Distributed cooperative stabilisation of continuous-time uncertain nonlinear multi-agent systems

Abstract

This paper addresses the distributed cooperative stabilisation problem of continuous-time uncertain nonlinear multi-agent systems. By approximating the uncertain dynamics using neural networks, a distributed adaptive cooperative controller, based on the state information of the neighbouring agents, is proposed. The control design is developed for any undirected connected communication topologies without requiring the accurate model of each agent. This result is further extended to the output feedback case. An observer-based distributed cooperative controller is devised and a parameter dependent Riccati inequality is employed to prove stability of the overall multi-agent systems. This design is less complex than the other design methods and has a favourable decouple property between the observer design and the controller design for uncertain nonlinear multi-agent systems. For both cases, the developed controllers guarantee that all signals in the closed-loop network are uniformly ultimately bounded, and the states of all agents cooperatively converge to a small neighbourhood of origin. A comparative study is given to show the efficacy of the proposed method.

Keywords:

• distributed control
• robust stabilisation
• neural networks
• uncertain multi-agent system

Acknowledgements

The authors would like to thank the reviewers for their constructive comments and suggestions to improve the quality of the paper. They also thank Prof. Yiguang Hong for his valuable suggestions on this paper. This work was supported in part by the National Nature Science Foundation of China under Grant Nos. 61074017, 61273137 and 51209026, by the Program for Liaoning Excellent Talents in Universities under Grant No. 2009R06 and by the Fundamental Research Funds for the Central Universities.

Additional information

Notes on contributors

Zhouhua Peng

Zhouhua Peng received the BA degree, the MA degree and the PhD degree from Dalian Maritime University, Dalian, China, in 2005, 2008 and 2011, respectively. Since 2011, he has been a Lecturer in Department of Marine Electric Engineering, School of Marine Engineering, Dalian Maritime University. His research interests are cooperative control of multi-agent systems and adaptive control.

Dan Wang

Dan Wang received the BEng degree in Industrial Automation Engineering from Dalian University of Technology, Dalian, in 1982, the MEng degree in Marine Automation Engineering from Dalian Maritime University, Dalian, China, in 1987, and the PhD degree in Mechanical and Automation Engineering from The Chinese University of Hong Kong, Shatin, Hong Kong, in 2001. He was with Dalian Maritime University from 1987 to 2001, as a Lecturer from 1987, an Associate Professor from 1992, and a Professor from 2001. From 2001 to 2005, he was a Research Scientist with Temasek Laboratories, National University of Singapore, Singapore. Since 2006, he has been with Dalian Maritime University, where he is currently a Professor with the Department of Marine Electrical Engineering, School of Marine Engineering. His research interests include nonlinear control theory and applications, neural networks, adaptive control, robust control, fault detection and isolation and system identification. He is the author of over 70 refereed publications.

Gang Sun

Gang Sun received the BS degree in Mathematics Education from Tonghua Normal University, Tonghua, China, the MS degree in Applied Mathematics from Dalian Maritime University, Dalian, China, in 2001 and 2008, respectively. He is currently working towards the PhD degree in Control Theory and Control Engineering at Dalian Maritime University, Dalian, China. His current research interests include nonlinear systems adaptive control and neural network control.

Hao Wang

Hao Wang received the BE degree from the School of Physics, Liaoning University, Shenyang, China, in 2009, the ME degree from the Information Science and Technology College, Dalian Maritime University, Dalian, China, in 2011. He is now pursuing his PhD degree in Control Theory and Control Engineering at Dalian Maritime University. His current research interests include cooperative control of marine surface vessels and adaptive control.