Control systems of zero curvature are not necessarily trivializable
نویسنده
چکیده
A control system q̇ = 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 q̇ = f(u). In this paper we characterize trivializable control systems and control systems for which, up to a feedback transformation, f and ∂f/∂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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