Skip to main content
SpringerLink
Log in

Adaptive consensus control of fractional multi-agent systems by distributed event-triggered strategy

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

Abstract

In this paper, based on adaptive control, the consensus problem of fractional general linear multi-agent systems is studied. A new adaptive consensus control is designed and applied to the fractional multi-agents systems by distributed event-triggered strategy. The consensus can be achieved for any undirected connection network in the proposed method. Meanwhile, in order to ensure the feasibility of designed controller, a proof is strictly given to exclude Zeno behavior. Furthermore, an adaptive self-triggered algorithm is also proposed to relax the requirement for continuously checking the measurement errors, in which the next update time for each agent is determined according to its local history state information. Effectiveness of proposed control strategies is verified by some numerical simulations.

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
Fig. 6
Fig. 7

Similar content being viewed by others

References

  1. Huang, C., Ye, X.: Pairwise synchronization of multi-agent systems with nonuniform information exchange. Syst. Control Lett. 74, 58–63 (2014)

    MathSciNet  MATH  Google Scholar 

  2. Zhan, J., Li, X.: Flocking of multi-agent systems via model predictive control based on position-only measurements. IEEE Trans. Ind. Inf. 9(1), 377–385 (2013)

    Google Scholar 

  3. Tang, Y., Xing, X., Karimi, H.R., Kocarev, L., Kurths, J.: Tracking control of networked multi-agent systems under new characterizations of impulses and its applications in robotic systems. IEEE Trans. Ind. Electron. 63(2), 1299–1307 (2016)

    Google Scholar 

  4. Ge, C., Park, J.H., Hua, C., Guan, X.: Nonfragile consensus of multiagent systems based on memory sampled-datacontrol. IEEE Trans. Syst. Man Cybem. Syst. (2018). https://doi.org/10.1109/TSMC.2018.2874305

    Article  Google Scholar 

  5. Gil, P., Santos, A., Cardoso, A.: Dealing with outliers in wireless sensor networks: an oil refinery application. IEEE Trans. Control Syst. Technol. 22(4), 1589–1596 (2014)

    Google Scholar 

  6. Zhang, B., Jia, Y.: Fixed-time consensus protocols for multi-agent systems with linear and nonlinear state measurements. Nonlinear Dyn. 82(4), 1683–1690 (2015)

    MathSciNet  MATH  Google Scholar 

  7. Su, Y., Huang, J.: Cooperative output regulation of linear multi-agent systems. IEEE Trans. Autom. Control 57(99), 1062–1066 (2012)

    MathSciNet  MATH  Google Scholar 

  8. Zhai, S., Yang, X.: Consensus of second-order multi-agent systems with nonlinear dynamics and switching topology. Nonlinear Dyn. 77(4), 1667–1675 (2014)

    MathSciNet  MATH  Google Scholar 

  9. Qiu, Z., Xie, L., Hong, Y.: Quantized leaderless and leader-following consensus of high-order multi-agent systems with limited data rate. IEEE Trans. Autom. Control 61(9), 2432–2447 (2016)

    MathSciNet  MATH  Google Scholar 

  10. Wang, X., Li, S., Yu, X., Yang, J.: Distributed active anti-disturbance consensus for leader-follower higher-order multi-agent systems with mismatched disturbances. IEEE Trans. Autom. Control. 62(11), 5795–5801 (2016)

    MathSciNet  MATH  Google Scholar 

  11. Cao, M., Xiao, F., Wang, L.: Event-based second-order consensus control for multi-agent systems via synchronous periodic event detection. IEEE Trans. Autom. Control 60(9), 2452–2457 (2015)

    MathSciNet  MATH  Google Scholar 

  12. Yu, W., Zhou, L., Yu, X., Lu, J., Lu, R.: Consensus in multi-agent systems with second-order dynamics and sampled data. IEEE Trans. Ind. Inf. 9(4), 2137–2146 (2013)

    Google Scholar 

  13. Chen, S., Ho, D.W.C., Li, L., Liu, M.: Fault-tolerant consensus of multi-agent system with distributed adaptive protocol. IEEE Trans. Cybern. 45(10), 2142–2155 (2015)

    Google Scholar 

  14. Ge, C., Park, J.H., Hua, C., Shi, C.: Robust passivity analysis for uncertain neural networks with discrete and distributed time-varying delays. Neurocomputing 364, 330–337 (2019)

    Google Scholar 

  15. Lee, T.H., Park, J.H.: Improved stability conditions of time-varying delay systems based on new Lyapunov functionals. J. Frankl. Inst. 355, 1176–1191 (2018)

    MathSciNet  MATH  Google Scholar 

  16. Lee, T.H., Park, J.H.: Stability analysis of sampled-data systems via free-matrix-based time-dependent discontinuous Lyapunov approach. IEEE Trans. Autom. Control 62(7), 3653–3657 (2017)

    MathSciNet  MATH  Google Scholar 

  17. Shi, K., Wang, J., Zhong, S., Tang, Y., Cheng, J.: Hybrid-driven finite-time \(H^\infty \) sampling synchronization control for coupling memory complex networks with stochastic cyber attacks. Neurocomputing (2020). https://doi.org/10.1016/j.neucom.2020.01.022

    Article  Google Scholar 

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

    MATH  Google Scholar 

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

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  21. Arshad, S., Lupulescu, V.: On the fractional differential equations with uncertainty. Nonlinear Anal.-Theory Methods Appl. 74(11), 3685–3693 (2011)

    MathSciNet  MATH  Google Scholar 

  22. Yin, C., Cheng, Y.H., Chen, Y.Q., Stark, B., Zhong, S.M.: Adaptive fractional-order switching-type control method design for 3d fractional-order nonlinear systems. Nonlinear Dyn. 82(1), 39–52 (2015)

    MathSciNet  MATH  Google Scholar 

  23. Yin, C., Chen, Y.Q., Zhong, S.M.: Fractional-order sliding mode based extremum seeking control of a class of nonlinear system. Automatica 50, 3173–3181 (2014)

    MathSciNet  MATH  Google Scholar 

  24. 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)

    Google Scholar 

  25. 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)

    MathSciNet  MATH  Google Scholar 

  26. Gong, P., Lan, W.: Adaptive robust tracking control for multiple unknown fractional-order nonlinear systems. IEEE Trans. Cybern. 49(4), 1365–1376 (2019)

    Google Scholar 

  27. Ye, Y., Su, H.: Leader-following consensus of nonlinear fractional-order multi-agent systems over directed networks. Nonlinear Dyn. 96, 1391–1403 (2019)

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  30. Yu, Z., Jiang, H., Hu, C.: Leader-following consensus of fractional-order multi-agent systems under fixed topology. Neurocomputing 149, 613–620 (2015)

    Google Scholar 

  31. Yin, X., Yue, D., Hu, S.: Brief paper—consensus of fractional-order heterogeneous multi-agent systems. IET Contr. Theory Appl 7(2), 314–322 (2013)

    Google Scholar 

  32. Bai, J., Wen, G., Rahmani, A., Yu, Y.: Consensus for the fractional-order double-integrator multi-agent systems based on the sliding mode estimator. IET Contr. Theory Appl. 12(5), 621–628 (2018)

    MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  34. Ge, C., Park, J.H., Hua, C., Guan, X.: Dissipativity analysis for T–S fuzzy system under memory sampled-data control. IEEE Trans. Cybern. (2019). https://doi.org/10.1109/TCYB.2019.2918793

    Article  Google Scholar 

  35. Ge, C., Shi, Y., Park, J.H., Hua, C.: State estimate for fuzzy neural networks with random uncertainties based on sampled-data control. J. Frankl. Inst. 357, 635–650 (2020)

    MathSciNet  MATH  Google Scholar 

  36. Shi, K., Wang, J., Zhong, S., Tang, Y., Cheng, J.: Non-fragile memory filtering of T-S fuzzy delayed neural networks based on switched fuzzy sampled-data control. Fuzzy Sets Syst. (2019). https://doi.org/10.1016/j.fss.2019.09.001

    Article  Google Scholar 

  37. Lee, T.H., Park, J.H.: New methods of fuzzy sampled-data control for stabilization of chaotic systems. IEEE Trans. Syst. Man Cybern. Syst. 48(12), 2026–2034 (2018)

    Google Scholar 

  38. Shi, K., Wang, J., Tang, Y., Zhong, S.: Reliable asynchronous sampled-data filtering of TCS fuzzy uncertain delayed neural networks with stochastic switched topologies. Fuzzy Sets Syst. 381, 1–25 (2020)

    Google Scholar 

  39. Wang, X., She, K., Zhong, S.M., Cheng, J.: Synchronization of complex networks with non-delayed and delayed couplings via adaptive feedback and impulsive pinning control. Nonlinear Dyn. 86(1), 165–176 (2016)

    MathSciNet  MATH  Google Scholar 

  40. Xing, L., Wen, C., Liu, Z., Su, H., Cai, J.: Event-triggered adaptive control for a class of uncertain nonlinear systems. IEEE Trans. Autom. Control 62(4), 2071–2076 (2017)

    MathSciNet  MATH  Google Scholar 

  41. Xu, C., Wu, B., Cao, X., Zhang, Y.: Distributed adaptive event-triggered control for attitude synchronization of multiple spacecraft. Nonlinear Dyn. 95(4), 2625–2638 (2019)

    Google Scholar 

  42. Yin, C., Dadras, S., Zhong, S.M., Chen, Y.Q.: Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach. Appl. Math. Model. 37(4), 2469–2483 (2013)

    MathSciNet  MATH  Google Scholar 

  43. 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)

    MathSciNet  MATH  Google Scholar 

  44. Wang, Q.G., Feng, W.J., Chen, M.Z.Q., Wang, L.: Consensus of nonlinear multi-agent systems with adaptive protocols. IET Contr. Theory Appl. 8(18), 2245–2252 (2014)

    MathSciNet  Google Scholar 

  45. Ma, T., Song, Y., Feng, C., Lewis, F.L., Zhao, C., Cui, B.: Distributed adaptive consensus control of heterogeneous multi-agent chaotic systems with unknown time delays. IET Contr. Theory Appl. 9(16), 2414–2422 (2015)

    MathSciNet  Google Scholar 

  46. Qian, Y., Liu, L., Feng, G.: Output consensus of heterogeneous linear multi-agent systems with adaptive event-triggered control. IEEE Trans. Autom. Control 64(6), 2606–2613 (2019)

    MathSciNet  MATH  Google Scholar 

  47. Chen, W., Li, X., Ren, W., Wen, C.: Adaptive consensus of multi-agent systems with unknown identical control directions based on a novel nussbaum-type function. IEEE Trans. Autom. Control 59(7), 1887–1892 (2014)

    MathSciNet  MATH  Google Scholar 

  48. Liu, L., Member, S.: Adaptive cooperative output regulation for a class of nonlinear multi-agent systems. IEEE Trans. Autom. Control 60(6), 1677–1682 (2015)

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  50. Yang, J., Luo, W., Yi, H., Xu, W.: Adaptive consensus control of nonlinear fractional-order multi-agent systems with a leader. In: The 3rd International Symposium on Autonomous Systems (ISAS), pp. 528-533 (2019)

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

    MATH  Google Scholar 

  52. 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)

    MathSciNet  MATH  Google Scholar 

  53. 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)

    MathSciNet  MATH  Google Scholar 

  54. Ren, G., Yu, Y., Xu, C., Hai, X.: Consensus of fractional multi-agent systems by distributed event-triggered strategy. Nonlinear Dyn. 95(1), 541–555 (2019)

    Google Scholar 

  55. Yu, J., Hu, C., Jiang, H., Fan, X.: Projective synchronization for fractional neural networks. Neural Netw. 49, 87–95 (2014)

    MATH  Google Scholar 

Download references

Funding

The research was partially supported by the National Natural Science Foundation of China (NSFC) under Grants 11571083, 61771004 and 61873305.

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, China

    Li Luo, Wen Mi & Shouming Zhong

Authors
  1. Li Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wen Mi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shouming Zhong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Wen Mi.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The research was supported by National Natural Science Foundation of China (NSFC) under Grant 11571083.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Luo, L., Mi, W. & Zhong, S. Adaptive consensus control of fractional multi-agent systems by distributed event-triggered strategy. Nonlinear Dyn 100, 1327–1341 (2020). https://doi.org/10.1007/s11071-020-05586-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-020-05586-7

Keywords

Search

Navigation