发表机构
School of Mathematical Sciences, Fudan University; Shanghai Key Laboratory for Contemporary Applied Mathematics, Fudan University（复旦大学数学科学学院; 复旦大学当代应用数学上海市重点实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对比例边界反馈无法镇定的零特征速度线性双曲系统，提出反步控制设计，构造Volterra变换得到目标系统，通过两种方法证明其稳定性，求解核方程得到显式反馈律，经数值仿真验证有效性。
AI 中文摘要
本文研究具有零特征速度的线性双曲系统的边界镇定问题，针对比例边界反馈无法镇定的情形，在零速度子系统无内在耗散的临界场景下，提出反步设计方案。为此，构造Volterra变换得到非标准积分-微分目标系统，通过Lyapunov-LaSalle方法和谱半群论证建立其L2渐近稳定性；明确求解反步核方程，得到可渐近镇定原系统的显式边界反馈律，并通过数值仿真验证所提控制设计的有效性。
英文摘要
This paper investigates the boundary stabilization of a linear hyperbolic system with a zero characteristic speed. We address a case that cannot be stabilized by proportional boundary feedback and develop a backstepping design for the critical setting where the zero-speed subsystem has no intrinsic dissipation. To this end, we construct a Volterra transformation leading to a nonstandard integro-differential target system. Its asymptotic stability in L2 is established by both the Lyapunov-LaSalle method and a spectral semigroup argument. The backstepping kernel equations are explicitly solved, yielding an explicit boundary feedback law that asymptotically stabilizes the original system. Numerical simulations are provided to illustrate the effectiveness of the proposed control design.
Comments20 pages, 6 figures
