Control contraction metrics on Lie groups
CoRR(2024)
摘要
In this paper, we extend the control contraction metrics (CCM) approach,
which was originally proposed for the universal tracking control of nonlinear
systems, to those that evolves on Lie groups. Our idea is to view the manifold
as a constrained set that is embedded in Euclidean space, and then propose the
sufficient conditions for the existence of a CCM and the associated controller
design. Notably, we demonstrate that the search for CCM on Lie groups can be
reformulated as convex conditions. The results extend the applicability of the
CCM approach and provide a framework for analyzing the behavior of control
systems with Lie group structures.
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