Bipartite Consensus Control of Multiagent Systems on Coopetition Networks

Cooperation and competition are two typical interactional relationships in natural and engineering networked systems. Some complex behaviors can emerge through local interactions within the networked systems. This paper focuses on the coexistence of competition and cooperation (i.e., coopetition) at the network level and, simultaneously, the collective dynamics on such coopetition networks. The coopetition network is represented by a directed signed graph. The collective dynamics on the coopetition network is described by a multiagent system. We investigate two bipartite consensus strategies for multiagent systems such that all the agents converge to a final state characterized by identical modulus but opposite sign. Under a weak connectivity assumption that the coopetition network has a spanning tree, some sufficient conditions are derived for bipartite consensus of multiagent systems with the help of a structural balance theory. Finally, simulation results are provided to demonstrate the bipartite consensus formation.

[1]  Claudio Altafini,et al.  Consensus Problems on Networks With Antagonistic Interactions , 2013, IEEE Transactions on Automatic Control.

[2]  Manfredi Maggiore,et al.  Necessary and sufficient graphical conditions for formation control of unicycles , 2005, IEEE Transactions on Automatic Control.

[3]  F. Harary.  On the notion of balance of a signed graph. , 1953 .

[4]  Stanley Wasserman,et al.  Social Network Analysis: Methods and Applications , 1994, Structural analysis in the social sciences.

[5]  Lin Huang,et al.  Consensus of Multiagent Systems and Synchronization of Complex Networks: A Unified Viewpoint , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[6]  S. Strogatz,et al.  Synchronization of pulse-coupled biological oscillators , 1990 .

[7]  Wenwu Yu,et al.  Synchronization via Pinning Control on General Complex Networks , 2013, SIAM J. Control. Optim..

[8]  M. Degroot.  Reaching a Consensus , 1974 .

[9]  Albert-László Barabási,et al.  The sound of many hands clapping: Tumultuous applause can transform itself into waves of synchronized clapping. , 2000 .

[10]  William H. Flanigan,et al.  The Theory of Political Coalitions. , 1965 .

[11]  Marco Dorigo,et al.  Swarm intelligence: from natural to artificial systems , 1999 .

[12]  J. M. González-Miranda,et al.  Synchronization of Chaotic Oscillators , 2011 .

[13]  T. Carroll,et al.  MASTER STABILITY FUNCTIONS FOR SYNCHRONIZED COUPLED SYSTEMS , 1999 .

[14]  Xiaoming Hu,et al.  Opinion consensus of modified Hegselmann-Krause models , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[15]  Randal W. Beard,et al.  Distributed Consensus in Multi-vehicle Cooperative Control - Theory and Applications , 2007, Communications and Control Engineering.

[16]  Vicsek,et al.  Novel type of phase transition in a system of self-driven particles. , 1995, Physical review letters.

[17]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[18]  S. Fortunato,et al.  Statistical physics of social dynamics , 2007, 0710.3256.

[19]  Wenwu Yu,et al.  An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination , 2012, IEEE Transactions on Industrial Informatics.

[20]  Young-Jai Park,et al.  Anti-synchronization of chaotic oscillators , 2003 .

[21]  Claudio Altafini,et al.  Dynamics of Opinion Forming in Structurally Balanced Social Networks , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[22]  E. Ising.  Beitrag zur Theorie des Ferromagnetismus , 1925 .

[23]  Jessika Eichel.  The Dynamics Of Two Party Politics Party Structures And The Management Of Competition , 2016 .

[24]  Shihua Chen,et al.  Adaptive control for anti-synchronization of Chua's chaotic system , 2005 .

[25]  W. Zheng,et al.  Emergent collective behaviors on coopetition networks , 2014 .

[26]  Mark Newman,et al.  Complex Systems Theory and Evolution , 2002 .

[27]  Guanghui Wen,et al.  Distributed consensus control for linear multi-agent systems with discontinuous observations , 2013, Int. J. Control.

[28]  Wai Keung Wong,et al.  Distributed Synchronization of Coupled Neural Networks via Randomly Occurring Control , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[29]  M. Pagel.  Encyclopedia of evolution , 2002 .

[30]  Marco Dorigo,et al.  From Natural to Artificial Swarm Intelligence , 1999 .

[31]  Jiangping Hu,et al.  Leader-following coordination of multi-agent systems with coupling time delays , 2007, 0705.0401.