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Abstract
This paper investigates consensus of fractional-order multi-agent systems (MASs) with a reference state. First, a consensus control law with a constant reference state is given using graph theory and stability analysis of fractional-order. Then, a general control law and a particular one for consensus of fractional-order MASs with a time-varying reference state are proposed. Next, the above control laws are extended to solve formation tracking problem. Finally, several simulations are presented to verify the effectiveness of the obtained results.
Acknowledgements
The authors want to thank the support of National Nature Science Foundation of China (No. 11371049), and also thank the editor and the anonymous reviewers for their valuable comments and suggestions that have improved the presentation of this paper.
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Funding
Notes on contributors
Jing Bai
Jing Bai received her BS degree at the Department of Mathematical Science, Beijing jiaotong University, China, in 2010, and MS degree at the Department of Mathematical Science, Beijing jiaotong University, China, in 2012. She is currently pursuing her PhD degree at CRIStAL, UMR CNRS 9189, Ecole Centrale de Lille, France. Her research interests focus on formation control of multi-agent systems, consensus of multi-agent systems, chaos control and synchronisation.
Guoguang Wen
Guoguang Wen received his BS degree at the Department of Mathematical Science, Inner Mongolia University, China, in 2007, MS degree at the Department of Mathematics, School of Science, Beijing Jiaotong University, China, in 2009, and PhD degree at LAGIS, UMR 8219 CNRS, Ecole Centrale de Lille, France, in 2012. Currently, he is working at the Department of Mathematics, School of Science, and Beijing Jiaotong University, China. His research interests focus on cooperative control for multi-agent systems, control of multi-robots formation, nonlinear dynamics and control, and neural networks.
Ahmed Rahmani
Ahmed Rahmani received his PhD degree in automatic control engineering and computer science from Lille University of Technology and Ecole Centrale de Lille, France, in 1993. He has been an associate professor at Ecole Centrale de Lille since 1995. His current research interests are in graphic methods and tools for analysis and control of complex systems: application to mobile robotics and intelligent transport.
Xing Chu
Xing Chu received his BS degree at the Department of Automotive Engineering, Kunming University of Science and Technology, China, in 2011, and MS degree at the Department of Mechanical Engineering, Hunan University, China, in 2014. He is currently pursuing his PhD degree at CRIStAL, UMR CNRS 9189, Ecole Centrale de Lille, France. His research interests focus on distributed cooperative control of multi-agent/vehicle systems and autonomous vehicle.
Yongguang Yu
Yongguang Yu received his MS degree at the Department of Mathematical Science, Inner Mongolia University, China, in 2001, and PhD degree at the Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, China, in 2004. From 2007 to 2009, he was a research fellow at the City University of Hong Kong, China. Since 2010, he has been a professor with the Department of Mathematics, School of Science, and Beijing Jiaotong University, China. His research interests include chaotic dynamics, Chaos control and synchronisation, complex networks, nonlinear control and multi-agent systems.