Local asymptotic approximation of non-linear control systems!

Let g₁, …, g_m be smooth vector fields on R^d. 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 g_i.