Observer-Based PD Boundary Control for Nonlinear Reaction-Diffusion Systems with Non-Collocated Measurement

This paper mainly addresses the design problem of proportional-differential (PD) boundary controller for a class of nonlinear reaction-diffusion system. Different with the existing non-collocated controller, a PD boundary controller with non-collocated observation is proposed to stabilize the system. A Luenberger type observer is constructed to estimate the complete system state. Meanwhile, a sufficient linear matrix inequalities (LMIs) constraint condition is proposed by combining Lyapunov-based approach, integration by parts, Lipschitz condition and a variant of Wirtinger's inequality. Finally, the numerical simulation results of FitzHugn-Nagumo (FHN) model is provided to verify the effectiveness of the proposed boundary controller.