Pontryagin's maximum principle for optimal control of an extrusion process

Abstract

In this article, two optimal control problems of an extrusion process are considered in the isothermal case. The controlled system consists of a hyperbolic partial differential equation coupled with a nonlinear ordinary differential equation. Equipped with two control variables, the system describes the evolution of a moving interface between a fully filled zone and a partially filled zone. The Dubovitskii and Milyutin functional analytical approach is adopted in the investigation of the Pontryagin maximum principle for the optimal control problem. In both fixed and free final horizon cases, the corresponding necessary optimality conditions are, respectively, established. A remark is then made for illustrating the applicability of the obtained results.

Keywords:

• Extrusion process
• moving interface
• optimal control
• maximum principle
• necessary optimality condition

AMS subject classifications:

• 35L60
• 35R37
• 49K20
• 93C95

Acknowledgments

The authors would like to thank the editor and the anonymous referees for their very careful reading and constructive suggestions that improve the manuscript substantially.

Disclosure statement

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

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [Grant No. 11471036].

Notes on contributors

Cheng-Cheng Ma

Cheng-Cheng Ma received her B.Sc. degree in mathematics at Shandong Normal University, China, in 2016; M. Sc. degree in mathematics at Beijing Institute of Technology, China, in 2019. Currently, she is pursuing her Ph.D. degree in School of Mathematics and Statistics, Beijing Institute of Technology, China. Her research interest includes the optimal control theory of distributed parameter systems.

Bing Sun

Bing Sun received his Ph.D. degree in operational research and control theory from the Academy of Mathematics and Systems Science, the Chinese Academy of Sciences in 2005. From 2005 to 2006, he was a Postdoctoral Fellow at the School of Computational and Applied Mathematics, University of the Witwatersrand, South Africa. Since 2008, he has been with the Beijing Institute of Technology, first as an Assistant Professor (2008–2010), an Associate Professor (2010–2015) and subsequently a Professor (since 2015) in mathematical system theory. He is the author or coauthor approximate 40 international peer/refereed journal papers. His research interests include the optimal control theory of systems described by partial differential equations and numerical solutions of optimal feedback control for both finite- and infinite dimensional systems. Dr. Sun received the Training Program Foundation for the Beijing Municipal Excellent Talents in 2012.