This monograph is driven by the ambition to thoroughly investigate and advance the field of discrete-time sliding mode design based on difference equations with minima for dynamical systems. The motivation behind this exploration lies in the recognition of limitations inherent in classical and conventional control techniques, prompting a quest for methodologies that can effectively address the evolving demands of modern applications. The overarching objective of this monograph is to introduce innovative approaches capable of enabling timely and precise control, even in the presence of uncertainties and exogenous perturbations. Through the development of sophisticated discrete control strategies designed to ensure finite-time convergence, this research aims to enhance the capabilities and operational efficiency of diverse engineering systems, thereby contributing to the ongoing evolution of control methodologies in response to contemporary challenges.

Presents the authors' work on discrete-time sliding mode control design based on the minimum operator Investigates field of discrete-time sliding mode design based on difference equations with minima for dynamical systems Introduces innovative approaches capable of enabling timely and precise control

Autorentext

Shyam Kamal received his Bachelor's degree in Electronics and Communication Engineering from the Gurukula Kangri Vishwavidyalaya Haridwar, Uttarakhand, India in 2009, and Ph.D. in Systems and Control Engineering from the Indian Institute of Technology Bombay, India in 2014. From 2015 to 2016, he was with the Department of Systems Design and Informatics, Kyushu Institute of Technology, Japan as a Project Assistant Professor. Currently, he is an Associate Professor in the Department of Electrical Engineering., Indian Institute of Technology (BHU) Varanasi, India. He has published one monograph, two book chapters and 105 journal articles and conference papers. His research interests include the areas of nonlinear control and its applications. Particularly he is working on fractional-order systems, contraction analysis, discrete and continuous higher-order sliding mode control and multi-agent systems. He has received excellence awards in Ph.D. thesis from IIT Bombay in 2015 for his thesis Sliding Mode Control of Fractional-order Systems and INAE Young Engineer Award in 2019 for his research work. He is now an INAE Young Associate. He has also received honorary appointment as a Visiting professor from RMIT Melbourne Australia in July 2017 and in the duration of November and December 2019 and Visiting Professor from Harbin Institute on Technology China in August 2019.

Parijat Prasun obtained his B.Tech. degree in Electrical and Electronics Engineering from the College of Engineering Roorkee, Uttarakhand, India, in 2015. He earned his M.Tech. degree in Electrical Engineering with a specialization in Power and Energy Systems from the National Institute of Technology Meghalaya, India, in 2018. He later completed his Ph.D. in Control Systems at the Indian Institute of Technology (BHU) Varanasi, India, in 2024. His research interests include nonlinear control, discrete sliding mode control, and finite- and fixed-time control design.

Inhalt

A Journey from Classical Control towards Variable Structure Control.- Mathematical Preliminaries.- Continuous-Time Sliding Mode Control: Foundations and Transition to Digital Implementation.- A Difference Equation with Minima based Reaching Law for Discrete Sliding Mode Control.- Reaching Laws Based on Difference Equations with Minima and Rate-Regulatory Function.- A Lyapunov Characterization of Difference Equation with Minima based Discrete Sliding Mode Control.- DEM based Discrete-Time Twisting-like Algorithm and Discrete-Time Super-Twisting-like Algorithm.- Application with Simulation and Experimental Validation.- Conclusions and Future Perspectives.