K.B. Mansimov, V.G. Rzayeva.
The Pontryagin maximum principle as a necessary and sufficient optimality condition in a variable structure optimal control problem

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.

Keywords: Pontryagin maximum principle, Necessary and sufficient optimality condition, Increment formula, Volterra integral equation, System of hyperbolic equations, Linear equation

DOI: https://www.doi.org/10.54381/icp.2021.2.02
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