# Control systems of zero curvature are not necessarily trivializable

1 CORIDA - Robust control of infinite dimensional systems and applications
IECN - Institut Élie Cartan de Nancy, LMAM - Laboratoire de Mathématiques et Applications de Metz, Inria Nancy - Grand Est
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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Cited literature [8 references]

https://hal.archives-ouvertes.fr/hal-00361312
Contributor : Ulysse Serres <>
Submitted on : Friday, February 13, 2009 - 4:43:48 PM
Last modification on : Saturday, March 30, 2019 - 1:18:11 AM
Long-term archiving on: : Tuesday, June 8, 2010 - 6:24:01 PM

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### Identifiers

• HAL Id : hal-00361312, version 1
• ARXIV : 0902.2332

### Citation

Ulysse Serres. Control systems of zero curvature are not necessarily trivializable. 2009. ⟨hal-00361312⟩

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