Optimal control of nonlinear stochastic differential equations on Hilbert spaces

Viorel Barbu; Michael Röckner; Deng Zhang

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arXiv · 1912.06541

Optimal control of nonlinear stochastic differential equations on Hilbert spaces

Viorel Barbu·Michael Röckner·Deng Zhang

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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 $L^2(H,\nu)$, where $\nu$ is the related infinitesimally invariant measure for the Kolmogorov operator.

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Viorel Barbu, Michael Röckner, Deng Zhang. 2019-12-13. Optimal control of nonlinear stochastic differential equations on Hilbert spaces. https://arxiv.org/abs/1912.06541

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