Sliding-mode boundary control of a class of perturbed reaction-diffusion processes

We study the stabilization problem in the space L₂(0, 1) for a class of parabolic PDEs of the reaction-diffusion type equipped with destabilizing Robin-type boundary conditions. The considered class of PDEs is also affected by a matching boundary disturbance with an a-priori known constant upperbound to its magnitude. The problem is solved by means of a suitable synergic combination between the infinite-dimensional backstepping methodology and the sliding mode control approach. A constructive Lyapunov analysis supports the presented synthesis, and simulation results validate the developed technique.