Robust sliding mode boundary control for uncertain reaction–diffusion systems

Abstract

This paper investigates the robust sliding mode boundary stabilization for uncertain reaction–diffusion systems (URDSs). Firstly, to drive the state trajectories to reach equilibrium within the sliding phase, a specified sliding mode surface (SMS) is constructed. Emphasis is placed on designing a suitable sliding mode boundary controller (SMBCr), which guides the state trajectories to the designed SMS in finite time. Furthermore, by employing the Lyapunov functional method and advanced inequality techniques, a sufficient criterion is established to ensure robust asymptotic stability. Secondly, the observer-based robust sliding mode boundary stabilization is addressed for cases where system information is inaccessible. An appropriate observer-based SMBCr is developed to guarantee the finite-time reachability of the observer-based SMS. Based on this, the system’s robust asymptotic stability under observer-based sliding mode boundary control (SMBC) is ensured. Finally, the theoretical results are validated through two illustrative examples.