MAXIMUM PRINCIPLE IN THE LINEAR MINIMUM-TIME CONTROL PROBLEM

In a minimum-time control problem, both with an autonomous and with a non-autonomous system, the question of the sufficient conditions for the maximum principle is solved. The question of the uniqueness of optimal control is also considered. New conditions are obtained that guarantee the sufficiency of the maximum principle in terms of the geometry of the reachability set and the geometry of the control set. Examples that demonstrate the non-improvability of the obtained results are considered.