H∞ robust synchronisation of nonlinear multi-agent systems with sampled-data information

ABSTRACT

A distributed ${\mathcal{H}}_{\infty }$ controller is presented for nonlinear multi-agent systems in this paper. The nonlinear dynamics of each agent are characterised by the Lipschitz condition. With the appearance of system uncertainty and external disturbance, a sampled-data feedback control protocol is carried out along the Lyapunov functional approach. Meanwhile, a state observer is incorporated to reinforce the capability of the proposed control strategy. It is demonstrated that the synchronisation of the networked nonlinear agents are essentially achieved with locally shared information. Remarkably, the system uncertainty and external disturbance are considered in the controller design and the influence caused by ${\mathcal{L}}_2$-bounded disturbance is minimised effectively. Furthermore, the control gain and observer gain derivation are equivalently transformed to a convex optimisation problem, which is solved by an iterative algorithm developed based on the sufficient conditions of system stability. The effectiveness of the proposed controller is verified by simulations.

KEYWORDS:

• Distributed control
• Lipschitz nonlinear system
• sampled-data control
• ${\mathcal{H}}_{\infty }$ robust control

Acknowledgments

The authors would like to thank the anonymous reviewers for their valuable comments and suggestions, which have significantly improved the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Lei Liu

Lei Liu received his BSc and MSc degrees from Jilin University, Changchun, China, in 2007 and 2009, respectively. He is currently working towards his Ph.D. degree at the Department of Earth and Space Science and Engineering, York University, Toronto, Canada. His research interests include cooperative control of multi-agent system, robust control, sampled-data control, nonlinear control and fault diagnosis.

Jinjun Shan

Jinjun Shan received his BSc, MSc, and Ph.D. degrees all in spacecraft design from Harbin Institute of Technology, Harbin, China, in 1997, 1999 and 2002, respectively. He is currently an associate professor of space engineering in the Department of Earth and Space Science and Engineering, York University, Toronto, Canada. Prior to his appointment in York, he was a post-doctoral fellow at the University of Toronto Institute for Aerospace Studies (UTIAS) and a research assistant at the City University of Hong Kong. Dr. Shan was awarded the Alexander von Humboldt (AvH) Research Fellowship for Experienced Researchers and JSPS Invitation Fellowship in 2012. He is a professional engineer in Ontario since 2007. His current research interests include dynamics, control and navigation.