Existence results and optimality conditions of time optimal control problem

Sevilay Demir Sağlam

Article Details

Existence results and optimality conditions of time optimal control problem

Authors:

Sevilay Demir Sağlam

Publisher:

Ankara University

Main Topics:

Ordinary Differential Equations | Difference Equations and Dynamical Systems | Calculus of Variations | Mathematical Aspects of Systems Theory and Control Theory

Journal:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 3, pp.355-363

Document Type:

Article

Publication Date:

9/2025

Document Language:

English

Document ID (Org No.):

2001357870

pISSN:

1303-5991

Keywords:

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.

 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.

 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.

 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.

Article Details

Existence results and optimality conditions of time optimal control problem

Authors:

Sevilay Demir Sağlam

Publisher:

Ankara University

Main Topics:

Ordinary Differential Equations | Difference Equations and Dynamical Systems | Calculus of Variations | Mathematical Aspects of Systems Theory and Control Theory

Journal:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 3, pp.355-363

Document Type:

Article

Publication Date:

9/2025

Document Language:

English

Document ID (Org No.):

2001357870

pISSN:

1303-5991

Time-optimal control

differential inclusions

optimality conditions

existence solutions

Issues

Article Details

Existence results and optimality conditions of time optimal control problem

Authors: Sevilay Demir Sağlam

Publisher: Ankara University

Main Topics: Ordinary Differential Equations | Difference Equations and Dynamical Systems | Calculus of Variations | Mathematical Aspects of Systems Theory and Control Theory

Journal: Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 3, pp.355-363

Document Type: Article

Publication Date: 9/2025

Document Language: English

Document ID (Org No.): 2001357870

pISSN: 1303-5991

Time-optimal control

differential inclusions

optimality conditions

existence solutions

Issues

Authors:

Sevilay Demir Sağlam

Publisher:

Ankara University

Main Topics:

Ordinary Differential Equations | Difference Equations and Dynamical Systems | Calculus of Variations | Mathematical Aspects of Systems Theory and Control Theory

Journal:

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Vol.74 Issue 3, pp.355-363

Document Type:

Article

Publication Date:

9/2025

Document Language:

English

Document ID (Org No.):

2001357870

pISSN:

1303-5991