基于PD-空间积分复合控制的一类不稳定波方程的跟踪问题
Tracking Problem for a Class of Unstable Wave Equation via PD-Space Integral Composite Control
摘要: 本文通过设计比例–微分–空间积分复合控制，研究一类不稳定波动方程的输出追踪问题。利用Lyapunov方法，我们能够证明闭环系统是指数稳定的，并且输出能够跟踪任意给定的常值参考信号。最后，给出了一些数值模拟来验证所提出控制器的有效性。
Abstract: This paper investigates the output tracking problem for a class of unstable wave equations. A proportional-derivative-spatial integral composite controller is proposed. By constructing a suitable Lyapunov functional, we prove that the closed-loop system is exponentially stable and the output can successfully track any given constant reference signal. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed controller.
文章引用：郭玥萌, 王紫薇, 刘军军. 基于PD-空间积分复合控制的一类不稳定波方程的跟踪问题[J]. 应用数学进展, 2026, 15(4): 528-537. https://doi.org/10.12677/aam.2026.154180

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