures on path space

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