用神经网络设计在李群上运行的鲁棒控制器，确保几何约束并控制扰动影响
Neural Robust Control on Lie Groups Using Contraction Methods (Extended Version)
- 联合训练神经反馈控制器与鲁棒控制收缩度量
- 在扰动下保证轨迹被约束在动态包络带内
- 适用于无人机等需保持几何结构的系统控制
本文提出一种用于在李群上演化动力系统的鲁棒控制器学习框架。通过联合训练鲁棒控制收缩度量（RCCM）和神经反馈控制器，确保在李群流形上满足收缩条件。推导了此类RCCM与神经控制器存在的充分条件，既尊重流形结构的几何约束，又建立依赖于扰动的轨迹包络带，限制输出轨迹的偏离。以四旋翼飞行器为例，采用该框架设计反馈控制器，并通过数值仿真评估性能，与几何控制器进行对比。
原文摘要 · Abstract (English)
In this paper, we propose a learning framework for synthesizing a robust controller for dynamical systems evolving on a Lie group. A robust control contraction metric (RCCM) and a neural feedback controller are jointly trained to enforce contraction conditions on the Lie group manifold. Sufficient conditions are derived for the existence of such an RCCM and neural controller, ensuring that the geometric constraints imposed by the manifold structure are respected while establishing a disturbance-dependent tube that bounds the output trajectories. As a case study, a feedback controller for a quadrotor is designed using the proposed framework. Its performance is evaluated using numerical simulations and compared with a geometric controller.
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