Design of switched high-gain observer for nonlinear systems

Abstract

This paper proposes a switched high-gain observer with the desired convergence time for nonlinear systems. The proposed approach is based on a switching structure that plays an essential role, resulting in desired convergence and avoiding the observer's states' singularity. The main feature of this paper is that the observer's state converges to the actual state within the desired convergence time, where the convergence time is invariant with respect to the initial errors of the system. Moreover, the convergence time can be chosen at the will of the designer. The proposed method's results involve the high-gain principle and recent advancements in fixed-time observers. Further, the system's gain varies linearly (rather than square) with the order of the system. Using the Lyapunov theorem, the stability analysis of the proposed approach is investigated. Finally, two examples, (i) the Van der Pol oscillator circuit and (ii) Genesio–Tesi chaotic system demonstrate the efficacy of the proposed approach.

Keywords:

• Nonlinear systems
• high-gain observer
• finite-time convergence
• fixed-time convergence

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

Funding

This paper was supported in part by the Shenzhen Science and Technology Program under Grant KQTD20190929172545139, and 20200803230628015, and patially supported by GuangDong Basic and Applied Basic Research Foundation [2022A1515011521].

Notes on contributors

Sunil Kumar

Sunil Kumar 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.

Anil Kumar Pal

Anil Kumar Pal (Student Member, IEEE) received the bachelor’s degree in electronics and telecommunication engineering from the Bhilai Institute of Technology, Durg, India, in 2008, and the M.Tech. degree with specialization in control systems from the Indian Institute of Technology (BHU) Varanasi, Varanasi, India, in 2013, where he received the Ph.D. degree. He is currently a Postdoctoral Associate at the University of Calgary, Alberta, Canada. His research interests include nonlinear control theory, finite-time control, multiagent systems, and sliding-mode control.

Shyam Kamal

Shyam Kamal (Member, IEEE) received the bachelor’s degree in electronics and communication engineering from the Gurukula Kangri Vishwavidyalaya Haridwar, Uttrakhand, India, in 2009, and the Ph.D. degree in systems and control engineering from the Indian Institute of Technology Bombay, Mumbai, India, in 2014. From 2014 to 2016, he was with the Department of Systems Design and Informatics, Kyushu Institute of Technology, Kitakyushu, Japan, as a Project Assistant Professor. He is currently an Assistant Professor with the Department of Electrical Engineering, Indian Institute of Technology (BHU) Varanasi, Varanasi, India. He has published one monograph and 64 journal articles and conference papers. His research interests include the areas of fractional-order systems, contraction analysis, discrete, and continuous higher order sliding-mode control. Dr. Kamal has received excellence in Ph.D. Thesis Award from IIT Bombay in 2015 for his thesis “Sliding Mode Control of Fractional-order Systems” and the INAE Young Engineer Award in 2019 for his research work. He is currently an INAE Young Associate.

Xiaogang Xiong

Xiaogang Xiong (Member, IEEE) received the Ph.D. degree in mechanical and science engineering from Kyushu University, Fukuoka, Japan, in 2014. From 2014 to 2015, he was a Researcher with the Kyushu Institute of Technology, Iizuka, Japan. From 2015 to 2016, he was a Research Fellow with Singapore Institute of Manufacturing Technology, Singapore. He is currently an Assistant Professor with the Department of Mechanical Engineering and Automation, Harbin Institute of Technology (Shenzhen), Shenzhen, China. His research interests include human–robot coordination, circuit and system, nonsmooth system, and robot real-time control.