Robust sliding mode boundary control for uncertain reaction–diffusion systems

• Published in: Journal of the Franklin Institute Vol. 362; no. 6; p. 107623
• Main Authors: Zhou, Wei-Jie, Wu, Kai-Ning, Liu, Xiao-Zhen
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.04.2025
• Subjects: Boundary control; Observer; Reaction–diffusion systems; Robust asymptotic stability; Sliding mode control; Boundary control; Robust asymptotic stability; Reaction–diffusion systems; Sliding mode control; Observer
• ISSN: 0016-0032
• DOI: 10.1016/j.jfranklin.2025.107623

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. •The SMBC of URDSs is investigated and the results contribute to the theoretical foundations of SMBC for systems with uncertainties and spatially distributed dynamics.•To address the inherent challenges posed by the diffusion term and the complexities of boundary control in RDSs, the innovative SMS and SMBC are constructed.•This work provides a foundational reference for future research on observer-based SMBC for RDSs.