Skip to main content
SpringerLink
Log in

Observer-based robust synchronization of fractional-order multi-weighted complex dynamical networks

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

Abstract

In this paper, the problem of robust synchronization of fractional-order multi-weighted complex dynamical networks in the presence of time-varying coupling delay and disturbances is studied via fractional-order equivalent-input-disturbance (FOEID) estimator-based non-fragile feedback control scheme. Precisely, FOEID-based disturbance estimator is incorporated in the feedback control input to compensate the disturbance effect in the resulting closed-loop system, which removes the disturbance effect without any prior knowledge of it. By utilizing FOEID method and synchronization error dynamics, the synchronization problem of fractional-order complex dynamical network is transformed into the stability problem of the augmented form of the closed-loop error system. Based on the Lyapunov stability theory, fractional calculus theory and some advanced integral inequalities, a novel set of sufficient conditions is established to ensure the robust asymptotic stability of the augmented error system subject to time-varying delay and disturbances. Finally, two numerical examples including a comparison study are given to illustrate the obtained theoretical results and the control design.

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
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  1. Xu, Y., Lu, R., Shi, P., Li, H., Xie, S.: Finite-time distributed state estimation over sensor networks with round-robin protocol and fading channels. IEEE Trans. Cybern. 48(1), 336–345 (2018)

    Google Scholar 

  2. Wan, Y., Cao, J., Chen, G., Huang, W.: Distributed observer-based cyber-security control of complex dynamical networks. IEEE Trans. Circuits Syst. I Reg. Pap. 64(11), 2966–2975 (2017)

    MathSciNet  Google Scholar 

  3. Park, J.H., Tang, Z., Feng, J.: Pinning cluster synchronization of delay-coupled Lur’e dynamical networks in a convex domain. Nonlinear Dyn. 89(1), 623–638 (2017)

    MATH  Google Scholar 

  4. Selvaraj, P., Sakthivel, R., Kwon, O.M.: Finite-time synchronization of stochastic coupled neural networks subject to Markovian switching and input saturation. Neural Netw. 105, 154–165 (2018)

    Google Scholar 

  5. 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)

    MATH  Google Scholar 

  6. N’Doye, I., Salama, K.N., Laleg-Kirati, T.M.: Robust fractional-order proportional-integral observer for synchronization of chaotic fractional-order systems. IEEE/CAA J. Autom. Sin. 6(1), 268–277 (2019)

    MathSciNet  Google Scholar 

  7. Wang, H., Jing, X.J.: A sensor network based virtual beam-like structure method for fault diagnosis and monitoring of complex structures with improved bacterial optimization. Mech. Syst. Signal Process. 84, 15–38 (2017)

    Google Scholar 

  8. Abdurahman, A., Jiang, H., Teng, Z.: Finite-time synchronization for fuzzy cellular neural networks with time-varying delays. Fuzzy Sets Syst. 297, 96–111 (2016)

    MathSciNet  MATH  Google Scholar 

  9. Li, X.J., Yang, G.H.: Fuzzy approximation-based global pinning synchronization control of uncertain complex dynamical networks. IEEE Trans. Cybern. 47(4), 873–883 (2016)

    Google Scholar 

  10. Zhang, D., Wang, Q.G., Srinivasan, D., Li, H., Yu, L.: Asynchronous state estimation for discrete-time switched complex networks with communication constraints. IEEE Trans. Neural Netw. Learn. Syst. 29(5), 1732–1746 (2018)

    MathSciNet  Google Scholar 

  11. Aouiti, C., Coirault, P., Miaadi, F., Moulay, E.: Finite time boundedness of neutral high-order Hopfield neural networks with time delay in the leakage term and mixed time delays. Neurocomputing 260, 378–392 (2017)

    Google Scholar 

  12. Liu, M., Wu, J., Sun, Y.Z.: Adaptive finite-time outer synchronization between two complex dynamical networks with noise perturbation. Nonlinear Dyn. 89(4), 2967–2977 (2017)

    MathSciNet  MATH  Google Scholar 

  13. Li, H., Wu, C., Jing, X., Wu, L.: Fuzzy tracking control for nonlinear networked systems. IEEE Trans. Cybern. 47(8), 2020–2031 (2017)

    Google Scholar 

  14. Li, H., Wu, C., Yin, S., Lam, H.K.: Observer-based fuzzy control for nonlinear networked systems under unmeasurable premise variables. IEEE Trans. Fuzzy Syst. 24(5), 1233–1245 (2016)

    Google Scholar 

  15. Feng, J., Li, N., Zhao, Y., Xu, C., Wang, J.: Finite-time synchronization analysis for general complex dynamical networks with hybrid couplings and time-varying delays. Nonlinear Dyn. 88(4), 2723–2733 (2017)

    MathSciNet  MATH  Google Scholar 

  16. Wang, J.L., Wu, H.N., Huang, T., Ren, S.J., Wu, J., Zhang, X.X.: Analysis and control of output synchronization in directed and undirected complex dynamical networks. IEEE Trans. Neural Netw. Learn. Syst. 29(8), 3326–3338 (2018)

    MathSciNet  Google Scholar 

  17. Wang, J.L., Wu, H.N., Huang, T., Ren, S.Y., Wu, J.: Passivity of directed and undirected complex dynamical networks with adaptive coupling weights. IEEE Trans. Neural Netw. Learn. Syst. 28(8), 1827–1839 (2017)

    MathSciNet  Google Scholar 

  18. Wang, Y.W., Bian, T., Xiao, J.W., Wen, C.: Global synchronization of complex dynamical networks through digital communication with limited data rate. IEEE Trans. Neural Netw. Learn. Syst. 26(10), 2487–2499 (2015)

    MathSciNet  Google Scholar 

  19. Wang, J.L., Wu, H.N., Huang, T., Ren, S.Y., Wu, J.: Passivity and output synchronization of complex dynamical networks with fixed and adaptive coupling strength. IEEE Trans. Neural Netw. Learn. Syst. 29(2), 364–376 (2018)

    MathSciNet  Google Scholar 

  20. Su, L., Shen, H.: Mixed \(H_\infty /\) passive synchronization for complex dynamical networks with sampled-data control. Appl. Math. Comput. 259, 931–942 (2015)

    MathSciNet  MATH  Google Scholar 

  21. Wang, J.L., Xu, M., Wu, H.N., Huang, T.: Passivity analysis and pinning control of multi-weighted complex dynamical networks. IEEE Trans. Netw. Sci. Eng. 6(1), 60–73 (2019)

    MathSciNet  Google Scholar 

  22. Qin, Z., Wang, J.L., Huang, Y.L., Ren, S.Y.: Synchronization and \(H_\infty \) synchronization of multi-weighted complex delayed dynamical networks with fixed and switching topologies. J. Frankl. Inst. 354(15), 7119–7138 (2017)

    MATH  Google Scholar 

  23. Shen, J., Lam, J.: Stability and performance analysis for positive fractional-order systems with time-varying delays. IEEE Trans. Autom. Control 61(9), 2676–2681 (2016)

    MathSciNet  MATH  Google Scholar 

  24. Chen, L., Cao, J., Wu, R., Machado, J.T., Lopes, A.M., Yang, H.: Stability and synchronization of fractional-order memristive neural networks with multiple delays. Neural Netw. 94, 76–85 (2017)

    Google Scholar 

  25. Zhang, H., Ye, M., Ye, R., Cao, J.: Synchronization stability of Riemann–Liouville fractional delay-coupled complex neural networks. Physica A Stat. Mech. Appl. 508, 155–165 (2018)

    MathSciNet  Google Scholar 

  26. Jiang, H.P., Liu, Y.Q.: Disturbance rejection for fractional-order time-delay systems. Math. Probl. Eng. 2016, 1–6 (2016)

    MathSciNet  Google Scholar 

  27. Zhang, H., Ye, R., Liu, S., Cao, J., Alsaedi, A., Li, X.: LMI-based approach to stability analysis for fractional-order neural networks with discrete and distributed delays. Int. J. Syst. Sci. 49(3), 537–545 (2018)

    MathSciNet  MATH  Google Scholar 

  28. Zhang, H., Ye, R., Cao, J., Alsaedi, A.: Delay-independent stability of Riemann–Liouville fractional neutral-type delayed neural networks. Neural Process. Lett. 47(3), 427–442 (2018)

    Google Scholar 

  29. Boukal, Y., Michel, Z., Mohamed, D., Radhy, N.D.: Fractional order time-varying-delay systems: a delay-dependent stability criterion by using diffusive representation. In: Azar, A.T., Radwan, A.G., Vaidyanathan, S. (eds.) Mathematical Techniques of Fractional Order Systems, pp. 133–158. Elsevier, Amsterdam (2018)

    Google Scholar 

  30. Zhang, H., Ye, R., Cao, J., Ahmed, A., Li, X., Wan, Y.: Lyapunov functional approach to stability analysis of Riemann–Liouville fractional neural networks with time-varying delays. Asian J. Control 20(5), 1938–1951 (2018)

    MathSciNet  MATH  Google Scholar 

  31. Luo, S., Li, S., Tajaddodianfar, F., Hu, J.: Observer-based adaptive stabilization of the fractional-order chaotic MEMS resonator. Nonlinear Dyn. 92(3), 1079–1089 (2018)

    MATH  Google Scholar 

  32. Chen, X., Zhang, J., Ma, T.: Parameter estimation and topology identification of uncertain general fractional-order complex dynamical networks with time delay. IEEE/CAA J. Autom. Sin. 3(3), 295–303 (2016)

    MathSciNet  Google Scholar 

  33. Bao, H., Park, J.H., Cao, J.: Synchronization of fractional-order complex-valued neural networks with time delay. Neural Netw. 81, 16–28 (2016)

    MATH  Google Scholar 

  34. Li, R., Gao, X., Cao, J.: Non-fragile state estimation for delayed fractional-order memristive neural networks. Appl. Math. Comput. 340, 221–233 (2019)

    MathSciNet  Google Scholar 

  35. Kong, S., Saif, M., Liu, B.: Observer design for a class of nonlinear fractional-order systems with unknown input. J. Frankl. Inst. 354(13), 5503–5518 (2017)

    MathSciNet  MATH  Google Scholar 

  36. Wei, Y.Q., Liu, D.Y., Boutat, D., Chen, Y.M.: An improved pseudo-state estimator for a class of commensurate fractional order linear systems based on fractional order modulating functions. Syst. Control Lett. 118, 29–34 (2018)

    MathSciNet  MATH  Google Scholar 

  37. Dadkhah, N., Rodrigues, L.: Non-fragile state-feedback control of uncertain piecewise-affine slab systems with input constraints: a convex optimisation approach. IET Control Theory Appl. 8(8), 626–632 (2014)

    MathSciNet  Google Scholar 

  38. Zhang, D., Shi, P., Wang, Q.G., Yu, L.: Distributed non-fragile filtering for T–S fuzzy systems with event-based communications. Fuzzy Sets Syst. 306, 137–152 (2017)

    MathSciNet  MATH  Google Scholar 

  39. Yu, H., Hao, F.: Design of event conditions in event-triggered control systems: a non-fragile control system approach. IET Control Theory Appl. 10(9), 1069–1077 (2016)

    MathSciNet  Google Scholar 

  40. Zhang, Z., Zhang, H., Wang, Z., Shan, Q.: Non-fragile exponential \(H_\infty \) control for a class of nonlinear networked control systems with short time-varying delay via output feedback controller. IEEE Trans. Cybern. 47(8), 2008–2019 (2017)

    Google Scholar 

  41. Liu, Y., Guo, B.Z., Park, J.H., Lee, S.M.: Non-fragile exponential synchronization of delayed complex dynamical networks with memory sampled-data control. IEEE Trans. Neural Netw. Learn. Syst. 29(1), 118–128 (2018)

    MathSciNet  Google Scholar 

  42. Gyurkovics, E., Kiss, K., Kazemy, A.: Non-fragile exponential synchronization of delayed complex dynamical networks with transmission delay via sampled-data control. J. Frankl. Inst. 355(17), 8934–8956 (2018)

    MathSciNet  MATH  Google Scholar 

  43. Zhou, J., Park, J.H., Ma, Q.: Non-fragile observer-based \(H_\infty \) control for stochastic time-delay systems. Appl. Math. Comput. 291, 69–83 (2016)

    MathSciNet  MATH  Google Scholar 

  44. Su, L., Ye, D., Yang, X.: Dissipative-based sampled-data synchronization control for complex dynamical networks with time-varying delay. J. Frankl. Inst. 354(15), 6855–6876 (2017)

    MathSciNet  MATH  Google Scholar 

  45. Chen, M., Shao, S.Y., Shi, P., Shi, Y.: Disturbance-observer-based robust synchronization control for a class of fractional-order chaotic systems. IEEE Trans. Circuits Syst. II Exp. Briefs 64(4), 417–421 (2016)

    Google Scholar 

  46. Li, M., Li, D., Wang, J., Zhao, C.: Active disturbance rejection control for fractional-order system. ISA Trans. 52(3), 365–374 (2013)

    Google Scholar 

  47. Ouyang, L., Wu, M., She, J.: Estimation of and compensation for unknown input non-linearities using equivalent-input-disturbance approach. Nonlinear Dyn. 88(3), 2161–2170 (2017)

    MATH  Google Scholar 

  48. She, J., Fang, M., Ohyama, Y., Hashimoto, H., Wu, M.: Improving disturbance-rejection performance based on an equivalent-input-disturbance approach. IEEE Trans. Ind. Electron. 55(1), 380–389 (2008)

    Google Scholar 

  49. Sakthivel, R., Mohanapriya, S., Selvaraj, P., Karimi, H.R., Marshal Anthoni, S.: EID estimator-based modified repetitive control for singular systems with time-varying delay. Nonlinear Dyn. 89(2), 1141–1156 (2017)

    MATH  Google Scholar 

  50. Liu, R.J., Nie, Z.Y., Wu, M., She, J.: Robust disturbance rejection for uncertain fractional-order systems. Appl. Math. Comput. 322, 79–88 (2018)

    MathSciNet  MATH  Google Scholar 

  51. Lan, Y.H., Zhou, Y.: Non-fragile observer-based robust control for a class of fractional-order nonlinear systems. Syst Control Lett. 62, 1143–1150 (2013)

    MathSciNet  MATH  Google Scholar 

  52. Trigeassou, J.C., Maamri, N., Sabatier, J., Oustaloup, A.: A Lyapunov approach to the stability of fractional differential equations. Signal Process. 91(3), 437–445 (2011)

    MATH  Google Scholar 

  53. Kaviarasan, B., Sakthivel, R., Lim, Y.: Synchronization of complex dynamical networks with uncertain inner coupling and successive delays based on passivity theory. Neurocomputing 186, 127–138 (2016)

    Google Scholar 

  54. Lan, Y.H., Gu, H.B., Chen, C.X., Zhou, Y., Luo, Y.P.: An indirect Lyapunov approach to the observer-based robust control for fractional-order complex dynamic networks. Neurocomputing 136, 235–242 (2015)

    Google Scholar 

  55. Qing, Z.H., Wei, J.Y.: Robust \(H_\infty \) observer-based control for synchronization of a class of complex dynamical networks. Chin. Phys. B 20(6), 060504 (2011)

    Google Scholar 

  56. Tang, Z., Park, J.H., Zheng, W.X.: Distributed impulsive synchronization of Lur’e dynamical networks via parameter variation methods. Int. J. Robust Nonlinear 28(3), 1001–1015 (2018)

    MathSciNet  MATH  Google Scholar 

  57. Tang, Z., Park, J.H., Wang, Y., Feng, J.: Distributed impulsive quasi-synchronization of Lur’e networks with proportional delay. IEEE Trans. Cybern. 49(8), 3105–3115 (2019)

    Google Scholar 

  58. Tang, Z., Park, J.H., Feng, J.: Novel approaches to pin cluster synchronization on complex dynamical networks in Lur’e forms. Commun. Nonlinear Sci. Numer. Simul. 57, 422–438 (2018)

    MathSciNet  Google Scholar 

Download references

Acknowledgements

The work of first and fifth authors was supported by the NBHM/DAE under Grant No. 2/48(4)/2013/ NBHM (R.P)/R & D ll/687.

Author information

Authors and Affiliations

  1. Department of Mathematics, Anna University Regional Campus, Coimbatore, Coimbatore, 641046, India

    Ramalingam Sakthivel & Selvaraj Marshal Anthoni

  2. Department of Applied Mathematics, Bharathiar University, Coimbatore, 641046, India

    Rathinasamy Sakthivel

  3. Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, South Korea

    Rathinasamy Sakthivel

  4. School of Electrical Engineering, Chungbuk National University, 1 Chungdae-ro, Cheongju, 28644, South Korea

    Oh-Min Kwon & Palanisamy Selvaraj

Authors
  1. Ramalingam Sakthivel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rathinasamy Sakthivel
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Oh-Min Kwon
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Palanisamy Selvaraj
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Selvaraj Marshal Anthoni
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Rathinasamy Sakthivel or Oh-Min Kwon.

Ethics declarations

Conflict of interest

The authors declare that there is no conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sakthivel, R., Sakthivel, R., Kwon, OM. et al. Observer-based robust synchronization of fractional-order multi-weighted complex dynamical networks. Nonlinear Dyn 98, 1231–1246 (2019). https://doi.org/10.1007/s11071-019-05258-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-019-05258-1

Keywords

Search

Navigation