A Characterization of the Reachable Set for Nonlinear Control Systems

The question of whether a set is reachable by a nonlinear control system is answered in terms of the properties of a convex optimization problem. The set is reachable or not according to whether the value of the optimization problem is zero or infinity. Our findings strengthen earlier sufficient conditions for a point not to be reachable, given in terms of Lyapunov-like functions, in that we assure that the functions exist. Our approach is to embed admissible trajectories in a space of measures, and to apply recently obtained results on the properties of measures arising in this way.