Output feedback control for non-linear stochastic reaction–diffusion system via modal decomposition techniques

Abstract This paper proposes a novel feedback control design for a one-dimensional non-linear stochastic reaction–diffusion system subject to non-local measurement. The system is first divided into finite-dimensional and infinite-dimensional parts by the modal decomposition techniques. A finite-dimensional Luenberger-type observer is proposed to estimate the state of the system, based on which an observer-based feedback control strategy is developed to stabilize the system despite the presence of stochastic noise with any potentially large bound. The closed-loop system is shown to be well-posed. The mean-square exponential stability of the closed-loop system is demonstrated by the Lyapunov approach together with Itô’s formula under certain conditions. Finally, some numerical examples are presented to illustrate the effectiveness of the proposed control design.