用神经算子解决多输入延迟非线性系统的稳定控制问题
Delay compensation of multi-input distinct delay nonlinear systems via neural operators
- 将时滞转化为传输型偏微分方程，分析耦合常微分-偏微分系统
- 在统一误差界下实现半全局实用稳定性，且误差依赖于吸引域和输入数
- 理论与机器人实验验证神经算子可满足所需误差约束
本文首次为具有不同执行器时滞的多输入非线性系统中近似预测器提供了稳定性结果。若预测器近似满足关于时间一致的误差上界，则可实现半全局实用稳定性。该误差上界大小取决于期望吸引域范围及系统控制输入数量。方法通过将时滞转化为传输型偏微分方程（PDE），对耦合的常微分方程-偏微分方程（ODE-PDE）级联系统进行分析而达成。为验证此类误差上界的可行性，本文以神经算子（neural operators）为例，从理论上证明其满足统一误差界，并在移动机器人实验中通过仿真予以验证。
原文摘要 · Abstract (English)
In this work, we present the first stability results for approximate predictors in multi-input non-linear systems with distinct actuation delays. We show that if the predictor approximation satisfies a uniform (in time) error bound, semi-global practical stability is correspondingly achieved. For such approximators, the required uniform error bound depends on the desired region of attraction and the number of control inputs in the system. The result is achieved through transforming the delay into a transport PDE and conducting analysis on the coupled ODE-PDE cascade. To highlight the viability of such error bounds, we demonstrate our results on a class of approximators - neural operators - showcasing sufficiency for satisfying such a universal bound both theoretically and in simulation on a mobile robot experiment.
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