@article{article_1512521, title={Existence results and optimality conditions of time optimal control problem}, journal={Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics}, volume={74}, pages={355–363}, year={2025}, DOI={10.31801/cfsuasmas.1512521}, author={Demir Sağlam, Sevilay}, keywords={Time-optimal control, differential inclusions, optimality conditions, existence solutions}, 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.}, number={3}, publisher={Ankara University}, organization={No}