Optimal Control of General McKean-Vlasov Stochastic Evolution Equations on Hilbert Spaces and Necessary Conditions of Optimality
Journal Title: Discussiones Mathematicae Differential Inclusions Control and Optimization - Year 2015, Vol 35, Issue 2
Abstract
In this paper we consider controlled McKean-Vlasov stochastic evolution equations on Hilbert spaces. We prove existence and uniqueness of solutions and regularity properties thereof. We use relaxed controls, adapted to a current of sub-sigma algebras generated by observable processes, and taking values from a Polish space. We introduce an appropriate topology based on weak star convergence. We prove continuous dependence of solutions on controls with respect to appropriate topologies. Theses results are then used to prove existence of optimal controls for Bolza problems. Then we develop the necessary conditions of optimality based on semi-martingale representation theory on Hilbert spaces. Next we show that the adjoint processes arising from the necessary conditions optimality can be constructed from the solution of certain BSDE.
Authors and Affiliations
NasirUddin Ahmed
Keywords
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- DOI 10.7151/dmdico.1171
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