Leader-following consensus for single-integrator multi-agent systems with multiplicative noises in directed topologies

Abstract

This paper proposes a leader-following consensus control for continuous-time single-integrator multi-agent systems with multiplicative measurement noises under directed fixed and switching topologies. The consensus controller is developed by combining the graph theory and stochastic tools. The control input for each agent relies on its own state and its neighbours’ states corrupted by noises, the noises are considered proportional to the relative distance between agents, both of the noisy case and the noise-free case are studied, and conditions to achieve mean square convergence under noisy measurement and asymptotic convergence in absence of noises are derived. Finally, in order to prove the validity of the consensus control, some simulations were carried out.

Keywords:

• single-integrator
• multi-agent systems
• leader-following
• multiplicative noises
• directed topologies

Acknowledgements

The authors would like to sincerely thank the editors and the reviewers for their valuable comments and suggestions, which helped significantly to improve the quality of this paper.

Additional information

Funding

This work was supported by the National Nature Science Foundation of P.R. China [grant number 61074031] and the programme for Changjiang scholars and innovative Research Team in university under Grant IRT [grant number 1208].

Notes on contributors

Sabir Djaidja

Djaidja Sabir was born in 1985. He received the BE degree in control system from ENPEI and EMP, Algiers, Algeria in 2009. He is currently a PhD student with the school of automation in Beijing Institute of Technology, Beijing, China. His research interests include control of multi-agent systems, stochastic systems, optimal cooperative control, etc.

Qinghe Wu

QingHe Wu received the BE degree in electrical engineering from Huazhong University of Science and Technology, Wuhan, China in 1982, and the post-graduate diploma and the Dr Tech. Sci. degrees from the Swiss Federal Institute of Technology (ETHZ), Zurich, Switzerland, in 1984 and 1990, respectively. From 1986 to 1994, he has been assistant and oberassistant with the Institute of Automatic Control, ETHZ. Since 1995, he has been with the Beijing Institute of Technology, Beijing, China, where he has been professor since 1997. He was a Visiting Research Fellow from July 2002 to June 2003 in Akita Prefectural University, Akita, Japan. His research interests include H-infinity control and robust control theory.