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arXiv · 0902.2332

Control systems of zero curvature are not necessarily trivializable

Ulysse Serres
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Abstract

A control system $\dot{q} = f(q,u)$ is said to be trivializable if there exists local coordinates in which the system is feedback equivalent to a control system of the form $\dot{q} = f(u)$. In this paper we characterize trivializable control systems and control systems for which, up to a feedback transformation, $f$ and $\partial f/\partial u$ commute. Characterizations are given in terms of feedback invariants of the system (its control curvature and its centro-affine curvature) and thus are completely intrinsic. To conclude we apply the obtained results to Zermelo-like problems on Riemannian manifolds.

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Ulysse Serres. 2009-02-13. Control systems of zero curvature are not necessarily trivializable. https://arxiv.org/abs/0902.2332

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