Title: The Pontryagin maximum principle as a necessary and sufficient optimality condition in a variable structure optimal control problem
Abstract: The authors consider one optimal control problem with a variable structure, described in various domains by a Goursat-Darboux system and a two-dimensional Volterra integral equation. Using one version of the method of increments, a necessary and sufficient condition for optimality is proved in the form of the Pontryagin maximum principle.