In this paper, we study the
multi-equilibrium consensus problem for a time-varying network of n agents where the agents are modeled as
integrators. Instead of the joint connectivity condition which is widely used
in the literature, we propose an integral K
connectivity condition that allows us to examine the network through a constant
matrix. Based on this new concept, we present necessary and sufficient
conditions on networks modeled with undirected graphs so that multi-equilibrium
consensus states are achieved. Theoretical results are verified by numerical
simulations.
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Vicsek T, Czirók A, Ben-Jacob E, Cohen I, and Shochet O. Novel type of phase transition in a system of self-driven particles. Physical Review Letters 1995; 75(6): 1226.
Jadbabaie A, Lin J, and Morse AS. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE T Automat Contr 2003; 48(6):988-1001.
Moreau L. Stability of multiagent systems with time-dependent communication links. IEEE T Automat Contr 2005; 50(2): 169-182.
Ren W, Beard RW. Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE T Automat Contr 2005; 50(5):655-661.
Olfati-Saber R, Murray, RM. Consensus problems in networks of agents with switching topology and time-delays. IEEE T Automat Contr 2004; 49(9):1520-1533.
Akar M, Shorten R. Distributed probabilistic synchronization algorithms for communication networks. IEEE T Automat Contr 2008; 53(1):389-393.
Cihan O, Akar M. Fastest mixing reversible Markov chains on graphs with degree proportional stationary distributions. IEEE T Automat Contr 2015; 60(1): 227-232.
Cihan O, Akar M. Effect of nonuniform varying delay on the rate of convergence in averaging-based consensus. Turk J Elec Eng & Comp Sci 2015; 23(4):1069-1080.
Yu J, Wang L. Group consensus of multi-agent systems with directed information exchange. Int J Syst Sci 2012; 43(2): 334-348.
Xia W, Cao M. Clustering in diffusively coupled networks. Automatica 2011; 47(11):2395-2405.
Qin J, Yu C. Cluster consensus control of generic linear multi-agent systems under directed topology with acyclic partition. Automatica 2013; 49(9):2898-2905.
Chen Y, Lü J, Han F, Yu X. On the cluster consensus of discrete-time multi-agent systems. Syst Control Lett 2011; 60(7):517-523.
Han Y, Lu W, Chen T. Cluster consensus in discrete-time networks of multiagents with inter-cluster nonidentical inputs. IEEE T Neural Netw Learn Syst 2013; 24(4): 566-578.
Qin J, Yu C, Anderson, BD. On leaderless and leader-following consensus for interacting clusters of second-order multi-agent systems. Automatica 2016; 74:214-221.
Erkan OF, Akar M. Distributed Consensus with Multiple Equilibria in Continuous-Time Multi-Agent Networks under Undirected Topologies. IFAC-PapersOnLine 2015, 48(24):225-230.
Cao L, Zheng Y, Zhou Q. A necessary and sufficient condition for consensus of continuous-time agents over undirected time-varying networks. IEEE T Automat Contr 2011;56(8):1915-1920.
Year 2017,
Volume: 18 Issue: 4, 842 - 848, 31.10.2017
Beard RW, McLain TW, Goodrich MA, and Anderson EP. Coordinated target assignment and intercept for unmanned air vehicles. IEEE T Robotic Autom 2002; 18(6): 911-922.
Vicsek T, Czirók A, Ben-Jacob E, Cohen I, and Shochet O. Novel type of phase transition in a system of self-driven particles. Physical Review Letters 1995; 75(6): 1226.
Jadbabaie A, Lin J, and Morse AS. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE T Automat Contr 2003; 48(6):988-1001.
Moreau L. Stability of multiagent systems with time-dependent communication links. IEEE T Automat Contr 2005; 50(2): 169-182.
Ren W, Beard RW. Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE T Automat Contr 2005; 50(5):655-661.
Olfati-Saber R, Murray, RM. Consensus problems in networks of agents with switching topology and time-delays. IEEE T Automat Contr 2004; 49(9):1520-1533.
Akar M, Shorten R. Distributed probabilistic synchronization algorithms for communication networks. IEEE T Automat Contr 2008; 53(1):389-393.
Cihan O, Akar M. Fastest mixing reversible Markov chains on graphs with degree proportional stationary distributions. IEEE T Automat Contr 2015; 60(1): 227-232.
Cihan O, Akar M. Effect of nonuniform varying delay on the rate of convergence in averaging-based consensus. Turk J Elec Eng & Comp Sci 2015; 23(4):1069-1080.
Yu J, Wang L. Group consensus of multi-agent systems with directed information exchange. Int J Syst Sci 2012; 43(2): 334-348.
Xia W, Cao M. Clustering in diffusively coupled networks. Automatica 2011; 47(11):2395-2405.
Qin J, Yu C. Cluster consensus control of generic linear multi-agent systems under directed topology with acyclic partition. Automatica 2013; 49(9):2898-2905.
Chen Y, Lü J, Han F, Yu X. On the cluster consensus of discrete-time multi-agent systems. Syst Control Lett 2011; 60(7):517-523.
Han Y, Lu W, Chen T. Cluster consensus in discrete-time networks of multiagents with inter-cluster nonidentical inputs. IEEE T Neural Netw Learn Syst 2013; 24(4): 566-578.
Qin J, Yu C, Anderson, BD. On leaderless and leader-following consensus for interacting clusters of second-order multi-agent systems. Automatica 2016; 74:214-221.
Erkan OF, Akar M. Distributed Consensus with Multiple Equilibria in Continuous-Time Multi-Agent Networks under Undirected Topologies. IFAC-PapersOnLine 2015, 48(24):225-230.
Cao L, Zheng Y, Zhou Q. A necessary and sufficient condition for consensus of continuous-time agents over undirected time-varying networks. IEEE T Automat Contr 2011;56(8):1915-1920.
Erkan, Ö. F., & Akar, M. (2017). AN INTEGRAL CONNECTIVITY CONDITION FOR MULTI-EQUILIBRIA CONSENSUS IN NETWORKS EVOLVING OVER UNDIRECTED GRAPHS. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering, 18(4), 842-848. https://doi.org/10.18038/aubtda.341599
AMA
Erkan ÖF, Akar M. AN INTEGRAL CONNECTIVITY CONDITION FOR MULTI-EQUILIBRIA CONSENSUS IN NETWORKS EVOLVING OVER UNDIRECTED GRAPHS. AUJST-A. October 2017;18(4):842-848. doi:10.18038/aubtda.341599
Chicago
Erkan, Özlem Feyza, and Mehmet Akar. “AN INTEGRAL CONNECTIVITY CONDITION FOR MULTI-EQUILIBRIA CONSENSUS IN NETWORKS EVOLVING OVER UNDIRECTED GRAPHS”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 18, no. 4 (October 2017): 842-48. https://doi.org/10.18038/aubtda.341599.
EndNote
Erkan ÖF, Akar M (October 1, 2017) AN INTEGRAL CONNECTIVITY CONDITION FOR MULTI-EQUILIBRIA CONSENSUS IN NETWORKS EVOLVING OVER UNDIRECTED GRAPHS. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 18 4 842–848.
IEEE
Ö. F. Erkan and M. Akar, “AN INTEGRAL CONNECTIVITY CONDITION FOR MULTI-EQUILIBRIA CONSENSUS IN NETWORKS EVOLVING OVER UNDIRECTED GRAPHS”, AUJST-A, vol. 18, no. 4, pp. 842–848, 2017, doi: 10.18038/aubtda.341599.
ISNAD
Erkan, Özlem Feyza - Akar, Mehmet. “AN INTEGRAL CONNECTIVITY CONDITION FOR MULTI-EQUILIBRIA CONSENSUS IN NETWORKS EVOLVING OVER UNDIRECTED GRAPHS”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 18/4 (October 2017), 842-848. https://doi.org/10.18038/aubtda.341599.
JAMA
Erkan ÖF, Akar M. AN INTEGRAL CONNECTIVITY CONDITION FOR MULTI-EQUILIBRIA CONSENSUS IN NETWORKS EVOLVING OVER UNDIRECTED GRAPHS. AUJST-A. 2017;18:842–848.
MLA
Erkan, Özlem Feyza and Mehmet Akar. “AN INTEGRAL CONNECTIVITY CONDITION FOR MULTI-EQUILIBRIA CONSENSUS IN NETWORKS EVOLVING OVER UNDIRECTED GRAPHS”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering, vol. 18, no. 4, 2017, pp. 842-8, doi:10.18038/aubtda.341599.
Vancouver
Erkan ÖF, Akar M. AN INTEGRAL CONNECTIVITY CONDITION FOR MULTI-EQUILIBRIA CONSENSUS IN NETWORKS EVOLVING OVER UNDIRECTED GRAPHS. AUJST-A. 2017;18(4):842-8.