Backstepping Output Feedback Control for a Class of Coupled Reaction-Advection-Diffusion Systems with the Same Diffusion

This paper aims to design a backstepping observer-based output feedback controller for a class of coupled reaction-advection-diffusion processes with the same diffusion. The considered system is endowed with a sensor at the left boundary and an actuator at the right boundary. Firstly, a backstepping observer is designed for the considered system, where the existence of the solution of the kernel function for the backstepping transformation is proven. Secondly, a backstepping state feedback controller is designed. Thirdly, using the separation principle, an observer-based output feedback controller is proposed based on the designed observer and controller. Moreover, the numerical methods to calculate the design gains and kernel functions are provided.