Abstract
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.
Abstract (translated)
在这项工作中，我们首次提出了多输入非线性系统中具有不同执行器延迟的近似预测器的稳定性结果。我们展示了如果预测器的近似误差满足一个在时间上一致的界限，则相应的半全局实际稳定性可以实现。对于这样的逼近器，所需的一致误差界限取决于期望吸引域和系统中的控制输入数量。通过将延迟转换为传输偏微分方程（PDE）并分析耦合的常微分方程-偏微分方程级联，我们实现了这一结果。 为了突出这些误差界限的有效性，我们在一类逼近器——神经算子上展示了我们的研究成果，从理论上和在移动机器人实验中的模拟中证明了满足这种通用界限的充分条件。
URL
https://arxiv.org/abs/2509.17131
