Existence results and optimality conditions of time optimal control problem

Year 2025, Volume: 74 Issue: 3, 355 - 363, 23.09.2025

Sevilay Demir Sağlam

https://doi.org/10.31801/cfsuasmas.1512521

Abstract

The paper is concerned with the existence of theorems and optimality conditions for a time-optimal control problem. The first aim deals with the existence theorem of an optimal solution for a time-optimal control problem in the calculus of variations. We prove the existence theorem utilizing a result on the existence of continuous maps from the space of absolutely continuous functions to the set of solutions to a differential inclusion with Lipschitzian right-hand side. The second goal is to formulate the optimality conditions for the time-optimal minimization problem. We examine necessary optimality conditions which play a significant role in finding candidates to be optimal solutions among all admissible solutions via the normal cones.

Keywords

Time-optimal control , differential inclusions , optimality conditions , existence solutions

Ethical Statement

No

Supporting Institution

No

Project Number

--

Thanks

No

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