Measurement feedback control of nonlinear systems: a small-gain approach

Abstract

This paper presents a new tool for feedback control design of nonlinear systems in the presence of non-smooth measurement errors. We introduce a small-gain design approach to robust control of nonlinear uncertain systems with disturbed measurement. As a design ingredient, a modified gain assignment technique for measurement feedback control of nonlinear uncertain systems is proposed. Through a recursive control design approach, the closed-loop system is transformed into a network of input-to-state stable (ISS) systems and the influences of the measurement errors are represented by ISS gains. The feedback control objective is achieved by applying the cyclic-small-gain theorem to the closed-loop system. Moreover, event-triggered control of nonlinear systems is studied in a unified framework of measurement feedback control.

Keywords:

• Nonlinear systems
• measurement error
• nonlinear small-gain theorem
• input-to-state stability

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 A function $h:\mathcal{X}\to \mathcal{Y}$ with $\mathcal{X}\subseteq {\mathbb{R}}^n$ and $\mathcal{Y}\subseteq {\mathbb{R}}^m$ is said to be Lipschitz on compact sets, if h is Lipschitz on every compact set $\mathcal{D}\subseteq \mathcal{X}$.

Additional information

Funding

This work was supported in part by NSFC grants 61633007 and 61533007, in part by NSF grants ECCS-1501044 and EPCN-1903781, and in part by State Key Laboratory of Intelligent Control and Decision of Complex Systems at BIT.

Notes on contributors

Tengfei Liu

Tengfei Liu received the B.E. degree in automation in 2005 and the M.E. degree in control theory and control engineering in 2007, both from South China University of Technology, and the Ph.D. degree in engineering from RSISE, the Australian National University, in 2011. He was a postdoc with faculty fellowship at Polytechnic Institute of New York University from 2011 to 2013. He has been a faculty member at Northeastern University, China since 2014. His research interests include stability and control of interconnected nonlinear systems.

Zhong-Ping Jiang

Zhong-Ping Jiang received the B.Sc. degree in mathematics from the University of Wuhan, Wuhan, China, in 1988, the M.Sc. degree in statistics from the University of Paris XI, France, in 1989, and the Ph.D. degree in automatic control and mathematics from the ParisTech-Mines, France, in 1993, under the direction of Prof. Laurent Praly.

Currently, he is a Professor of Electrical and Computer Engineering at the Tandon School of Engineering, New York University. His main research interests include stability theory, robust/adaptive/distributed nonlinear control, adaptive dynamic programming and their applications to information, mechanical and biological systems. He is coauthor of four books Stability and Stabilization of Nonlinear Systems (with Dr I. Karafyllis, Springer, 2011), Nonlinear Control of Dynamic Networks (with Drs T. Liu and D.J. Hill, Taylor & Francis, 2014), Robust Adaptive Dynamic Programming (with Y. Jiang, Wiley-IEEE Press, 2017) and Nonlinear Control Under Information Constraints (with T. Liu, Science Press, 2018).

Dr Jiang is a Deputy Editor-in-Chief of the Journal of Control and Decision and of the IEEE/CAA Journal of Automatica Sinica, and has served as senior/associate/guest editor for several journals. Dr Jiang is a recipient of the prestigious Queen Elizabeth II Fellowship Award from the Australian Research Council (1998), the CAREER Award from the U.S. National Science Foundation (2001), JSPS Invitation Fellowship from the Japan Society for the Promotion of Science (2005), the Distinguished Overseas Chinese Scholar Award from the NSF of China (2007), and the Chair Professorship by the Ministry of Education of China (2009).

Prof. Jiang is a Fellow of the IEEE, a Fellow of the IFAC, and a Clarivate Analytics Highly Cited Researcher.