Switching controller for nonlinear systems: an invariant [K, KL] sector approach*

Abstract

This paper addresses the invariant $\mathcal{[}\mathcal{K}\mathcal{,}\mathcal{K}\mathcal{L}\mathcal{]}$ sector as a special class of $\mathcal{[}\mathcal{K}\mathcal{,}\mathcal{K}\mathcal{L}\mathcal{]}$ sector that holds the invariant characteristics with some appropriate control input, i.e. the energy of the system drastically decreases and state trajectory always remains inside the sector once it moves into it by the suitable control signal. The analysis of the nonlinear sector is regarded in comparison function prospective to outreach the property of uniformity. Here, the construction of $\mathcal{[}\mathcal{K}\mathcal{,}\mathcal{K}\mathcal{L}\mathcal{]}$ sector and invariant $\mathcal{[}\mathcal{K}\mathcal{,}\mathcal{K}\mathcal{L}\mathcal{]}$ sector relies on the selection of well-suited control-Lyapunov function. The switching control with invariant $\mathcal{[}\mathcal{K}\mathcal{,}\mathcal{K}\mathcal{L}\mathcal{]}$ sector is designed to ensure the state trajectories move inside the nonlinear sector in finite-time and stay inside for all future time. Finally, the effectiveness of the proposed algorithm is illustrated with real physical examples.

Keywords:

• $\mathcal{[}\mathcal{K}\mathcal{,}\mathcal{K}\mathcal{L}\mathcal{]}$ sector
• invariant $\mathcal{[}\mathcal{K}\mathcal{,}\mathcal{K}\mathcal{L}\mathcal{]}$ sector
• control-Lyapunov function
• switching control law
• asymptotic stability

Disclosure statement

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

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article.

Additional information

Notes on contributors

Ankit Sachan

Ankit Sachan received the Ph.D. (Engg.) degree in electrical engineering from IIT BHU Varanasi, India, in 2019. He worked as visiting scholar at Harbin institute of technology, Shenzhen, China, in 2018 and 2019. Presently, he is working as an assistant professor at Hiroshima University, Japan. His research interests include nonlinear sector design, multiagent systems, implicit Euler discretization, and Lyapunov stabilization.

Neeraj Gupta

Neeraj Gupta received his master's degree in electrical engineering, specializing in Control & instrumentation, from Motilal Nehru National Institute of Technology, Allahabad, India, in 2015. Received his graduation degree in Electronics & Instrumentation Engineering from Uttar Pradesh Technical University in 2007, Lucknow, India. He has been associated with Anand Engineering College, Agra, India, as an Assistant Professor. Currently, he is working in the capacity of Assistant Professor at Ajay Kumar Garg Engineering College, Ghaziabad, India. His research interests include model order reduction, nonlinear control design, and stability preservation algorithms.

Sunil Kumar

Sunil Kumar was born in Uttar Pradesh, India, in 1992. He received the M.Tech. degree in Instrumentation and Control Engineering from the Electrical and Instrumentation Engineering Department, Sant Longowal Institute of Engineering & Technology, Longowal, Punjab, India, in 2018. He is currently pursuing the Ph.D. degree in Electrical Engineering with IIT (BHU) Varanasi, India. His research interests include observers, guidance law, continuous nonlinear control, rated convergence of systems and Lyapunov analysis.

Kranthi Kumar Deveerasetty

Kranthi Kumar Deveerasetty received a bachelor's degree in electrical and electronics engineering from Andhra University, A.P, India, in 2008. He completed his M.Tech and Ph.D. degrees in electrical engineering from the Indian Institute of Technology (BHU), Varanasi, India, in 2010 and 2016, respectively. He worked as a Post-doctoral Fellow at Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Shenzhen, China, from August 2017 to November 2019. He is currently working as a Post-Doctoral Fellow at the Kochi University of Technology, Japan. He has published 33 journal articles and conference papers. He received the best application paper award at the 11th international conference on modelling, identification, and control (ICMIC 2019). He is a life member of the System Society of India (SSI), the Japan Society of Aeronautical and Space Sciences, a professional member of ACDOS, and an IEEE member. His research interests include model order reduction, the stability of interval systems, modelling and control design for UAVs, and Sliding mode control.