Computing the reachable set boundary for an abstract control problem

The problems of reachability for control systems with integral constraints on the control variables have been studied in the literature on the optimal control theory. For a nonlinear control-affine system on a finite time interval it was shown that every admissible control that steers the control system to the boundary of its reachable set is a local solution of some auxiliary optimal control problem with an integral cost. In this paper we prove...