具有并发输入和状态时滞的一阶偏积分-微分方程的镇定
Stabilization of First-Order Partial Integro-Differential Equations with Concurrent Input and State Delays
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中文总结 AI 辅助
针对带并发输入与状态时滞的一阶偏积分-微分方程，本文提出基于反步的边界控制器，通过构造两类积分变换实现镇定与时滞补偿，经数值仿真验证了控制器的有效性。
中文摘要 AI 辅助
本文研究受并发输入和状态时滞影响的一阶双曲型偏积分-微分方程（PIDE）的边界镇定问题。这两种时滞的共存使控制器设计变得复杂，尤其是在输入时滞较大时，需要预测更多状态信息。本文开发了一种基于反步（backstepping）的边界控制器，以实现镇定和时滞补偿。该设计依赖于包含Fredholm型和Volterra型积分项的两个仿射Volterra变换，从而得到四个PIDE核方程。为建立这些方程的适定性，核域沿特征线被划分为有限个三角形子区域，且核解在子区域间依次构造。本文还建立了所得闭环系统的有限时间稳定性，并通过数值仿真验证了所提控制器的有效性。
英文摘要
This paper considers boundary stabilization problems for a first-order hyperbolic partial integro-differential equation (PIDE) subject to concurrent input and state delays. The coexistence of these two types of delays complicates control design, especially under the case of large input delay that requires to predict more state information. A backstepping-based boundary controller is developed to achieve stabilization and delay compensation. The design relies on two affine Volterra transformations involving both Fredholm- and Volterra-type integral terms, which results in a four-PIDE kernel equations. To establish their well-posedness, the kernel domain is partitioned along characteristic lines into a finite number of triangular subregions, and the kernel solution is constructed successively in the preceding subregion to the next one. The finite-time stability of the resulting closed-loop system is established. Numerical simulations are provided to demonstrate the effectiveness of the proposed controller.
