Finite-dimensional observer-based boundary control for a one-dimensional stochastic heat equation

Abstract

In this article, we investigate the finite-dimensional observer-based boundary control for a one-dimensional stochastic heat equation with nonlinear multiplicative noise and non-local sensing measurement. We adopt the modal decomposition to divide the system into two subsystems: one unstable with finite positive eigenvalues and the other essentially stable. We design the controller for the unstable subsystem by dynamic extension and demonstrate that the proposed controller actually leads to the resulting closed-loop system to be well-posed and exponentially stable, both in the mean square and almost sure senses. Finally, some numerical simulations are performed to illustrate the effectiveness of the proposed method.