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Allocating Minimum Number of Leaders for Seeking Consensus over Directed Networks with Time-varying Nonlinear Multi-agents

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  • Control Theory and Applications
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Abstract

In this paper, we consider how to determine the minimum number of leaders with allocation and how to achieve consensus over directed networks consisting of time-varying nonlinear multi-agents. Firstly, the problem of finding minimum number of leaders is formulated as a minimum spanning forest problem, i.e., finding the minimum population of trees in the network. By introducing a toll station connecting with each agent, this problem is converted to a minimum spanning tree problem. In this way, the minimum number of leaders is determined and these leaders are found locating at the roots of each tree in the obtained spanning forest. Secondly, we describe a virtual leader connected with the allocated leaders, which indicates that the number of edges connected the follower agents with the virtual leader is the least in an arbitrary directed network. This method is different from the existing consensus problem of redundant leaders or edges that connect the follower with one leader in special networks. A distributed consensus protocol is revisited for achieving final global consensus of all agents. It is theoretically shown that such a protocol indeed ensures consensus. Simulation examples in real-life networks are also provided to show the effectiveness of the proposed methodology. Our works enable studying and extending application of consensus problems in various complex networks.

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Author information

Authors and Affiliations

  1. School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, China

    Leitao Gao & Guangshe Zhao

  2. Qingdao R&D Institute, Xi’an Jiaotong University, Qingdao, Shandong, 266300, China

    Guangshe Zhao

  3. Department of Precision Instrument, Tsinghua University, Beijing, 100084, China

    Guoqi Li & Yuming Liu

  4. School of Automation, Chongqing University, Chongqing, 400044, China

    Jiangshuai Huang

  5. School of EEE, Nanyang Technological University, 639798, Singapore, Singapore

    Changyun Wen

Authors
  1. Leitao Gao
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  2. Guangshe Zhao
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  3. Guoqi Li
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  4. Yuming Liu
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  5. Jiangshuai Huang
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  6. Changyun Wen
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Corresponding authors

Correspondence to Guangshe Zhao or Guoqi Li.

Additional information

Recommended by Associate Editor Bin Jiang under the direction of Editor Hamid Reza Karimi. The work was supported partially by National Science Foundation of China (No. 61603209, 61876215), and National Basic Research Program of China (973 Program, Grant No. 2015CB057406), and Independent Research Plan of Tsinghua University (20151080467).

Leitao Gao received his Bachelor degree from Taiyuan University of Technology, Taiyuan, China, in 2014. He is a Ph.D student in School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, China, from 2014. His research interests include complex networks, multi-agent system control.

Guangshe Zhao is currently a professor in School of Electronic and Information Engineering, Xi’an Jiaotong University. His research interests include complex networks, fuzzy systems, intelligent control and multi-agent system control.

Guoqi Li received the B.Eng. and M.Eng. degrees from Xi’an University of Technology and Xi’an Jiaotong University, P. R. China, in 2004 and 2007, respectively, and his Ph.D. degree from Nanyang Technological University, Singapore in 2011. He was a Scientist with Data Storage Institute and Institute of High Performance Computing, Agency for Science, Technology and Research (A*STAR), Singapore, from September 2011 to March 2014. Since March 2014, he has been with the Department of Precision Instrument, Tsinghua University, P. R. China, where he is currently a Associate Professor. His current research interests include brain inspired computing, complex systems, neuromorphic computing, machine learning and system identification. Dr. Li has published more than 60 journal and conference papers. He services as a reviewer for a number of international journals and has also been actively involved in professional services such as serving as an International Technical Program Committee member, and a Track Chair for international conferences.

Yuming Liu was born in China in 1998. He is an undergraduate student of Center for Brain Inspired Computing Research in Tsinghua University. He majors in measurement and control technology. His research interests are brain-inspired computing and graph theory.

Jiangshuai Huang received his B.Eng. and M.Sc. degrees from School of Automation, Huazhong University of Science and Technology, Wuhan, China, in July 2007 and August 2009, respectively, and his Ph.D. degree from Nanyang Technological University in 2015. He is currently with the Key Laboratory of Dependable Service Computing in Cyber Physical Society, Ministry of Education, China and with School of Automation, Chongqing University, Chongqing 400044, China. His research interests include adaptive control, nonlinear systems control, underactuated mechanical system control and multi-agent system control.

Changyun Wen received his B.Eng. degree from Xi’an Jiaotong University, China in 1983 and his Ph.D. degree from the University of Newcastle, Australia in 1990. From August 1989 to August 1991, he was a Postdoctoral Fellow at University of Adelaide. Since August 1991, he has been with School of EEE, Nanyang Technological University, where he is currently a Full Professor. His main research activities are control systems and applications, intelligent power management system, smart grids, model based online learning and system identification. He is an Associate Editor of a number of journals including Automatica, IEEE Transactions on Industrial Electronics and IEEE Control Systems Magazine. He is the Executive Editorin- Chief, Journal of Control and Decision. He served the IEEE Transactions on Automatic Control as an Associate Editor from January 2000 to December 2002. He has been actively involved in organizing international conferences playing the roles of General Chair, General Co-Chair, Technical Program Committee Chair, Program Committee Member, General Advisor, Publicity Chair and so on. He received the IES Prestigious Engineering Achievement Award 2005 from the Institution of Engineers, Singapore (IES) in 2005. He is a Fellow of IEEE, a member of IEEE Fellow Committee from 2011 to 2013 and a Distinguished Lecturer of IEEE Control Systems Society from February 2010 to February 2013.

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Gao, L., Zhao, G., Li, G. et al. Allocating Minimum Number of Leaders for Seeking Consensus over Directed Networks with Time-varying Nonlinear Multi-agents. Int. J. Control Autom. Syst. 17, 57–68 (2019). https://doi.org/10.1007/s12555-018-0057-2

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