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Title: Stochastic Maximum Principle for Optimal Control of SPDEs

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}.
Authors:
 [1] ;  [2] ;  [3]
  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)
Publication Date:
OSTI Identifier:
22210464
Resource Type:
Journal Article
Resource Relation:
Journal Name: Applied Mathematics and Optimization; Journal Volume: 68; Journal 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)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DIFFUSION; OPTIMAL CONTROL; PARTIAL DIFFERENTIAL EQUATIONS; STOCHASTIC PROCESSES