Synthesis of adaptive gain robust model-following/tracking controllers for uncertain systems with multiple unknown dead-zone inputs via piecewise Lyapunov functions

ABSTRACT

This paper considers a design problem of adaptive gain robust model-following/tracking controllers for a class of uncertain systems with multiple unknown dead-zone inputs via piecewise Lyapunov functions. The parameters for dead-zone characteristics are assumed to be unknown, and an adaptive dead-zone inverse method is applied so as to reduce the effect for dead-zone non-linearities. Moreover, for the purpose of reducing the effects of matched and mismatched uncertainties, compensation inputs are introduced. The proposed adaptive gain robust model-following/tracking controller can achieve that the tracking error asymptotically converges to zero. In this paper, by using piecewise Lyapunov functions, we show sufficient conditions for the existence of the proposed adaptive gain robust model-following/tracking controller. Finally, an example is given to demonstrate the effectiveness of the proposed controller design method.

KEYWORDS:

• Dead-zone
• piecewise Lyapunov functions
• adaptive gain robust model-following/tracking controller
• LMI (linear matrix inequality)
• adaptive dead-zone inverse method

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

Satoshi Hayakawa

Satoshi Hayakawa has received the B.Eng. and M. Eng. degrees from Tokyo City University, Tokyo, Japan, in 2021 and 2023, respectively. Currently, he has joined SCSK Corporation in 2023. His research interest includes robust control strategies for uncertain dynamical systems with constraints.

Takuya Nakagawa

Takuya Nakagawa has received the B.Eng. degree from the Tokyo City University, Tokyo, Japan, in 2022. Currently, he is a master course student of the Graduate School of Integrative Science and Engineering at Tokyo City University. His research interest includes robust control for uncertain dynamical systems and formation control for multi-agent systems.

Kazuma Hasegawa

Kazuma Hasegawa has received the B. and M. Degrees in Engineering from the Tokyo City University, Tokyo, Japan, in 2021 and 2023. Currently, he works for a company.

Hidetoshi Oya

Hidetoshi OYA has received the B.Eng., M.Eng. and D.Eng. degrees from the University of Electro-Communications, Tokyo Japan, in 1996, 1998 and 2003, respectively. From 2003 to 2006, he was a Research Associate in the Dept. of Systems Eng. at the same university. From 2006 to 2009, he was an Assistant Professor at Shonan Institute of Technology, Kanagawa, Japan. From 2009 to 2016, he was an Associate Professor at Tokushima University, Tokushima, Japan. Since 2016, he has been with a full professor in the Department of Computer Science at Tokyo City University. He has received 2011 Commissioner Award from The Fire and Disaster Management Agency of the Ministry of Internal Affairs and Communications. His current research interests are robust/adaptive control for uncertain dynamical systems and bio-signal processing.

Yoshikatsu Hoshi

Yoshikatsu Hoshi received his Ph.D. degree in Engineering from Tokyo Institute of Technology in 2005. He was an Assistant Professor in the Faculty of Engineering, Musashi Institute of Technology from 2005 to 2008. Since 2008, he has been a Senior Lecturer in the Faculty of Knowledge Engineering (currently Faculty of Information Technology), Tokyo City University, Japan. His current research interests include Systems and Control Theory and its Applications. He is a member of IEEE, SICE, RSJ and ISCIE.