Robust sliding mode boundary control for uncertain reaction–diffusion systems

IF 3.7 3区计算机科学 Q2 AUTOMATION & CONTROL SYSTEMS

Journal of The Franklin Institute-engineering and Applied Mathematics Pub Date : 2025-03-11 DOI:10.1016/j.jfranklin.2025.107623

Wei-Jie Zhou , Kai-Ning Wu , Xiao-Zhen Liu

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引用次数: 0

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.

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本文研究了不确定反应扩散系统（URDS）的鲁棒性滑模边界稳定。首先，为了驱动状态轨迹在滑动阶段内达到平衡，需要构建一个指定的滑动模态面（SMS）。重点是设计合适的滑模边界控制器（SMBCr），引导状态轨迹在有限时间内到达设计的 SMS。此外，通过采用 Lyapunov 函数方法和先进的不等式技术，建立了确保稳健渐近稳定性的充分准则。其次，针对无法获取系统信息的情况，研究了基于观测器的鲁棒滑模边界稳定。开发了一种适当的基于观测器的 SMBCr，以保证基于观测器的 SMS 的有限时间可达性。在此基础上，确保了系统在基于观测器的滑模边界控制（SMBC）下的鲁棒性渐近稳定性。最后，通过两个示例验证了理论结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of The Franklin Institute-engineering and Applied Mathematics 工程技术-工程：电子与电气

CiteScore

7.30

自引率

14.60%

发文量

586

审稿时长

6.9 months

期刊介绍： The Journal of The Franklin Institute has an established reputation for publishing high-quality papers in the field of engineering and applied mathematics. Its current focus is on control systems, complex networks and dynamic systems, signal processing and communications and their applications. All submitted papers are peer-reviewed. The Journal will publish original research papers and research review papers of substance. Papers and special focus issues are judged upon possible lasting value, which has been and continues to be the strength of the Journal of The Franklin Institute.