Optimal control of nonlinear stochastic differential equations on Hilbert spaces

2019/12/13 by Barbu, Viorel, Röckner, Michael, Zhang, Deng · 1 citation
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1912.06541

Abstract

We here consider optimal control problems governed by nonlinear stochastic equations on a Hilbert space H with nonconvex payoff, which is rewritten as a deterministic optimal control problem governed by a Kolmogorov equation in H. We prove the existence and first-order necessary condition of closed loop optimal controls for the above control problem. The strategy is based on solving a deterministic bilinear optimal control problem for the corresponding Kolmogorov equation on the space L²(H,ν), where ν is the related infinitesimally invariant measure for the Kolmogorov operator.

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• Optimality Conditions for Control Systems Governed by Monotone Stochastic Evolution Equations

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