Estimator-Based H_∞ Boundary Control for Semilinear Itô-Type Stochastic Parabolic Partial Differential Systems

This paper deals with the problem of designing an estimator-based H_∞ boundary controller for semilinear parabolic Itô-type stochastic partial differential systems suffered from the intrinsic random fluctuation, external random disturbance, and stochastic measurement noise. A state estimator is first constructed for the stochastic system by using the collocated boundary observation. On the basis of Lyapunov technique, an estimator-based H_∞ boundary controller is then designed guaranteeing closed-loop mean-square exponential stability of the augmented system with an H_∞ control performance. Well-posedness and stability analysis of a mild solution for the disturbance-free closed-loop augmented system are deduced via C₀-semigroup approach. Finally, a numerical example is given to confirm the performance of the developed approach.