Leaderless consensus for the fractional-order nonlinear multi-agent systems under directed interaction topology

ABSTRACT

Leaderless consensus for the fractional-order nonlinear multi-agent systems is investigated in this paper. At the first part, a control protocol is proposed to achieve leaderless consensus for the nonlinear single-integrator multi-agent systems. At the second part, based on sliding mode estimator, a control protocol is given to solve leaderless consensus for the the nonlinear single-integrator multi-agent systems. It shows that the control protocol can improve the systems’ convergence speed. At the third part, a control protocol is designed to accomplish leaderless consensus for the nonlinear double-integrator multi-agent systems. To judge the systems’ stability in this paper, two classic continuous Lyapunov candidate functions are chosen. Finally, several worked out examples under directed interaction topology are given to prove above results.

KEYWORDS:

• Leaderless consensus
• fractional-order nonlinear MASs
• sliding mode estimator
• Lyapunov candidate function

Acknowledgments

This work was supported by National Natural Science Foundation of China [grant number 61703035]; China Postdoctoral Science Foundation [grant number 2017M610772]; Fundamental Research Funds for the Central Universities [grant number FRF-TP-16-011A1]; National Key R&D Program of China [grant number 2017YFF0207400].

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

China Postdoctoral Science Foundation [grant number 2017M610772]. National Natural Science Foundation of China [grant number 61703035]. Fundamental Research Funds for the Central Universities [grant number FRF-TP-16-011A1]. National Key R&D Program of China [grant number 2017YFF0207400].

Notes on contributors

Jing Bai

Jing Baireceived  the B.S. degree and master degree at the Department of Mathematical Science, Beijing jiaotong University, China in 2010 and 2012, and the PhD degree at CRIStAL, Ecole Centrale de Lille, France in 2015. She is currently working at School of Mathematics and Physics, University of Science and Technology, Beijing, China. Her research interest focuses on formation control of multi-agent systems, consensus of multi-agent, Chaos control and synchronization.

Guoguang Wen

Guoguang Wen received the B.S. degree at the Department of Mathematical Science, Inner Mongolia University, China in 2007, the MS degree at the Department of Mathematics, School of Science, Beijing Jiaotong University, China in 2009, and the PhD degree at CRIStAL, 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 interest focuses on cooperative control for multi-agent systems, control of multi-robots formation, nonlinear dynamics and control, neural networks.

Ahmed Rahmani

Ahmed Rahmani received his Ph.D. degree in Automatic Control Engineering and Computer Science from Lille University of Technology and Ecole Centrale de Lille, France in 1993. He is a full professor at Ecole Centrale de Lille. His current research interests are in graphic methods and tools for analysis and control of complex systems: application to mobile robotics and intelligent transport.