Output regulation for the reaction‐diffusion equation with time‐varying disturbances and non‐collocated observation

Abstract

The present article focuses on the output regulation problem for uncertain 1‐d reaction‐diffusion equation(RDE), in which the disturbance inputs are located at both the interior of the equation and uncontrolled end. Both the reference signal and the disturbances signal are specified due to an exosystem of time‐varying coefficients. The difficulty of the problem is that the control end is noncollocated with the regulated output. The so‐called feedforward control is designed by introducing an regulator, which is determined by infinite‐dimensional equation. A state observer is proposed based on the measurement output to recover the original and the external systems. The suitable feedback control has to be integrated by replacing the states in the expression of feedforward control law. As a result, exponential convergence of the error between the reference signal and the output, and the closed‐loop stability are established. Numerical results are performed the effectiveness of the results.