Discussion on optimal feedback control for stochastic fractional differential system by hemivariational inequalities

Abstract

This study focuses on optimal feedback control for stochastic Caputo fractional evolution systems in separable Hilbert spaces. Initially, we deal with the existence of a mild solution, establishing it through the application of the generalised Clarke's subdifferential and a fixed point theorem for multivalued maps. Then, we utilise the Cesari property and the Filippov theorem to demonstrate the existence of feasible pairs. Additionally, we provide pairs of suitable feedback controls under specific conditions. Finally, we present a simple illustration to support our theoretical findings.

Keywords:

• Hemivariational inequalities
• fractional calculus
• functional–differential inclusions
• feedback control

2020 Mathematics Subject Classifications:

• 26A33
• 47J20
• 93B52
• 34K09

Disclosure statement

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

Additional information

Notes on contributors

S. Vivek

S. Vivek obtained his MSc and MPhil 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 seven papers in reputed scientific journals.

V. Vijayakumar

Dr. V. Vijayakumar received BSc, MSc, MPhil, and PhD 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 and 2022.