Pontryagin's maximum principle for optimal boundary control of a generalised Korteweg–de Vries equation

Abstract

In this article, the optimal boundary control for a generalised Korteweg–de Vries equation is considered. The Dubovitskii and Milyutin functional analytical approach is adopted in the investigation of Pontryagin's maximum principles of the system in both fixed and free final horizon cases. The necessary conditions are, respectively, presented for the optimal boundary control problems in these two cases.

Keywords:

• maximum principle
• Korteweg–de Vries equation
• optimal boundary control
• necessary condition

AMS Subject Classifications::

• 49B22
• 49K20
• 35Q20
• 35Q53

Acknowledgements

The author appreciates the suggestions and comments presented by the editors and the anonymous reviewers, which have greatly improved this work. The author gratefully acknowledges the hospitality offered to him by the Center for Talented Youth, The Johns Hopkins University, United States, where part of this article was written.