Distributed Consensus of Stochastic Delayed Multi-agent Systems Under Asynchronous Switching

  • Xiaotai WuEmail author
  • Yang Tang
  • Jinde Cao
  • Wenbing Zhang
Living reference work entry


In this chapter, the distributed exponential consensus of stochastic delayed multi-agent systems with nonlinear dynamics is investigated under asynchronous switching. The asynchronous switching considered here is to account for the time of identifying the active modes of multi-agent systems. After receipt of confirmation of mode’s switching, the matched controller can be applied, which means that the switching time of the matched controller in each node usually lags behind that of system switching. In order to handle the coexistence of switched signals and stochastic disturbances, a comparison principle of stochastic switched delayed systems is firstly proved. By means of this extended comparison principle, several easy to verified conditions for the existence of an asynchronously switched distributed controller are derived such that stochastic delayed multi-agent systems with asynchronous switching and nonlinear dynamics can achieve global exponential consensus. Two examples are given to illustrate the effectiveness of the proposed method.


Consensus Multi-agent systems Switched systems Asynchronous switching Comparison principle 


  1. X. Ban, X. Gao, X. Huang, A. Vasilakos, Stability analysis of the simplest takagi-sugeno fuzzy control system using circle criterion. Inf. Sci. 177, 4387–4409 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  2. D. Carboni, R. Williams, A. Gasparri, G. Ulivi, G. Sukhatme, Rigidity-preserving team partitions in multiagent networks. IEEE Trans. Cybern. 45, 2640–2653 (2014)CrossRefGoogle Scholar
  3. Z.-H. Guan, D.J. Hill, X. Shen, On hybrid impulsive and switching systems and application to nonlinear control. IEEE Trans. Autom. Control 50(7), 1058–1062 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  4. Z. Guan, Z. Liu, G. Feng, Y. Wang, Synchronization of complex dynamical networks with time-varying delays via impulsive distributed control. IEEE Trans. Circuits Syst. I: Reg. papers 56(4), 2182–2195 (2010)MathSciNetCrossRefGoogle Scholar
  5. J. Hespanha, A. S. Morse, Stability of switched systems with average dwell time, in: 38th proc. IEEE Conf. Decision Control, Vol. 3, 1999, pp. 2655–2660Google Scholar
  6. Y. Hong, J. Hu, L. Gao, Tracking control for multi-agent consensus with an active leader and variable topology. Automatica 42, 1177–1182 (2006)MathSciNetzbMATHCrossRefGoogle Scholar
  7. M. Khan, H. Tembine, A. Vasilakos, Game dynamics and cost of learning in heterogeneous 4G networks. IEEE J. Sel. Areas Commun. 30, 198–213 (2012)CrossRefGoogle Scholar
  8. V. Lakshmikantham, D.D. Bainov, P.S. Simeonov, Theory of Impulsive Differential Equations (World Scientific, Singapore, 1989)CrossRefGoogle Scholar
  9. M. Li, Z. Li, A. Vasilakos, A survey on topology control in wireless sensor networks: Taxonomy, comparative study, and open issues. Proc. IEEE 101, 2538–2557 (2013)CrossRefGoogle Scholar
  10. D. Liberzon, Switching in Systems and Control (Birkhauser, Boston, 2003)zbMATHCrossRefGoogle Scholar
  11. H. Lin, P.J. Antsaklis, Stability and stabilizability of switched linear systems: A survey of recent results. IEEE Trans. Autom. Control 54, 308–322 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  12. Y. Liu, Z. Wang, J. Liang, X. Liu, Stability and synchronization of discrete-time Markovian jumping neural networks with mixed mode-depent time delays. IEEE Trans. Neural Netw. 20(7), 1102–1116 (2009)CrossRefGoogle Scholar
  13. T. Liu, J. Zhao, D.J. Hill, Exponential synchronization of complex delayed dynamical networks with switching topology. IEEE Trans. Circuits Syst. I: Reg. papers 57(11), 2967–2980 (2010)MathSciNetCrossRefGoogle Scholar
  14. T. Liu, D. Hill, J. Zhao, Synchronization of dynamical networks by network control. IEEE Trans. Autom. Control 57(6), 1574–1580 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  15. H. Lu, Chaotic attractors in delayed neural networks. Phys. Lett. A 298, 109–116 (2002)zbMATHCrossRefGoogle Scholar
  16. J. Lu, D.W.C. Ho, L. Wu, Exponential stabilization of switched stochastic dynamical networks. Nonlinearity 22(4), 889–911 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  17. C. Maia, M. Goncalves, Application of switched adaptive system to load forecasting. Electr. Power Syst. Res. 78, 721–727 (2008)CrossRefGoogle Scholar
  18. X. Mao, Stochastic Differentail Equations and Applications, 2nd edn. (Horwood, Chichester, 2007)Google Scholar
  19. Z. Meng, Z. Li, A. Vasilakos, S. Chen, Delay-induced synchronization of identical linear multiagent systems. IEEE Trans. Cybern. 43, 476–489 (2013)CrossRefGoogle Scholar
  20. M.A. Muller, D. Liberzon, Input/output-to-state stability and state-norm estimators for switched nonlinear systems. Automatica 48, 2029–2039 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  21. L. Sabattini, C. Secchi, N. Chopra, Decentralized estimation and control for preserving the strong connectivity of directed graphs. IEEE Trans. Cybern. 45, 2273–2286 (2014)CrossRefGoogle Scholar
  22. S. Seifzadeh, B. Khaleghi, F. Karray, Distributed soft-data-constrained multi-model particle filter. IEEE Trans. Cybern. 45, 384–394 (2015)CrossRefGoogle Scholar
  23. G. Shi, M. Johansson, K.H. Johansson, How agreement and disagreement evolve over random dynamic networks. IEEE J. Sel. Areas Commun. 31, 1061–1071 (2013)CrossRefGoogle Scholar
  24. Y. Tang, H. Gao, J. Kurths, Multiobjective identification of controlling areas in neuronal networks. IEEE/ACM Trans. Comput. Biol. Bioinform. 10(3), 708–720 (2013a)CrossRefGoogle Scholar
  25. Y. Tang, H. Gao, W. Zou, J. Kurths, Distributed synchronization in networks of agent systems with nonlinearities and random switchings. IEEE Trans. Cybern. 43(1), 358–370 (2013b)CrossRefGoogle Scholar
  26. Y. Tang, Z. Wang, H. Gao, H. Qiao, J. Kurths, On controllability of neuronal networks with constraints on the average of control gains. IEEE Trans. Cybern. 44(12), 2670–2681 (2014a)CrossRefGoogle Scholar
  27. Y. Tang, F. Qian, H. Gao, J. Kurths, Synchronization in complex networks and its application-a survey of recent advances and challenges. Annu. Rev. Control. 38(2), 184–198 (2014b)CrossRefGoogle Scholar
  28. Y. Tang, H. Gao, J. Lu, J. Kurths, Pinning distributed synchronization of stochastic dynamical networks: A mixed optimization approach. IEEE Trans. Neural Netw. Learn. Syst. 25(10), 1804–1815 (2014c)CrossRefGoogle Scholar
  29. Y. Tang, H. Gao, W. Zhang, J. Kurths, Leader-following consensus of a class of stochastic delayed multi-agent systems with partial mixed impulses. Automatica 53(1), 346–354 (2015)MathSciNetzbMATHCrossRefGoogle Scholar
  30. A.R. Teel, A. Subbaraman, A. Sferlazza, Stability analysis for stochastic hybrid systems: A survey. Automatica 50, 2435–2456 (2014)MathSciNetzbMATHCrossRefGoogle Scholar
  31. A. Vasilakos, C. Ricudis, K. Anagnostakis, W. Pedryca, A. Pitsillides, Evolutionary-fuzzy prediction for strategic qos routing in broadband networks, in: IEEE conference on Fuzzy Systems Proceedings, Vol. 2, 1998, pp. 1488–1493Google Scholar
  32. R. Wang, Z.-G. Wu, P. Shi, Dynamic output feedback control for a class of switched delay systems under asynchronous switching. Inf. Sci. 225, 72–80 (2013a)MathSciNetzbMATHCrossRefGoogle Scholar
  33. Y. Wang, X. Sun, P. Shi, J. Zhao, Input-to-state stability of switched nonlinear systems with time delays under asynchronous switching. IEEE Trans. Cybern. 43, 2261–2265 (2013b)CrossRefGoogle Scholar
  34. G. Wei, A.V. Vasilakos, Y. Zheng, N. Xiong, A game-theoretic method of fair resource allocation for cloud computing services. J. Supercomput. 54, 252–269 (2010)CrossRefGoogle Scholar
  35. F. Wei, T. Jie, Z. Ping, Stability analysis of switched stochastic systems. Automatica 47(1), 148–157 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  36. Z. Wu, P. Shi, H. Su, J. Chu, Local synchronization of chaotic neural networks with sampled-data and saturating actuators. IEEE Trans. Cybern. 44, 2635–2645 (2014a)CrossRefGoogle Scholar
  37. X. Wu, Y. Tang, W. Zhang, Stability analysis of switched stochastic neural networks with time-varying delays. Neural Netw. 41, 39–49 (2014b)zbMATHCrossRefGoogle Scholar
  38. Z.-G. Wu, P. Shi, H. Su, J. Chu, Asynchronous l2 − l filtering for discrete-time stochastic markov jump systems with randomly occurred sensor nonlinearities. Automatica 50, 180–186 (2014c)zbMATHCrossRefGoogle Scholar
  39. G. Xie, L. Wang, Stabilization of switched linear systems with time-delay in detection of switching signal. J. Math. Anal. Appl. 305(6), 077–290 (2005)MathSciNetGoogle Scholar
  40. Z. Yang, D. Xu, Stability analysis and design of impulsive control systems with time delay. IEEE Trans. Autom. Control 52, 1448–1454 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  41. S. Yin, Z. Huang, Performance monitoring for vehicle suspension system via fuzzy positivistic c-means clustering based on accelerometer measurements. IEEE/ASME Trans. Mechatron. 20, 2613–2620 (2014). Scholar
  42. S. Yin, X. Zhu, O. Kaynak, Improved pls focused on key-performance-indicator-related fault diagnosis. IEEE Trans. Ind. Electron. 62, 1651–1658 (2015)CrossRefGoogle Scholar
  43. G. Zhai, B. Hu, K. Yasuda, A.N. Michel, Piecewise lyapunov function for switched systems with average dwell time. Asian J. Control 2(3), 192–197 (2000)CrossRefGoogle Scholar
  44. L. Zhang, H. Gao, Asynchronously switched control of switched linear systems with average dwell time. Automatica 46(5), 953–958 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  45. L. Zhang, N. Cui, M. Liu, Y. Zhao, Asynchronous filtering of discrete-time switched linear systems with average dwell time. IEEE Trans. Circuits Syst. I: Reg. papers 58(5), 1109–1118 (2011)MathSciNetCrossRefGoogle Scholar
  46. W. Zhang, Y. Tang, X. Wu, J. Fang, Synchronization of nonlinear dynamical networks with heterogeneous impulses. IEEE Trans. Circuits Syst. I: Reg. papers 61, 1220–1228 (2014)CrossRefGoogle Scholar
  47. J. Zhao, D.J. Hill, T. Liu, Synchronization of complex dynamical networks with switching topology: A switched system point of view. Automatica 45(11), 2502–2511 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  48. J. Zhao, D.J. Hill, T. Liu, Stability of dynamical networks with non-identical nodes: A multiple-Lyapunov function method. Automatica 47(12), 2615–2625 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  49. J. Zhao, D.J. Hill, T. Liu, Global bounded synchronization of general dynamical networks with nonidentical nodes. IEEE Trans. Autom. Control 57(10), 2656–2662 (2012a)MathSciNetzbMATHCrossRefGoogle Scholar
  50. X. Zhao, P. Shi, L. Zhang, Asynchronously switched control of a class of slowly switched linear systems. Syst. Control Lett. 61(12), 1151–1156 (2012b)MathSciNetzbMATHCrossRefGoogle Scholar
  51. C. Zhou, H. Chen, N. Xiong, X. Huang, A. Vasilakos, Model-driven development of reconfigurable protocol stack for networked control systems. IEEE Trans. Syst. Man Cybern. Part C 42, 1439–1453 (2012)CrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Xiaotai Wu
    • 1
    Email author
  • Yang Tang
    • 2
  • Jinde Cao
    • 3
  • Wenbing Zhang
    • 4
  1. 1.The School of Mathematics and PhysicsAnhui Polytechnic UniversityWuhuChina
  2. 2.The Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of EducationEast China University of Science and TechnologyShanghaiChina
  3. 3.The Department of MathematicsSoutheast UniversityNanjingChina
  4. 4.The Department of MathematicsYangzhou UniversityYangzhouChina

Section editors and affiliations

  • Yang Tang
    • 1
  1. 1.Key Laboratory of Advanced Control and Optimization for Chemical Processes, Ministry of EducationEast China University of Science and TechnologyShanghaiChina

Personalised recommendations