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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 17
141
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Research Article

Optimal control of differential inclusions with endpoint constraints and duality

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Pages 4717-4732 | Received 07 Jun 2022, Accepted 03 Oct 2022, Published online: 17 Oct 2022
 

Abstract

The article considers a high-order optimal control problem and its dual problems described by high-order differential inclusions. In this regard, the established Euler–Lagrange type inclusion, containing the Euler–Poisson equation of the calculus of variations, is a sufficient optimality condition for a differential inclusion of a higher order. It is shown that the adjoint inclusion for the first-order differential inclusions, defined in terms of a locally adjoint mapping, coincides with the classical Euler–Lagrange inclusion. Then the duality theorems are proved.

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

Acknowledgements

The author expresses his heartfelt gratitude to the Editor-in-Chief Prof. Yongzhi Xu journal and anonymous reviewers, whose comments and suggestions made it possible to improve the work.

Disclosure statement

No potential conflict of interest was reported by the author(s).

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