Neural Robust Control on Lie Groups Using Contraction Methods (Extended Version)
arXiv:2604.01448v1 Announce Type: cross Abstract: 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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Abstract: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.
Comments: An extended version of the conference paper submitted for publication in IEEE Conference of Decision and Control
Subjects:
Systems and Control (eess.SY); Robotics (cs.RO)
Cite as: arXiv:2604.01448 [eess.SY]
(or arXiv:2604.01448v1 [eess.SY] for this version)
https://doi.org/10.48550/arXiv.2604.01448
arXiv-issued DOI via DataCite (pending registration)
Submission history
From: Yi Lok Lo [view email] [v1] Wed, 1 Apr 2026 22:47:29 UTC (638 KB)
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