Leader-following Consensus Criterion for Multi-agent Systems with Probabilistic Self-delay

Authors: M.J. Park, K.H. Kim, O.M. Kwon

Abstract:

This paper proposes a delay-dependent leader-following consensus condition of multi-agent systems with both communication delay and probabilistic self-delay. The proposed methods employ a suitable piecewise Lyapunov-Krasovskii functional and the average dwell time approach. New consensus criterion for the systems are established in terms of linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Numerical example showed that the proposed method is effective.

Keywords: Multi-agent systems, probabilistic self-delay, consensus, Lyapunov method, LMI.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1077495

References:

[1] R.O. Saber, J.A. Fax, R.M. Murray, "Consensus and Cooperation in Networked Multi-Agent Systems", Proceedings of The IEEE, vol. 95, 2007, pp. 215-233.
[2] J. Wang, D. Cheng, X. Hu, "Consensus of Multi-agent Linear Dynamic Systems", Asian J Control, vol. 10, 2008, pp. 144-155.
[3] W. Ren, "Consensus strategies for cooperative control of vehicle formations", IET Control Theory Appl., vol. 1, 2007, pp. 505-512.
[4] W. Ren, E. Atkins, "Distributed multi-vehicle coordinated control via local information exchange", Int. J. Robust Nonlinear Control, vol. 17, 2007, pp. 1002-1033.
[5] A. Jadbabie, J. Lin, A.S. Morse, "Coordination of groups of mobile autonomous agents using nearest neighbor rules", IEEE Trans. Autom. Control, vol. 48, 2003, pp 988-1001.
[6] P. DeLellis, M. DiBernardo, F. Garofalo, D. Liuzza, "Analysis and stabililty of consensus in networked control systems", Appl. Math. Comput., vol. 217, 2010, pp. 988-1000.
[7] D. Lee, M.W. Spong, "Stable Flocking of Multiple Inertial Agents on Balanced Graphs", IEEE Trans. Autom. Control, vol. 52, 2007, pp. 1469- 1475.
[8] H. Kim, H. Shim, J.H. Seo, "Output Consensus of Heterogeneous Uncertain Linear Multi-Agent Systems", IEEE Trans. Autom. Control, vol. 56, 2011, pp. 200-206.
[9] J.P. Hu, Y.G. Hong, "Leader-following coordination of multi-agent systems with coupling time delay", Physica A, vol. 374, 2007, pp. 853-863.
[10] Y.P. Tian, C.L. Liu, "Consensus of Mulit-Agnet Systems With Diverse Input and Communication Delays", IEEE Trans. Autom. Control, vol. 53, 2008, pp. 2122-2128.
[11] F. Xiao, L. Wang, "State consensus for multi-agent systems with switching topologies and time-varying delays", Int. J. Control, vol. 79, 2006, pp. 1277-1284.
[12] J. Qin, H. Gao, W.X. Zheng, "On average consensus in directed networks of agents with switching topology and time delay", Int. J. Syst. Sci., vol. 42, 2011, pp. 1947-1956.
[13] S. Xu, J. Lam, "A survey of linear matrix inequality techniques in stability analysis of delay systems", Int. J. Syst. Sci., vol. 39, 2008, pp. 1095-1113.
[14] D. Liberzon, Switching in Systems and Control, Birkh¨auser, Boston; 2003.
[15] S. Boyd, L.E. Ghaoui, E. Feron E, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, Philadelphia; 1994.
[16] Z.G. Wu, Ju H. Park, H. Su, J. Chu, "Robust dissipativity analysis of nerual networks with time-vayring delay and randomly occurring uncertainties", Nonlinear Dyn., doi:10.1007/s11071-012-0350-1.
[17] J. Hu, Z. Wang, H. Gao, L.K. Stergioulas, "Robust sliding mode control for discrete stochastic systems with mixed time delays, randomly occurring uncertainties, and randomly occurring nonliearities", IEEE Trans. Ind. Electron., vol. 59, 2012, pp. 3008-3015.
[18] C. Godsil and G. Royle, Algebraic Graph Theory, Springer-Verlag, New York; 2001.
[19] W. Ni, D. Cheng, "Leader-following consensus of multi-agent systems under fixed and switching topologies", Syst. Contr. Lett., vol. 59, 2010, pp. 209-217.
[20] M.C. de Oliveira, R.E. Skelton, Stability tests for constrained linear systems, Springer-Verlag, Berlin; 2001, pp. 241-257.
[21] K. Gu, "An integral inequality in the stability problem of time-delay systems", in Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2000, pp. 2805-2810.
[22] S.H. Kim, P. Park, C.K. Jeong, "Robust H∞ stabilisation of networks control systems with packet analyser", IET Control Theory Appl., vol. 4, 2010, pp. 1828-1837.
[23] X.-M. Sun, J. Zhao, D.J. Hill, "Stability and L2-gain analysis for switched delay systems: A delay-dependent method", Automatica, vol. 42, 2006, pp. 1769-1774.
[24] D. Zhang, L. Yu, "Exponential stability analysis for neutral switched systems with interval time-varying mixed delays and nonlinear perturbations", Nonlinear Anal.-Hybrid Syst., vol. 6, 2012, pp. 775-786.