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An Optimal Control Problem for Stochastic Linear PDE’s Driven by a Gaussian White Noise

In: Numerical Mathematics and Advanced Applications

Author

Listed:
  • H. Manouzi

    (Laval University, Department of Mathematics and Statistic)

  • S. Hou

    (Iowa State University, Department of Mathematics)

Abstract

A computationally efficient technique for the numerical solution of constrained optimal control problems governed by linear stochastic partial differential equations (SPDEs) is considered in this paper. Using the Wiener-Itô chaos expansion of the solution and the control, the stochastic problem is reformulated to a set of deterministic equations. To obtain these chaos coefficients, we use the usual Galerkin finite element method using standard techniques. Once this representation is computed, the statistics of the numerical solution can be easily evaluated. To illustrate our ideas we consider an optimal control problem of a linear elliptic equation with a quadratic cost functional and a distributed stochastic control which lies in the Hida distribution spaces.

Suggested Citation

  • H. Manouzi & S. Hou, 2008. "An Optimal Control Problem for Stochastic Linear PDE’s Driven by a Gaussian White Noise," Springer Books, in: Karl Kunisch & Günther Of & Olaf Steinbach (ed.), Numerical Mathematics and Advanced Applications, pages 629-636, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69777-0_75
    DOI: 10.1007/978-3-540-69777-0_75
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