Optimal control of nonlinear renewal equation

Abstract

In this article, we study the optimal control for a nonlinear renewal equation popularly known as McKendrick–von Foerster (MV) equation. We establish necessary optimality conditions using the concept of normal cone. Finally, we prove the existence and uniqueness of optimal control using the Ekeland variational principle.

Keywords:

• Population dynamics
• age-structured population model
• optimal control

AMS Subject Classifications:

• 35A01
• 92D25
• 49J20

Acknowledgements

The author would like to thank Prof. Mythily Ramaswamy for fruitful discussions. The author is very grateful to the anonymous referee for his/her comments and suggestions that greatly helped to improve this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by SERB-NPDF [grant number PDF/2017/001305].