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An LQ Problem for the Heat Equation on the Halfline with Dirichlet Boundary Control and Noise

Author

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  • G. Fabbri

    (Dipartimento di Studi Economici S. Vinci - PARTHENOPE - Università degli Studi di Napoli “Parthenope” = University of Naples)

  • B. Goldys

Abstract

We study a linear quadratic problem for a system governed by the heat equation on a halfline with boundary control and Dirichlet boundary noise. We show that this problem can be reformulated as a stochastic evolution equation in a certain weighted $L^2$ space. An appropriate choice of weight allows us to prove a stronger regularity for the boundary terms appearing in the infinite dimensional state equation. The direct solution of the Riccati equation related to the associated nonstochastic problem is used to find the solution of the problem in feedback form and to write the value function of the problem.

Suggested Citation

  • G. Fabbri & B. Goldys, 2009. "An LQ Problem for the Heat Equation on the Halfline with Dirichlet Boundary Control and Noise," Post-Print hal-01615443, HAL.
    • Handle: RePEc:hal:journl:hal-01615443
    DOI: 10.1137/070711529
    as

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