Results on approximate controllability for a second-order semilinear nonlocal control system with monotonic nonlinearity

ABSTRACT

In this paper, we propose the approximate controllability analysis for a second semilinear system under nonlocal conditions using monotone nonlinearity as a tool. Monotonicity is a significant feature in many communications applications that use digital-to-analog converter circuits. While non-monotonicity prevents such applications from working, nonlinearity makes them work. Therefore, it is of great interest to study a problem while assuming the nonlinear function is monotonic. Nonlocal conditions have a finer effect on the solution and are additional specifications for the physical measurements beyond the conventional ones. In order to determine the controllability of the considered system, we formulate the control function. In addition to this, we have broadened the scope of the results for the impulsive system. At last, we discuss two examples.

KEYWORDS:

• Approximate controllability
• second order system
• monotone condition
• nonlocal conditions

MSC:

• 34K30
• 34K35
• 93C25

Disclosure statement

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

Data Availability Statement

My manuscript has no associated data.

Additional information

Notes on contributors

Urvashi Arora

Dr. Urvashi Arora completed her Ph.D. from Indian Institute of Technology Roorkee, Roorkee, India in 2017. After that she worked as an Assistant Professor in Bennett University, India for three years 4 months. She has published various research papers in various international journals. She has presented her research work at several international conferences.

V. Vijayakumar

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 120 papers in reputed scientific journals.

Arun Kumar Singh

Arun Kumar Singh obtained his B.E in Electronics and Instrumentation Engineering from BIET Jhansi in year 1997, M.Tech. in Digital Electronics and Systems, and Ph.D. in the area of distributed system (Adhoc networks) from Uttar Pradesh Technical University, Lucknow. Presently he is Dean (Academics/PGSR), CoE along with Head of Electronics Engineering Department at Rajkiya Engineering College, Kannauj, U.P and having more than 24 years of experience. Dr Singh is a Fellow member of IE (I), IETE, Senior member of IEEE & life member of ISTE. He wrote several books on digital electronics and microcontrollers and got CMI Level 5 Award in Management and Leadership. He contributed research papers in several national and international conferences/journals and also delivered many lectures/key note address; organised several FDP and workshop/training program for students and teachers. As a Technologist/Engineer, his interests are: Application of Technology driven Education Paradigm, Wireless Communication, Distributed System, Control System, Formal Methods and System Modelling.

Harish Kumar Sahu

Dr Harish Sahu, has 17+ years of R&D experience in DRDO, Delhi and He is MTech in CSE, PhD both from IIT Delhi. His current research interests are cyber security, cryptology, quantum computing, signal processing and quantum cryptography. He is reviewer of several conferences, journals and examined PhD theses in the area. In 2018, Dr Sahu has received Best Industry Expert Award by Amity University. In 2019, he received lab Scientist of the year award for his outstanding scientific contribution.

Anurag Shukla

Anurag Shukla received M.Sc, and Ph.D. degrees in Mathematics from the IIT Roorkee, Uttarakhand, India in 2011, and 2016, respectively. He was an Assistant Professor with the Department of Mathematics, UPES, Dehradun, Uttarakhand, India, from 2016 to 2017. Since 2017, he has been an Assistant Professor in the Department of Applied Sciences & Humanities, Rajkiya Engineering College, Kannauj, Uttar Pradesh, India. His current research interests include Fractional Differential Systems, Stochastic Differential Systems, Impulsive Differential Systems, Mathematical Control theory and Fluid Dynamics. To his credit, he has published more than 70 papers in reputed scientific journals.