Received: 30 March 2016 Revised: 4 August 2017 Accepted: 7 January 2018
Adaptive bipartite consensus control of high-order
multiagent systems on coopetition networks
School of Automation Engineering,
University of Electronic Science and
Technology of China, Chengdu, China
Department of Mechanical and
Biomedical Engineering, City University
of Hong Kong, Kowloon, Hong Kong
Jiangping Hu, School of Automation
Engineering, University of Electronic
Science and Technology of China,
Chengdu 611731, China.
National Natural Science Foundation of
China, Grant/Award Numbers: 61473061,
71503206 and 61104104; Program for New
Century Excellent Talents in University,
Grant/Award Number: NCET-13-0091;
Research Grants Council of the Hong
Kong Special Administrative Region of
China, Grant/Award Number: Project
In this paper, a bipartite consensus problem is considered for a high-order
multiagent system with cooperative-competitive interactions and unknown
time-varying disturbances. A signed graph is used to describe the interaction
network associated with the multiagent system. The unknown disturbances are
expressed by linearly parameterized models, and distributed adaptive laws are
designed to estimate the unknown parameters in the models. For the case that
there is no exogenous reference system, a fully distributed adaptive control law
is proposed to ensure that all the agents reach a bipartite consensus. For the
other case that there exists an exogenous reference system, another fully dis-
tributed adaptive control law is also developed to ensure that all the agents
achieve bipartite consensus on the state of the exogenous system. The stability
of the closed-loop multiagent systems with the 2 proposed adaptive control laws
are analyzed under an assumption that the interaction network is structurally
balanced. Moreover, the convergence of the parameter estimation errors is guar-
anteed with a persistent excitation condition. Finally, simulation examples are
provided to demonstrate the effectiveness of the proposed adaptive bipartite
consensus control laws for the concerned multiagent system.
bipartite consensus, coopetition networks, distributed adaptive control, high-order multiagent
Recent years have witnessed increasing research interest in distributed coordination control of multiagent systems, inves-
tigating a global pattern or behavior emerging from local cooperative interactions among agents. A popular topic in the
literature is the so-called consensus control, where agents cooperate to achieve a common goal or decision. A large num-
ber of interesting results have flourished since the pioneering works on consensus control have been reported in the works
Jadbabaie et al,
Olfati-Saber and Murray,
Ren and Beard,
and Knorn et al
as well as the references therein.
Very recently, a new topic, that is, bipartite consensus control of multiagent systems, has emerged. Contrary to consensus
control, bipartite consensus control enables all agents to reach a final state with identical magnitude but opposite sign
through cooperative and competitive interactions.
It is an extremely effective control strategy in those scenarios where
cooperation and competition coexist among agents.
In many real applications, it is more plausible for agents to have both cooperative and competitive relationships.
For example, in social networks, a pair of agents can be friends or rivals depending on their relationship such as
2868 Copyright © 2018 John Wiley & Sons, Ltd. wileyonlinelibrary.com/journal/rnc Int J Robust Nonlinear Control. 2018;28:2868–2886.