Local asymptotic approximation of non-linear control systems!

Abstract

Let g1, …, gm be smooth vector fields on Rd. Using a canonical linear rescaling of time and space coordinates, the control system is transformed into a system, on the same state space, which is arbitrarily close to a nilpotent one. This approximation takes place in the C∞ topology, and is particularly useful for the study of local properties of (*) which depend on the high-order variational structure of the vector fields gi.