Abstract
A stability analysis of general consensus algorithms in discrete-time networks of multi-agents is presented. Here, the networks can have time-varying topologies and delays, as well as nonlinearities. The Hajnal diameter approach is developed for synchronization analysis and sufficient conditions for both consensus at uniform value and synchronization at periodic trajectories are derived, which show how the periods depend on the transmission delay patterns.
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References
Lynch, N.A.: Distributed algorithms. Morgan Kaufmann, San Francisco (1996)
DeGroot, M.H.: Reaching a consensus. J. Amer. Statist. Assoc. 69, 118–121 (1974)
Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., Shochet, O.: Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75, 1226–1229 (1995)
Fax, J.A., Murray, R.M.: Information flow and cooperative control of vehicle formations. IEEE Trans. Autom. Control 49, 1465–1476 (2004)
Olfati-Saber, R., Shamma, J.S.: Consensus filters for sensor networks and distributed sensor fusion. In: 44th IEEE Conference on Decision and Control 2005, and 2005 European Control Conference, CDC-ECC 2005, pp. 6698–6703 (2005)
Winfree, A.T.: The Geometry of biological time. Springer, New York (1980)
Kuramoto, Y.: Chemical Oscillations, waves, and turbulence. Springer, New York (1984)
Pikovsky, A., Rosenblum, M., Kurths, J.: Synchronization: A universal concept in nonlinear sciences. Cambridge University Press (2001)
Lu, W., Atay, F.M., Jost, J.: Synchronization of Discrete-Time Dynamical Networks with Time-Varying Couplings. SIAM J. Math. Anal. 39(4), 1231–1259 (2007)
Olfati-Saber, R., Fax, J.A., Murray, R.M.: Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE 95, 215–233 (2007)
Olfati-Saber, R., Murray, R.M.: Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans. Autom. Control 49(9), 1520–1533 (2004)
Moreau, L.: Stability of multiagent systems with time-dependent communication links. IEEE Trans. Autom. Control 50(2), 169–182 (2005)
Cao, M., Morse, A.S., Anderson, B.D.O.: Reaching a consensus in a dynamically changing environment: a graphical approach. SIAM J. Control Optim. 47, 575–600 (2008)
Xiao, F., Wang, L.: Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays. IEEE Trans. Automatic Control 53(8), 1804–1816 (2008)
Bliman, P.-A., Ferrari-Trecate, G.: Average consensus problems in networks of agents with delayed communications. Automatica 44(8), 1985–1995 (2008)
Michiels, W., Morărescu, C.-I., Niculescu, S.-I.: Consensus problems with distributed delays, with application to traffic flow models. SIAM J. Control Optim. 48, 77–101 (2009)
Hatano, Y., Mesbahi, M.: Agreement over random networks. IEEE Trans. Autom. Control 50(11), 1867–1872 (2005)
Tahbaz-Salehi, A., Jadbabaie, A.: A necessary and sufficient condition for consensus over random networks. IEEE Trans. Autom. Control 53(3), 791–795 (2008)
Wu, C.W.: Synchronization and convergence of linear dynamics in random directed networks. IEEE Trans. Autom. 51(7), 1207–1210 (2006)
Lu, W., Atay, F.M., Jost, J.: Consensus and synchronization in discrete-time networks of multi-agents with stochastically switching topologies and time delays. Networks and Heterogeneous Media 6(2), 329–349 (2011)
Lu, W., Atay, F.M., Jost, J.: Consensus and Synchronization in Delayed Networks of Mobile Multi-agents. In: The 18th IFAC World Congress, Milano, Italy, August 28 - September 2 (2011)
Arnold, L.: Random Dynamical Systems. Springer, Heidelberg (1998)
Hajnal, J.: The ergodic properties of non-homogeneous finite Markov chains. Proc. Camb. Phil. Soc. 52, 67–77 (1956)
Hajnal, J.: Weak ergodicity in non-homogeneous Markov chains. Proc. Camb. Phil. Soc. 54, 233–246 (1958)
He, X., Lu, W., Chen, T.: On transverse stability of random dynamical systems. Discrete and Continuous Dynamic Systems 33(2), 701–721 (2013)
Godsil, C., Royle, G.: Algebraic graph theory. Springer, New York (2001)
Horn, R.A., Johnson, C.R.: Matrix analysis. Cambridge University Press (1985)
Shen, J.: A geometric approach to ergodic non-homogeneous Markov chains. Wavelet Anal. Multi. Meth., LNPAM 212, 341–366 (2000)
Johnson, D.B., Maltz, D.A.: Dynamic source routing in ad hoc wireless networks. In: Imielinski, T., Korth, H. (eds.) Mobile Computing, ch. 5, pp. 153–181. Kluwer Academic Publishers (1996)
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Lu, W., Atay, F.M., Jost, J. (2014). Consensus in Networks of Discrete-Time Multi-agent Systems: Dynamical Topologies and Delays. In: Vyhlídal, T., Lafay, JF., Sipahi, R. (eds) Delay Systems. Advances in Delays and Dynamics, vol 1. Springer, Cham. https://doi.org/10.1007/978-3-319-01695-5_12
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DOI: https://doi.org/10.1007/978-3-319-01695-5_12
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