Maximum principle in nonsmooth problems of optimal impulse control with multi-point phase constraints (Q1599408)

The authors obtain necessary conditions for optimality of generalized solutions of the problem of impulse control in the form of the maximum principle under the presence of multipoint phase constraints. Assumptions on the functions describing a controlled system are weakened. The problem considered is nonsmooth and a well-posedness condition of Frobenius type is not assumed to be fulfilled. The investigation is based on the authors' approach to problems without phase constraints [\textit{V. A. Dykhta} and \textit{O. N. Samsonyuk}, Russ. Math. 43, No. 12, 23--34 (1999); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1999, No. 12, 26--37 (1999; Zbl 1027.49028)].