Leader-following Consensus Criterion for Multi-agent Systems with Probabilistic Self-delay
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.
[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.
[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.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:60586", author = "M.J. Park and K.H. Kim and O.M. Kwon", title = "Leader-following Consensus Criterion for Multi-agent Systems with Probabilistic Self-delay", 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.", volume = "6", number = "12", pages = "1747-5", }
