Optimal control of a two-dimensional contact problem with multiple unilateral constraints

Abstract

In this article, we are concerned with optimal control of a frictionless contact problem with multiple unilateral constraints for a two-dimensional bar. The existence of an optimal trajectory-control pair is firstly proven under the framework of general cost functional. The Pontryagin maximum principle is then established for the investigational system equipped with many equality and inequality constraints in fixed final horizon case, owing to the Dubovitskii and Milyutin functional analytical approach. A remark concludes the article with the discussion, which address the utilization of obtained necessary optimality condition.

Keywords:

• Optimal control
• maximum principle
• inequality constraint
• contact problem
• unilateral constraint

AMS subject classifications:

• 49K20
• 49J40
• 74M05
• 74M15

Acknowledgments

The authors would like to thank the editor and the 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 number 12271034].