基于预测器的延迟异维海岸线-测深系统镇定
Predictor-Based Stabilization of a Delayed Hetero-Dimensional Shoreline--Bathymetry System
- CRAN-UMR-CNRS-7039 University of Lorraine（洛林大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
针对带输入延迟的异维海岸线-测深耦合系统，提出基于预测器的状态反馈镇定方法，通过谱分解与小增益条件实现指数稳定，仿真验证补偿有效抑制延迟放大。
AI中文摘要：
研究了一类异维抛物型系统的指数镇定问题，其中一维海岸线子系统受常输入延迟影响，并与未受控的二维测深动力学双向耦合。通过谱分解将有限维临界海岸线模态与指数稳定的剩余动力学分离。在临界子空间上设计状态反馈，并将其提升至整个海岸线空间。引入辅助输运方程表示延迟，而预测器则从标称预测动力学中消除显式输入延迟。通过结合海岸线镇定与测深强制性，利用加权输入-输出估计及异维相互作用上的小增益条件，建立了全耦合系统的指数稳定性。数值仿真表明，未补偿的延迟反馈会强烈放大海岸线和测深响应，而预测器补偿则恢复临界海岸线动力学的衰减，并防止延迟引起的放大传播至未受控的测深子系统。
英文摘要：
Exponential stabilization is investigated for a hetero-dimensional parabolic system in which a one-dimensional shoreline subsystem, subject to a constant input delay, is bidirectionally coupled with unactuated two-dimensional bathymetric dynamics. A spectral decomposition separates the finite-dimensional critical shoreline modes from the exponentially stable residual dynamics. State feedback is designed on the critical subspace and lifted to the full shoreline space. An auxiliary transport equation represents the delay, while a predictor removes the explicit input delay from the nominal predictor dynamics. Exponential stability of the full coupled system is established by combining shoreline stabilization and bathymetric coercivity using weighted input--output estimates and a small-gain condition on the hetero-dimensional interaction. Numerical simulations show that uncompensated delayed feedback can strongly amplify both shoreline and bathymetric responses, whereas predictor compensation restores decay of the critical shoreline dynamics and prevents delay-induced amplification from propagating to the unactuated bathymetric subsystem.
