Robust H_∞ containment control for uncertain multi-agent systems with inherent nonlinear dynamics

Abstract

This article considers the distributed containment control problem of nonlinear multi-agent systems subject to parameter uncertainties and external disturbances. An appropriate controlled output function is defined to quantitatively analyse the effect of external disturbances on the containment control problem. By employing robust H_∞ control approach, sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to ensure that all followers asymptotically converge to the convex hull spanned by the leaders with the prescribed H_∞ performance under fixed topology. Moreover, the unknown feedback matrix of the proposed protocol is determined by solving only two LMIs with the same dimensions as a single agent. Finally, a numerical example is provided to demonstrate the effectiveness of our theoretical results.

Keywords:

• multi-agent systems
• robust H_∞ control
• containment control
• inherent nonlinear dynamics
• parameter uncertainties

Acknowledgements

The authors would like to thank the anonymous reviewers for their constructive comments and valuable suggestions which greatly improved the presentation of this article.

Additional information

Funding

This work was supported by the National Basic Research Program of China (973 Program) [grant number 2012CB821200], [grant number 2012CB821201]; the National Natural Science Foundation of China [grant number 61134005], [grant number 60921001], [grant number 61327807].

Notes on contributors

Ping Wang

Ping Wang was born in Shannxi, China. She received her BS degree in applied mathematics from Northwestern University, Xi’an, China, in 2001, and her MS degree in control theory and control engineering from Beihang University (BUAA), Beijing, China, in 2006. Since 2009, she has been working towards her PhD degree in control theory and control engineering at Beihang University (BUAA), Beijing, China. Her current research interests include consensus and cooperative control of multi-agent systems.

Yingmin Jia

Yingmin Jia was born in Shandong, China. He received his BS degree in control theory from Shandong University, Ji’nan, China, in January 1982, and his MS and PhD degrees both in control theory and applications from Beihang University (BUAA), Beijing, China, in 1990 and 1993, respectively. From 1982 to 1987, he was with the Department of Electrical Engineering at Henan Polytechnic University, Jiaozuo, China. In 1993, he joined the Seventh Research Division at Beihang University, where he is currently a professor of automatic control. From February 1995 to February 1996, he was a visiting professor with the Institute of Robotics and Mechatronics of the German Aerospace Center (DLR), Oberpfaffenhofen, Germany. He held an Alexander von Humboldt (AvH) Research Fellowship with the Institute of Control Engineering at the Technical University Hamburg-Harburg, Hamburg, Germany, from December 1996 to March 1998, and a JSPS Research Fellowship with the Department of Electrical and Electronic Systems at the Osaka Prefecture University, Osaka, Japan, from March 2000 to March 2002. He was a visiting professor with the Department of Statistics at the University of California, Berkeley, from December 2006 to March 2007. His current research interests include robust control, adaptive control and intelligent control, and their applications in industrial processes and vehicle systems. He is an author and a co-author of numerous papers and of the book Robust H_∞ Control (Science Press, 2007).