Boundary Control of a Reaction-Diffusion PDE With Time-Varying Input Delay

• 成果类型: Article
• 署名作者: Cai, Xiushan; Lin, Yuhang
• 署名单位: Xiamen Institute of Technology; Hubei Normal University; Zhejiang Normal University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3626617
• 发表日期: 2026
• 关键词: systems; stabilization

摘要

We present a control design and stability analysis for a reaction-diffusion partial differential equation (PDE) with boundary control. The system admits an arbitrary number of unstable eigenvalues and is subject to a time-varying input delay, with an unbounded input operator. The unbounded nature of the input operator requires the stability analysis to be carried out in the H(1 )norm rather than the conventional L(2 )norm of the actuator state. The analysis reveals a cascaded structure composed of a parabolic PDE and a first-order hyperbolic PDE with nonconstant propagation velocity. We explicitly construct kernel functions for the backstepping transformations to map the cascaded system into the target system. Based on this, we design a boundary feedback law that compensates for the time-varying delay and guarantees exponential stability of the closed-loop system. Finally, we provide explicit formulas for both the control law and the closed-loop solutions.