用神经网络逼近时变延迟系统的预测时域，提升控制稳定性。
Predictor-Based Output-Feedback Control of Linear Systems with Time-Varying Input and Measurement Delays via Neural-Approximated Prediction Horizons
- 将延迟反函数建模为算子学习问题，通过数值积分与神经算子实现逼近
- 两种方法在紧集上均能达到任意精度，计算成本与可扩展性各有优劣
- 适用于输入与测量均存在时变延迟的输出反馈系统，适合工程控制场景
由于结构简单且具备强稳定性保证，预测反馈方法自20世纪50年代以来一直是时滞系统的重要手段。然而，对于时变延迟系统，其实现需要计算由延迟函数反函数定义的预测时域，该反函数通常无法解析求得，必须近似处理。本文将延迟反函数建模为算子学习问题，并研究在预测时域近似下的预测反馈设计。提出两种方法：(i) 基于等效常微分方程的时间积分数值方法；(ii) 利用神经算子的数据驱动学习方法。证明两者在紧集上均可实现任意逼近精度，且在计算成本与可扩展性方面具有互补优势。基于上述近似，进一步设计了同时存在输入与测量延迟的输出反馈预测控制器。理论证明：当预测时域近似误差足够小时，闭环系统全局指数稳定。数值实验验证了所提方法的有效性，并展示了精度与计算效率之间的权衡。
原文摘要 · Abstract (English)
Due to simplicity and strong stability guarantees, predictor feedback methods have stood as a popular approach for time delay systems since the 1950s. For time-varying delays, however, implementation requires computing a prediction horizon defined by the inverse of the delay function, which is rarely available in closed form and must be approximated. In this work, we formulate the inverse delay mapping as an operator learning problem and study predictor feedback under approximation of the prediction horizon. We propose two approaches: (i) a numerical method based on time integration of an equivalent ODE, and (ii) a data-driven method using neural operators to learn the inverse mapping. We show that both approaches achieve arbitrary approximation accuracy over compact sets, with complementary trade-offs in computational cost and scalability. Building on these approximations, we then develop an output-feedback predictor design for systems with delays in both the input and the measurement. We prove that the resulting closed-loop system is globally exponentially stable when the prediction horizon is approximated with sufficiently small error. Lastly, numerical experiments validate the proposed methods and illustrate their trade-offs between accuracy and computational efficiency.
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