On the reachable set of nonlinear control systems with a nilpotent Lie algebra

We consider control systems that are affine in the control and whose vector fields generate a nilpotent Lie algebra. Analysis of such systems can be reduced to the analysis of the associated canonical Hall-Sussmann (HS) system. We derive several new results revealing the elegant Lie-algebraic structure of the HS system. We also prove that local, or small-time, nice reachability results imply their global counterparts for nilpotent control systems.