Asymmetric bipartite consensus over directed networks with antagonistic interactions

This study deals with the bipartite consensus problem for multi-agent systems associated with signed digraphs. For structurally balanced signed digraphs, by constructing a new class of general Laplacian matrices, it is found that all agents will converge to two values with different modulus if the signed digraph is strongly connected. Interestingly, these two values completely depend on the left eigenvector of the general Laplacian matrix corresponding to the zero eigenvalue and the initial states of all agents. Furthermore, it is shown that all agents can reach interval asymmetric bipartite consensus if the associated signed digraph contains a spanning tree. In particular, some useful results are also presented for specific signed digraphs with spanning trees. Finally, two numerical examples are provided to demonstrate the effectiveness of the main results.

[1]  Junping Du,et al.  Finite-Time Consensus for Multiagent Systems With Cooperative and Antagonistic Interactions , 2016, IEEE Transactions on Neural Networks and Learning Systems.

[2]  Xu Zhang,et al.  Forwarding-based dynamic surface control for antagonistic actuated robots , 2016 .

[3]  P. Doreian,et al.  A partitioning approach to structural balance , 1996 .

[4]  Guo-Xing Wen,et al.  Neural-network-based adaptive leader-following consensus control for second-order non-linear multi-agent systems , 2015 .

[5]  R. Plemmons.  M-matrix characterizations.I—nonsingular M-matrices , 1977 .

[6]  Massimo Franceschetti,et al.  Lower bounds on data collection time in sensory networks , 2004, IEEE Journal on Selected Areas in Communications.

[7]  P M Hui,et al.  Dynamics of opinion formation in a small-world network. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Jingyuan Zhan,et al.  Cluster Consensus in Networks of Agents With Weighted Cooperative–Competitive Interactions , 2018, IEEE Transactions on Circuits and Systems II: Express Briefs.

[9]  Yingmin Jia,et al.  Adaptive finite-time bipartite consensus for second-order multi-agent systems with antagonistic interactions , 2017, Syst. Control. Lett..

[10]  Nicole Abaid,et al.  On the Effect of Collaborative and Antagonistic Interactions on Synchronization and Consensus in Networks of Conspecific Agents , 2016, IEEE Transactions on Automatic Control.

[11]  Yan-Wu Wang,et al.  Modulus consensus in a network of singularly perturbed systems with collaborative and antagonistic interactions , 2017, Int. J. Control.

[12]  Cuiqin Ma,et al.  Bipartite consensus on networks of agents with antagonistic interactions and measurement noises , 2016 .

[13]  Maria Elena Valcher,et al.  On the consensus and bipartite consensus in high-order multi-agent dynamical systems with antagonistic interactions , 2014, Syst. Control. Lett..

[14]  Wei Chen,et al.  Influence diffusion dynamics and influence maximization in social networks with friend and foe relationships , 2011, WSDM.

[15]  Colin R. Twomey,et al.  Visual sensory networks and effective information transfer in animal groups , 2013, Current Biology.

[16]  Qingdu Li,et al.  Practical bipartite synchronization via pinning control on a network of nonlinear agents with antagonistic interactions , 2017 .

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