Second-order viability problems for differential inclusions with endpoint constraint and duality

ABSTRACT

The paper deals with the optimal control of second-order viability problems for differential inclusions with endpoint constraint and duality. Based on the concept of infimal convolution and new approach to convex duality functions, we construct dual problems for discrete and differential inclusions and prove the duality results. It seems that the Euler–Lagrange type inclusions are ‘duality relations’ for both primary and dual problems. Finally, some special cases show the applicability of the general approach; duality in the control problem with second-order polyhedral DFIs and endpoint constraints defined by a polyhedral cone is considered.

KEYWORDS:

• Infimal convolution
• duality
• endpoint constraint
• Euler–Lagrange
• viability

AMS SUBJECT CLASSIFICATIONS:

• 34A60
• 49N15
• 49M25
• 90C46

Acknowledgments

The author would like to express sincere thanks to the Editor-in-Chief Prof. Yongzhi Xu of the Journal of Applicable Analysis and anonymous reviewers for valuable suggestions that improved the final manuscript.

Disclosure statement

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