On the boundary control of distributed parameter systems by second-order sliding-mode technique. Recent advances and new results

The primary concern of the present paper is to give an overview of the available results and methods in the field of second-order sliding mode based boundary control synthesis for uncertain and perturbed distributed parameter systems. We particularly aim at showing how the same basic algorithm (the combined Twisting/PD algorithm) can be applied to solve different problems involving parabolic and hyperbolic-type equations. Then, we deal with a reaction-diffusion process by also providing some novelty in that a destabilizing mixed-type boundary condition, which was not considered in the previous work [14], is taken into account. The effectiveness of the developed controller is supported by simulation results.