Existence results and optimality conditions of time optimal control problem

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DEMİR SAĞLAM S.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, vol.74, no.3, pp.355-363, 2025 (ESCI, TRDizin)

• Publication Type: Article / Article
• Volume: 74 Issue: 3
• Publication Date: 2025
• Doi Number: 10.31801/cfsuasmas.1512521
• Journal Name: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
• Journal Indexes: Emerging Sources Citation Index (ESCI), TR DİZİN (ULAKBİM)
• Page Numbers: pp.355-363
• Istanbul University Affiliated: Yes

Abstract

. The paper is concerned with the existence of theorems and optimality conditions for a timeoptimal 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.