An analysis on time optimal feedback control for Caputo fractional neutral systems with delay

ABSTRACT

This paper aims to provide a systematic approach to investigate the optimal feedback control systems governed by the fractional neutral evolution system with fixed delay in the sense of Caputo fractional derivatives in separable reflexive Banach spaces. Initially, we study the existence result of mild solutions for the system by applying fixed point theorem for a condensing map due to Martelli. The existence of feasible pairs is obtained by using the Filippov theorem and the Cesari property. Furthermore, the existence of optimal feedback control and time optimal control are studied for the corresponding control problem. Finally, an example is given to validate our findings.

KEYWORDS:

• Fractional calculus
• neutral systems
• optimal feedback control
• feasible pairs

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 34A08
• 35K40
• 49J15
• 93B52

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Notes on contributors

S. Vivek

S. Vivek obtained his M.Sc. and M.Phil. degrees in Mathematics from Bharathiar University, Coimbatore, Tamil Nadu, India, in 2016 and 2019, respectively. Now, he is pursuing his Ph.D. degree under the guidance of Prof. V. Vijayakumar at the Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu, India. His current research interests include Fractional Calculus, Dynamical systems, Stability analysis, and Control theory. To his credit, he has published 6 papers in reputed scientific journals.

V. Vijayakumar

Dr. V. Vijayakumar received B.Sc, M.Sc, M.Phil, and Ph.D. degrees in Mathematics from the Bharathiar University, Coimbatore, Tamil Nadu, India in 2002, 2004, 2006, and 2016 respectively. He was a Lecturer with the Department of Mathematics, Sri Nandhanam College of Engineering and Technology, Tirupattur, Vellore, Tamil Nadu, India, from 2006 to 2007. He was an Assistant Professor and an Associate Professor with the Department of Mathematics, Info Institute of Engineering, Coimbatore, Tamil Nadu, India, from 2007 to 2019. Since 2019, he has been an Assistant Professor at Vellore Institute of Technology, Vellore, Tamil Nadu, India. His current research interests include Fractional Calculus, Dynamical Systems, Control Theory, and Neural Networks. To his credit, he has published more than 175 papers in reputed scientific journals. He is listed as TOP 2% Scientists in the World (All Fields) by a survey conducted by Elsevier BV and Stanford University, based on the citations, h-index, and co-authorship adjusted hm-index, for the years 2020, 2021 & 2022.