The relaxed optimal control problem for Mean-Field SDEs systems and application |
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Authors: | Adel Chala |
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Affiliation: | Laboratory of Applied Mathematics, University of Mouhamed Khider, P.O. Box 145, Biskra 07000, Algeria |
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Abstract: | The present study deals with a new approach of optimal control problems where the state equation is a Mean-Field stochastic differential equation, and the set of strict (classical) controls need not be convex and the diffusion coefficient depends on the term control. Our consideration is based on only one adjoint process, and the necessary conditions as well as a sufficient condition for optimality in the form of a relaxed maximum principle are obtained, with application to Linear quadratic stochastic control problem with mean-field type. |
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Keywords: | Mean-Field stochastic differential equation Stochastic maximum principle Relaxed control Adjoint equation Variational inequality Linear quadratic controls |
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