Optimal control of differential inclusions with endpoint constraints and duality

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.

KEYWORDS:

• Endpoint constraints
• Hamiltonian
• necessary and sufficient
• duality
• support function
• Euler–Lagrange

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 49K15
• 34A60
• 49N15

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).