arXiv:2411.18964eess.SYcs.LG2024-11被引 11

用神经算子替代传统预测器,实现非线性时滞系统的高效稳定控制。

Neural Operators for Predictor Feedback Control of Nonlinear Delay Systems

  • 将预测器设计转化为神经算子学习问题,直接逼近系统映射。
  • 在5连杆机械臂上实现控制,速度提升显著且闭环稳定。
  • 适用于任意满足通用近似误差的黑箱预测器,适合复杂系统建模。

预测反馈设计对非线性时滞系统的延迟补偿控制器至关重要。然而,由于预测器无法直接实现,需依赖数值近似方案,当系统动态计算成本高时,这些方法变得计算繁重。为此,我们将预测器设计重构为算子学习问题,通过神经算子学习预测映射。我们证明了预测算子可被任意精确的神经算子近似。在近似预测器下,闭环非线性时滞系统实现半全局实用稳定性。该估计具有独特性——可任意扩大初始状态集合,但会增加神经算子训练难度,这在稳定性估计中体现。此外,我们的分析适用于任何满足通用近似误差界的黑箱预测器。我们在不同神经算子模型下对5连杆机械臂进行控制,相比经典预测反馈方案实现显著提速,同时保持闭环稳定性。

原文摘要 · Abstract (English)

Predictor feedback designs are critical for delay-compensating controllers in nonlinear systems. However, these designs are limited in practical applications as predictors cannot be directly implemented, but require numerical approximation schemes, which become computationally prohibitive when system dynamics are expensive to compute. To address this challenge, we recast the predictor design as an operator learning problem, and learn the predictor mapping via a neural operator. We prove the existence of an arbitrarily accurate neural operator approximation of the predictor operator. Under the approximated predictor, we achieve semiglobal practical stability of the closed-loop nonlinear delay system. The estimate is semiglobal in a unique sense - one can enlarge the set of initial states as desired, though this increases the difficulty of training a neural operator, which appears practically in the stability estimate. Furthermore, our analysis holds for any black-box predictor satisfying the universal approximation error bound. We demonstrate the approach by controlling a 5-link robotic manipulator with different neural operator models, achieving significant speedups compared to classic predictor feedback schemes while maintaining closed-loop stability.

控制理论神经算子时滞系统机器人控制

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