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In this paper we consider a reachability problem for a nonlinear affine-control system  with  integral constraints, which assumed to be quadratic in the control variables.  Under  controllability assumptions it was  proved [8] that any admissible control, that steers the control system to the boundary of its reachable set, is a local solution to an optimal control problem with an integral cost functional and terminal constraints. This results in the Pontriagyn maximum principle for boundary trajectories. We propose here an numerical algorithm for computing the reachable set boundary  based on the maximum principle and provide some numerical examples.

AN ALGORITHM FOR COMPUTING BOUNDARY POINTS OF REACHABLE SETS OF CONTROL SYSTEMS UNDER INTEGRAL CONSTRAINTS