Bang-Bang Property and Time-Optimal Control for Caputo Fractional Differential Systems-Reference-Cited by-同舟云学术

Bang-Bang Property and Time-Optimal Control for Caputo Fractional Differential Systems

Published:2024-01-26 Issue:2 Volume:8 Page:84
ISSN:2504-3110
Container-title:Fractal and Fractional
language:en
Short-container-title:Fractal Fract

Author:

Abel-Gaid Shimaa H.¹,Qamlo Ahlam Hasan²,Mohamed Bahaa Gaber¹

Affiliation:

1. Department of Mathematics and Computer Science, Faculty of Sciences, Beni-Suef University, Beni-Suef 62511, Egypt

2. Department of Mathematics, Faculty of Sciences, Umm Al-Qura University, Makkah 21955, Saudi Arabia

Abstract

In this paper, by using the controllability method, a bang-bang property and a time optimal control problem for time fractional differential systems (FDS) are considered. First, we formulate our problem and prove the existence theorem. We then state and prove the bang-bang theorem. Finally, we state the optimality conditions that characterize the optimal control. Some application examples are given to illustrate our results.

Funder

Umm al-Qura University

Publisher

MDPI AG

Subject

Statistics and Probability,Statistical and Nonlinear Physics,Analysis

Link

https://www.mdpi.com/2504-3110/8/2/84/pdf

Reference38 articles.

1. Integration by parts and its applications of a new nonlocal fractional derivative with Mittag-Leffler nonsingular kernel;Abdeljawad;J. Nonlinear Sci. Appl.,2017

2. Formulation of Euler-Lagrange equations for fractional variational problems;Agrawal;J. Math. Anal. Appl.,2002

3. Miller, K.S., and Ross, B. (1993). An Introduction to the Fractional Calculus and Fractional Differential Equations, John Wiley & Sons, Inc.. A Wiley- Interscience Pub.

4. Oldham, K.B., and Spanier, J. (1974). The Fractional Calculus, Academic Press.

5. Podlubny, I. (1999). Fractional Differential Equations, Academic Press.