Neural Robust Control on Lie Groups Using Contraction Methods (Extended Version)
This work addresses robust control for systems on Lie groups, such as quadrotors, but appears incremental as it builds on existing contraction methods with neural network integration.
The authors tackled the problem of synthesizing robust controllers for dynamical systems on Lie groups by jointly training a robust control contraction metric and a neural feedback controller to enforce contraction conditions, resulting in a framework that ensures geometric constraints are respected and establishes disturbance-dependent bounds on trajectories, with a case study on a quadrotor showing performance evaluated through numerical simulations and comparison to a geometric controller.
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.