Stochastic Maximum Principle for Optimal Control of SPDEs

Journal Article · Tue Oct 15 00:00:00 EDT 2013 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-013-9203-7· OSTI ID:22210464

Fuhrman, Marco ^[1]; Hu, Ying ^[2]; Tessitore, Gianmario ^[3]

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1. Politecnico di Milano, Dipartimento di Matematica (Italy)
2. Universite Rennes 1, IRMAR (France)
3. Universita di Milano-Bicocca, Dipartimento di Matematica e Applicazioni (Italy)

We prove a version of the maximum principle, in the sense of Pontryagin, for the optimal control of a stochastic partial differential equation driven by a finite dimensional Wiener process. The equation is formulated in a semi-abstract form that allows direct applications to a large class of controlled stochastic parabolic equations. We allow for a diffusion coefficient dependent on the control parameter, and the space of control actions is general, so that in particular we need to introduce two adjoint processes. The second adjoint process takes values in a suitable space of operators on L{sup 4}.

• OSTI ID: 22210464
• Journal Information: Applied Mathematics and Optimization, Vol. 68, Issue 2; Other Information: Copyright (c) 2013 Springer Science+Business Media New York; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DIFFUSION
OPTIMAL CONTROL
PARTIAL DIFFERENTIAL EQUATIONS
STOCHASTIC PROCESSES