Second-order sliding-mode control of the uncertain heat and wave equations

In the present paper, preliminary results towards the generalization to the infinite-dimensional setting of some known robust finite-dimensional control algorithms are illustrated. The main focus of the present paper is on the rejection of non-vanishing external disturbances. The generalization to the infinite-dimensional setting of some known finite-dimensional controllers, namely the “Power-fractional” controller, and two “Second-order sliding-mode” control algorithms (the “Twisting” and “Super-Twisting” algorithms) is performed to address control problems involving the uncertain wave and heat equations. Constructive proofs of stability are developed via Lyapunov functional technique, which leads to simple tuning rules for the controller parameters. Simulation results are discussed to verify the effectiveness of the proposed schemes.