On the Lyapunov-based second-order SMC design for some classes of distributed parameter systems

This paper addresses the Lyapunov-based design of second-order sliding mode controllers in the domain of distributed parameter systems (DPSs). To the best of our knowledge, the recent authors’ publications (Orlov et al., 2010, Continuous state-feedback tracking of an uncertain heat diffusion process. Syst. Control Lett., 59, 754–759; Orlov et al., 2011, Exponential stabilization of the uncertain wave equation via distributed dynamic input extension. IEEE Trans. Autom. Control, 56, 212–217; Pisano et al., 2011, Tracking control of the uncertain heat and wave equation via power-fractional and sliding-mode techniques. SIAM J. Control Optim., 49, 363–382) represent the seminal applications of second-order sliding mode control techniques to DPSs. A Lyapunov-based framework of analysis was found to be appropriate in the above publications. While reviewing the main existing results in this new field of investigation, the paper provides the novelty as well and gives several hints and perspectives for the generalization, listing some open problems.