Skip to main content
SpringerLink
Log in

Consensus of fractional multi-agent systems by distributed event-triggered strategy

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

In this manuscript, the problem of event-triggered consensus for fractional general linear multi-agent systems is investigated, which include integer-order general linear multi-agent systems as the special case. A distributed event-triggered strategy is proposed to utilize in fractional multi-agent systems, under which the network can achieve consensus. Also, Zeno behavior can be precluded to ensure the feasibility of the devised event-triggered strategy. Furthermore, in order to avoid keeping track of the measurement errors continuously, a self-triggered strategy is designed, in which the next update time instant of each agent can be computed by using its local history state information. Finally, some numerical simulations are presented to indicate the validity of the devised control strategies.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

References

  1. Fax, J.A., Murray, R.M.: Information flow and cooperative control of vehicle formations. IEEE Trans. Autom. Control 49(9), 1465–1476 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Xue, D., Cao, J., Chen, G., Yu, Y.L.: Formation control of networked multi-agent systems. IET Control Theory Appl. 4(10), 2168–2176 (2010)

    Article  MathSciNet  Google Scholar 

  3. Wen, G., Dusn, Z., Yu, W., Chen, G.: Consensus in multi-agent systems with communication constraints. Int. J. Robust Nonlinear Control 22(2), 170–182 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  4. Jadbabaie, A., Lin, J., Morse, S.A.: Coordination of groups of mobile agents using nearest neighbor rules. IEEE Trans. Autom. Control 48(6), 988–1001 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. Tian, Y.P., Liu, C.L.: Consensus of multi-agent systems with diverse input and communication delays. IEEE Trans. Autom. Control 53(9), 2122–2128 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Lü, J., Chen, G.: A time-varying complex dynamical network model and its controlled synchronization criteria. IEEE Trans. Autom. Control 50(6), 841–846 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  7. Yu, W., Chen, G., Cao, M.: Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems. Automatica 46(6), 1089–1095 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ren, W., Beard, R.W.: Distributed Consensus in Multi-Vehicle Cooperative Control. Springer, London (2008)

    Book  MATH  Google Scholar 

  9. Yu, W., Chen, G., Ren, W., Kurths, J., Zheng, W.: Distributed higher order consensus protocols in multiagent dynamical systems. IEEE Trans. Circuits Syst. I Reg. Papers 58(8), 1924–1932 (2011)

    Article  MathSciNet  Google Scholar 

  10. Li, Z., Ren, W., Liu, X., Fu, M.: Consensus of multi-agent systems with general linear and Lipschitz nonlinear dynamics using distributed adaptive protocols. IEEE Trans. Autom. Control 58(7), 1786–1791 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  11. Yu, W., Chen, G., Cao, M.: Consensus in directed networks of agents with nonlinear dynamics. IEEE Trans. Autom. Control 56(6), 1436–1441 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  12. Song, Q., Cao, J., Yu, W.: Second-order leader-following consensus of nonlinear multi-agents via pinning control. Syst. Control Lett. 59(9), 553–562 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  13. Podlubny, I.: Fractional Differential Equations. Academic Press, San Diego (1999)

    MATH  Google Scholar 

  14. Kilbas, A., Srivastava, H., Trujillo, J.: Theory and Applications of Fractional Differential Equations. Elsevier, Oxford (2006)

    MATH  Google Scholar 

  15. Hilfer, R.: Applications of Fractional Calculus in Physics. World Scientific, Singapore (2000)

    Book  MATH  Google Scholar 

  16. Bagley, R.L., Torvik, P.J.: A theoretical basis for the application of fractional calculus to viscoelasticity. J. Theol. 27(3), 201–210 (1983)

    MATH  Google Scholar 

  17. Cao, Y., Li, Y., Ren, W., Chen, Y.: Distributed coordination of networked fractional-order systems. IEEE Trans. Syst. Man Cybern. B Cybern. 40(2), 362–370 (2010)

    Article  Google Scholar 

  18. Yang, H., Zhu, X., Cao, K.: Distributed coordination of fractional order multi-agent systems with communication delays. Fract. Calc. Appl. Anal. 17, 23–37 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  19. Song, C., Cao, J., Liu, Y.: Robust consensus of fractional-order multi-agent systems with positive real uncertainty via second-order neighbors information. Neurocomputing 165, 293–299 (2015)

    Article  Google Scholar 

  20. Ren, G., Yu, Y.: Robust consensus of fractional multi-agent systems with external disturbances. Neurocomputin 218, 339–345 (2016)

    Article  Google Scholar 

  21. Yu, W., Li, Y., Wen, G., Yu, X., Cao, J.: Observer design for tracking consensus in second-order multi-agent systems: fractional order less than two. IEEE Trans. Autom. Control 62(2), 894–900 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  22. Ren, G., Yu, Y.: Consensus of fractional multi-agent systems using distributed adaptive protocols. Asian J. Control 19(6), 2076–2084 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  23. Yu, Z., Jiang, H., Hu, C., Yu, J.: Leader-following consensus of fractional-order multi-agent systems via adaptive pinning control. Int. J. Control 88(9), 1746–1756 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  24. Yin, X., Yue, D., Hu, S.: Consensus of fractional-order heterogeneous multi-agent systems. IET Control Theory A. 7(2), 314–322 (2013)

    Article  MathSciNet  Google Scholar 

  25. Bai, J., Wen, G., Rahmani, A., Chu, X., Yu, Y.: Consensus with a reference state for fractional-order multi-agent systems. Int. J. Syst. Sci. 47(1), 222–234 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  26. Chen, J., Guan, Z.H., Yang, C., Li, T., He, D.X., Zhang, X.H.: Distributed containment control of fractional-order uncertain multi-agent systems. J. Franklin I. 353(7), 1672–1688 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  27. Gong, P.: Distributed consensus of non-linear fractional-order multi-agent systems with directed topologies. IET Control Theory A. 10(18), 2515–2525 (2016)

    Article  MathSciNet  Google Scholar 

  28. Zhu, W., Chen, B., Yang, J.: Consensus of fractional-order multi-agent systems with input time delay. Fract. Calc. Appl. Anal. 20(1), 52–70 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  29. Ma, X., Sun, F., Li, H., He, B.: The consensus region design and analysis of fractional-order multi-agent systems. Int. J. Syst. Sci. 48(3), 629–636 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  30. Ma, T., Li, T., Cui, B.: Coordination of fractional-order nonlinear multi-agent systems via distributed impulsive control. Int. J. Syst. Sci. 49(1), 1–14 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  31. Abdulghafor, R., Turaev, S.: Consensus of fractional nonlinear dynamics stochastic operators for multi-agent systems. Inf. Fusion 44, 1–21 (2018)

    Article  Google Scholar 

  32. Liu, J., Qin, K., Chen, W., Li, P., Shi, M.: Consensus of fractional-order multiagent systems with nonuniform time delays. Math. Probl. Eng. 2018 (2018). https://doi.org/10.1155/2018/2850757

  33. Wang, F., Yang, Y.: Leader-following exponential consensus of fractional order nonlinear multi-agents system with hybrid time-varying delay: a heterogeneous impulsive method. Physica A 482, 158–172 (2017)

    Article  MathSciNet  Google Scholar 

  34. He, W., Chen, G., Han, Q.L., Qian, F.: Network-based leader-following consensus of nonlinear multi-agent systems via distributed impulsive control. Inf. Sci. 380, 145–158 (2017)

    Article  Google Scholar 

  35. Guan, Z.H., Hu, B., Chi, M., He, D.X., Cheng, X.M.: Guaranteed performance consensus in second-order multi-agent systems with hybrid impulsive control. Automatica 50(9), 2415–2418 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  36. Jiang, H., Yu, J., Zhou, C.: Consensus of multi-agent linear dynamic systems via impulsive control protocols. Int. J. Syst. Sci. 42(6), 967–976 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  37. Ding, L., Yu, P., Liu, Z.W., Guan, Z.H., Feng, G.: Consensus of second-order multi-agent systems via impulsive control using sampled hetero-information. Automatica 49(9), 2881–2886 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  38. Gao, Y., Wang, L.: Sampled-data based consensus of continuous-time multi-agent systems with time-varying topology. IEEE Trans. Autom. Control 56(5), 1226–1231 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  39. Liu, Z.W., Yu, X., Guan, Z.H., Hu, B., Li, C.: Pulse-modulated intermittent control in consensus of multiagent systems. IEEE Trans. Syst. Man Cybern. 47(5), 783–793 (2017)

    Article  Google Scholar 

  40. Yu, Z., Jiang, H., Hu, C., Yu, J.: Necessary and sufficient conditions for consensus of fractional-order multiagent systems via sampled-data control. IEEE Trans. Cybern. 47(8), 1892–1901 (2017)

    Article  Google Scholar 

  41. Li, H., Liao, X., Chen, G., Hill, D., Dong, Z., Huang, T.: Event-triggered asynchronous intermittent communication strategy for synchronization in complex dynamical networks. Neural Netw. 66, 1–10 (2015)

    Article  MATH  Google Scholar 

  42. Aström, K.J., Bernhardsson, B.M.: Comparison of Riemann and Lebesgue sampling for first order stochastic systems. IEEE Conference Decision and Control. pp. 2011–2016 (2002)

  43. Dimarogonas, D.V., Frazzoli, E., Johansson, K.H.: Distributed event-triggered control for multi-agent systems. IEEE Trans. Autom. Control 57(5), 1291–1297 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  44. Zhu, W., Jiang, Z., Feng, G.: Event-based consensus of multi-agent systems with general linear models. Automatica 50(2), 552–558 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  45. Hu, W., Liu, L., Feng, G.: Output consensus of heterogeneous linear multi-agent systems by distributed event-triggered/self-triggered strategy. IEEE Trans. Cybern. 47(8), 1914–1924 (2017)

    Article  Google Scholar 

  46. Cheng, Y., Ugrinovskii, V.: Event-triggered leader-following tracking control for multivariable multi-agent systems. Automatica 70, 204–210 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  47. Fan, Y., Feng, G., Wang, Y., Song, C.: Distributed event-triggered control of multi-agent systems with combinational measurements. Automatica 49(2), 671–675 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  48. Kia, S., Cortés, J., Martinez, S.: Distributed event-triggered communication for dynamic average consensus in networked systems. Automatic 59, 112–119 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  49. Nowzari, C., Cort’es, J.: Distributed event-triggered coordination for average consensus on weight-balanced digraphs. Automatica 68, 237–244 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  50. Meng, X., Xie, L., Soh, Y.: Asynchronous periodic event-triggered consensus for multi-agent systems. Automatica 84, 214–220 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  51. Gao, L., Liao, X., Li, H., Chen, G.: Event-triggered control for multi-agent network with limited digital communication. Nonlinear Dyn. 82(4), 1659–1669 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  52. Li, H., Liao, X., Huang, T., Zhu, W.: Event-triggering sampling based leader-following consensus in second-order multi-agent systems. IEEE Trans. Autom. Control 60(7), 1998–2003 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  53. Li, L., Ho, D.W., Lu, J.: Event-based network consensus with communication delays. Nonlinear Dyn. 87(3), 1847–1858 (2017)

    Article  MATH  Google Scholar 

  54. Zeng, D., Wu, K.T., Liu, Y., Zhang, R., Zhong, S.: Event-triggered sampling control for exponential synchronization of chaotic Lur’e systems with time-varying communication delays. Nonlinear Dyn. 91(2), 905–921 (2018)

    Article  MATH  Google Scholar 

  55. Xiao, F., Chen, T., Gao, H.: Synchronous hybrid event-and time-driven consensus in multiagent networks with time delays. IEEE Trans. Cybern. 46(5), 1165–1174 (2016)

    Article  Google Scholar 

  56. Hu, W., Liu, L.: Cooperative output regulation of heterogeneous linear multi-agent systems by event-triggered control. IEEE Trans. Cybern. 47(1), 105–116 (2017)

    Article  Google Scholar 

  57. Li, H., Chen, G., Huang, T., Dong, Z., Zhu, W., Gao, L.: Event-triggered distributed average consensus over directed digital networks with limited communication bandwidth. IEEE Trans. Cybern. 46(12), 3098–3110 (2016)

    Article  Google Scholar 

  58. Xing, L., Wen, C., Guo, F., Liu, Z., Su, H.: Event-based consensus for linear multiagent systems without continuous communication. IEEE Trans. Cybern. 47(8), 2132–2142 (2017)

    Article  Google Scholar 

  59. Liu, K., Ji, Z., Ren, W.: Necessary and sufficient conditions for consensus of second-order multiagent systems under directed topologies without global gain dependency. IEEE Trans. Cybern. 47(8), 2089–2098 (2017)

    Article  Google Scholar 

  60. Xu, W., Wang, Z., Daniel, W.: Finite-horizon \({H^\infty }\) consensus for multiagent systems with redundant channels via an observer-type event-triggered scheme. IEEE Trans. Cybern. 48, 1567–1576 (2017)

    Google Scholar 

  61. Zhao, M., Peng, C., He, W., Song, Y.: Event-triggered communication for leader-following consensus of second-order multiagent systems. IEEE Trans. Cybern. 48, 1888–1897 (2017)

    Article  Google Scholar 

  62. Seyboth, G.S., Dimarogonas, D.V., Johansson, K.H.: Event-based broadcasting for multi-agent average consensus. Automatica 49(1), 245–252 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  63. Wang, F., Yang, Y.: Leader-following consensus of nonlinear fractional-order multi-agent systems via event-triggered control. Int. J. Syst. Sci. 48(3), 571–577 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  64. Xu, G., Chi, M., He, D., Guan, Z., Zhang, D., Yu, Y.: Fractional-order consensus of multi-agent systems with event-triggered control. IEEE International Conference on Control Automation, pp. 619-624 (2014)

  65. Godsil, C.D., Royle, G.: Algebraic Graph Theory. Springer, New York (2001)

    Book  MATH  Google Scholar 

  66. Li, Y., Chen, Y., Podlubny, I.: Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag-Leffler stability. Comput. Math. Appl. 59(5), 1810–1821 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  67. Duarte-Mermoud, M.A., Aguila-Camacho, N., Gallegos, J.A., Castro-Linares, R.: Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems. Commun. Nonlinear Sci. Numer. Simul. 22(1–3), 650–659 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  68. Ni, W., Cheng, D.: Leader-following consensus of multi-agent systems under fixed and switching topologies. Syst. Control Lett. 59(3–4), 209–217 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  69. Gong, P., Lan, W.: Adaptive robust tracking control for uncertain nonlinear fractional-order multi-agent systems with directed topologies. Automatica 92, 92–99 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  70. Gong, P., Lan, W.: Adaptive robust tracking control for multiple unknown fractional-order nonlinear systems. IEEE Trans. Cybern. (2018). https://doi.org/10.1109/TCYB.2018.2801345

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, School of Science, Beijing Jiaotong University, Beijing, 100044, China

    Guojian Ren, Yongguang Yu, Conghui Xu & Xudong Hai

Authors
  1. Guojian Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yongguang Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Conghui Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xudong Hai
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yongguang Yu.

Ethics declarations

Conflict of interest

We declare that we have no conflict of interest.

Additional information

This work is supported by the National Natural Science Foundation of China under Grant 11371049 and 61772063, and the Fundamental Research Funds for the Central Universities under Grant 2016JBM070 and 2017YJS208.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ren, G., Yu, Y., Xu, C. et al. Consensus of fractional multi-agent systems by distributed event-triggered strategy. Nonlinear Dyn 95, 541–555 (2019). https://doi.org/10.1007/s11071-018-4580-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-018-4580-8

Keywords

Search

Navigation