An LQ problem for the heat equation on the halfline with Dirichlet boundary control and noise

G. Fabbri; B. Goldys

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arXiv · 0801.3888

An LQ problem for the heat equation on the halfline with Dirichlet boundary control and noise

G. Fabbri·B. Goldys

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Abstract

We study a linear quadratic problem for a system governed by the heat equation on a halfline with Dirichlet boundary control and Dirichlet boundary noise. We show that this problem can be reformulated as a stochastic evolution equation in a certain weighted L2 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 non-stochastic problem is used to find the solution of the problem in feedback form and to write the value function of the problem.

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BibTeX RIS

G. Fabbri, B. Goldys. 2009-02-03. An LQ problem for the heat equation on the halfline with Dirichlet boundary control and noise. https://arxiv.org/abs/0801.3888

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