Sliding mode control for N-coupled reaction-diffusion PDEs with boundary input disturbances

This paper develops the sliding mode control (SMC) design for N-coupled reaction-diffusion parabolic PDEs with boundary input disturbances. In order to reject the disturbances, the backstepping-based boundary SMC law is constructed to steer the system trajectory to a suitable sliding surface and then maintain sliding motion on the surface thereafter, resulting in the exponential convergence to the zero equilibrium state. The well-posedness of the closed-loop system is established based on a detailed spectral analysis and Riesz basis generation. Finally, a simulation example is provided to illustrate the effectiveness of the SMC design.