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Necessary optimality conditions for a class of optimal control problems with discontinuous integrand

Authors: Smirnov A

Publication Year: 2008

Reference: Proceedings of the Steklov Institute of Mathematics, 262(1): 213-230 [2008]

Abstract

We consider a nonlinear optimal control problem with an integral functional in which the integrand contains the characteristic function of a given closed subset of the phase space. Using an approximation method, we prove necessary optimality conditions in the form of the Pontryagin maximum principle without any a priori assumptions about the behavior of an optimal trajectory.