Some results on the controllability of forward stochastic heat equations with control on the drift

By Qi Lu. 2011

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Abstract In this paper, we establish the null/approximate controllability for forward stochastic heat equations with control on the drift. The null controllability is obtained by a time iteration method and an observability estimate on partial sums of eigenfunctions for elliptic operators. As a consequence of the null controllability, we obtain the observability estimate for backward stochastic heat equations, which leads to a unique continuation property for backward stochastic heat equations, and hence the desired approximate controllability for forward stochastic heat equations. It deserves to point out that one needs to introduce a little stronger assumption on the controller for the approximate controllability of forward stochastic heat equations than that for the null controllability. This is a new phenomenon arising in the study of the controllability problem for stochastic heat equations.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Finance

View Paper: https://www.semanticscholar.org/paper/f5672648901dcf90935c831cba4e2851d5902b90