Control systems of zero curvature are not necessarily trivializable

Ulysse Serres (1, 2)

1 CORIDA - Robust control of infinite dimensional systems and applications
2 IECN - Institut Élie Cartan de Nancy

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.

Mots clés: Control systems; control curvature; state-feedback equivalence; Zermelo-like problems

Domaines: Optimisation et contrôle [math.OC]; Géométrie différentielle [math.DG]

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