Exact Controllability for a Refined Stochastic Plate Equation

Abstract

The classical stochastic plate equation suffers from a lack of exact controllability, even with controls that are effective in both the drift and diffusion terms and on the boundary. To address this issue, a one-dimensional refined stochastic plate equation was previously proposed and established as exactly controllable in [Yu, Y. and Zhang, J. -F., Carleman estimates of refined stochastic beam equations and applications, SIAM J. Control Optim., 60, 2022, 2947–2970]. In this paper, the authors establish the exact controllability of the multidimensional refined stochastic plate equation with two interior controls and two boundary controls by a new global Carleman estimate. Furthermore, they show that at least one boundary control and the action of two interior controls are necessary for exact controllability.

Keywords

Stochastic plate equation / Exact controllability / Observability estimate / Carleman estimate

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