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Applicable Analysis
An International Journal
Volume 102, 2023 - Issue 18
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Research Article

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

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Pages 5195-5214 | Received 10 Aug 2021, Accepted 05 Jan 2023, Published online: 26 Jan 2023
 

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.

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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].

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