Control systems of zero curvature are not necessarily trivializable

Ulysse Serres

Control systems of zero curvature are not necessarily trivializable

Optimization and Control 2009-02-16 v1 Differential Geometry

Authors: Ulysse Serres

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.

Keywords

control system zero curvature trivializable feedback transformation Riemannian manifold

Cite

@article{arxiv.0902.2332,
  title  = {Control systems of zero curvature are not necessarily trivializable},
  author = {Ulysse Serres},
  journal= {arXiv preprint arXiv:0902.2332},
  year   = {2009}
}

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