Some remarks on nonconvex optimal control

AbstractThe problem of time-optimal control with nonconvex control counterdomain in an infinite-dimensional case is considered. A geometrical version of Pontriagin's maximum principle is formulated. The main result concerns certain necessary conditions of optimality, formulated in terms of quasitrajectories of the control system under consideration. The original control variable is eliminated from the condition of optimality, which is somewhat more abstract than the classical maximum principle, but, on the other hand, is valid even in the case when the optimal control does not exist. Some possible applications are pointed out