Skip to main content
SpringerLink
Log in

Event-Based Projective Synchronization for Different Dimensional Complex Dynamical Networks with Unknown Dynamics by Using Data-Driven Scheme

  • Published:
Neural Processing Letters Aims and scope Submit manuscript

Abstract

In this paper, the projective synchronization problem for different dimensional complex networks (CNs) with unknown dynamics is investigated. First, by selecting a projective matrix, the error system is obtained and an event-based projective synchronization control policy is proposed to realize the projective synchronization between two complex networks with different dimensions. It is revealed that the projective synchronization problem can be transformed into the optimal regulation of the error system with a performance function. Then, a data-driven control scheme is proposed to implement the event-trigged projective synchronization control policy, which is composed of identifier, critic network and actuator. The identifier is applied to estimate the unknown dynamics. The actuator is employed to construct the control inputs and the optimal value is estimated by the critic network. Both actuator and critic network are based on neural networks. The neural network weights and controller are updated at event-triggered instant so that the computing and communication resources can be saved. By employing appropriate event-triggered threshold and learning rate of neural network, the synchronization error is proved to be be asymptotically approaching zero and the Zeno behaviors are excluded. Finally, a numerical example is given to verify the effectiveness of the obtained results.

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.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

References

  1. Wu J, Xia Y (2016) Complex-network-inspired design of traffic generation patterns in communication networks. IEEE Trans Circuits Syst II Express Briefs 64(5):590–594

    Article  Google Scholar 

  2. Xuan Q, Zhang Y, Fu C (2018) Social synchrony on complex networks. IEEE Trans Cybern 48(99):1420–1431

    Article  Google Scholar 

  3. Chen Z, Wu J, Xia Y (2017) Robustness of interdependent power grids and communication networks: a complex network perspective. IEEE Trans Circuits Syst II Express Briefs 65(1):115–119

    Article  Google Scholar 

  4. Rubinov M, Sporns O (2010) Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52:1059–1069

    Article  Google Scholar 

  5. Dong T, Huang T (2020) Neural cryptography based on complex-valued neural network. IEEE Trans. Neural Netw. Learn. Syst. 31(11):4999–5004

    Article  MathSciNet  Google Scholar 

  6. Fan Y, Mei J, Liu H, Fan Y (2020) Fast synchronization of complex networks via aperiodically intermittent sliding mode control. Neural Process Lett 51:1331–1352

    Article  Google Scholar 

  7. Wang A, Dong T, Liao X (2016) Event-triggered synchronization strategy for complex dynamical networks with the Markovian switching topologies. Neural Netw 74:52–57

  8. Liu J, Wu H, Cao J (2020) Event-triggered synchronization in fixed time for semi-Markov switching dynamical complex networks with multiple weights and discontinuous nonlinearity. Commun Nonlinear Sci Numer Simul 90:1–21

    MathSciNet  MATH  Google Scholar 

  9. Dong T, Wang A, Zhu H, Liao X (2018) Event-triggered synchronization for reaction-diffusion complex networks via random sampling. Phys. A 495:454–462

    Article  MathSciNet  Google Scholar 

  10. Liu M, Wu H, Zhao W (2020) Event-triggered stochastic synchronization in finite time for delayed semi-Markovian jump neural networks with discontinuous activations. Comp. Appl. Math. 39(2):1–47

    MathSciNet  MATH  Google Scholar 

  11. Dong H, Zhou J, Wang B (2018) Synchronization of nonlinearly and stochastically coupled Markovian switching networks via event-triggered sampling. IEEE Trans Neural Netw Learn Syst 29(11):5691–5700

    Article  MathSciNet  Google Scholar 

  12. Zhao W, Wu H (2018) Fixed-time synchronization of semi-Markovian jumping neural networks with time-varying delays. Adv Differ Equ 213:1–21

    Article  MathSciNet  Google Scholar 

  13. Tang Z, Park J, Shen H (2017) Finite-time cluster synchronization of Lur’e networks: a nonsmooth approach. IEEE Trans Syst Man Cybern Syst 48(8):1213–1224

    Article  Google Scholar 

  14. Hou J, Huang Y, Yang E (2019) Finite-time anti-synchronization of multi-weighted coupled neural networks with and without coupling delays. Neural Process Lett 50:2871–2898

    Article  Google Scholar 

  15. Peng X, Wu H, Cao J (2019) Global nonfragile synchronization in finite time for fractional-order discontinuous neural networks with nonlinear growth activations. IEEE Trans Neural Netw Learn Syst 30(9):2123–2137

    Article  MathSciNet  Google Scholar 

  16. Zhang Y, Wu H, Cao J (2020) Group consensus in finite time for fractional multiagent systems with discontinuous inherent dynamics subject to holder growth. IEEE Trans Cybern. https://doi.org/10.1109/TCYB.2020.3023704

    Article  Google Scholar 

  17. Ali MS, Usha M, Alsaedi A (2020) Synchronization of stochastic complex dynamical networks with mixed time-varying coupling delays. Neural Process Lett 52:1233–1250

    Article  Google Scholar 

  18. Lin D, Liu J, Zhang F (2015) Adaptive outer synchronization of delay-coupled nonidentical complex networks in the presence of intrinsic time delay and circumstance noise. Nonlinear Dyn 80(1–2):117–128

    Article  MathSciNet  Google Scholar 

  19. Fan A, Li J (2018) Adaptive neural network prescribed performance matrix projection synchronization for unknown complex dynamical networks with different dimensions. Neurocomputing 281:55–66

    Article  Google Scholar 

  20. Ding D, Tang Z, Wang Y (2020) Adaptive synchronization of complex dynamical networks via distributed pinning impulsive control. Neural Process Lett 52:2669–2686

    Article  Google Scholar 

  21. Wu Y, Fu S, Li W (2019) Exponential synchronization for coupled complex networks with time-varying delays and stochastic perturbations via impulsive control. J Franklin Inst 356:492–513

    Article  MathSciNet  Google Scholar 

  22. Wang X, Liu X, Zhong S (2017) Pinning impulsive synchronization of complex dynamical networks with various time-varying delay sizes. Nonlinear Anal Hybrid Syst 26:307–318

    Article  MathSciNet  Google Scholar 

  23. Syed AM, Yogambigai J (2017) Exponential stability of semi-Markovian switching complex dynamical networks with mixed time varying delays and impulse control. Neural Process Lett 46:113–133

    Article  Google Scholar 

  24. Lu X, Li H (2020) Distributed pinning impulsive control for inner-outer synchronization of dynamical networks on time scales. Neural Process Lett 51:2481–2495

    Article  Google Scholar 

  25. Cao Y, Yang G, Li X (2019) Optimal synchronization controller design for complex dynamical networks with unknown system dynamics. J Franklin Inst 356(12):6071–6086

    Article  MathSciNet  Google Scholar 

  26. Wen G, Chen C, Feng J (2017) Optimized multi-agent formation control based on an identifier-actor-critic reinforcement learning algorithm. IEEE Trans Fuzzy Syst 26(5):2719–2731

    Article  Google Scholar 

  27. Zhang H, Jiang H, Luo Y (2016) Data-driven optimal consensus control for discrete-time multi-agent systems with unknown dynamics using reinforcement learning method. IEEE Trans Ind Electron 64(5):4091–4100

    Article  Google Scholar 

  28. Pang Z, Liu G, Zhou D (2016) Data-driven control with input design-based data dropout compensation for networked nonlinear systems. IEEE Trans Control Syst Technol 25(2):628–636

    Article  Google Scholar 

  29. Dong L, Zhong X, Sun C (2017) Event-triggered adaptive dynamic programming for continuous-time systems with control constraints. IEEE Trans Neural Netw Learn Syst 28(8):1941–1952

    Article  MathSciNet  Google Scholar 

  30. Yang X, Liu D, Wang D (2014) Reinforcement learning for adaptive optimal control of unknown continuous-time nonlinear systems with input constraints. Int J Control 87(3):553–566

    Article  MathSciNet  Google Scholar 

  31. Wang A, Liao X, Dong T (2018) Event-driven optimal control for uncertain nonlinear systems with external disturbance via adaptive dynamic programming. Neurocomputing 281:188–195

    Article  Google Scholar 

  32. Hu W, Gao L, Dong T (2020) Data-driven optimal synchronization for complex networks with unknown dynamics. IEEE Access 8:224083–224091

    Article  Google Scholar 

  33. Xue S, Luo B, Liu D (2018) Event-triggered adaptive dynamic programming for zero-sum game of partially unknown continuous-time nonlinear systems. IEEE Trans Syst Man Cybern Syst 50(9):3189–3199

    Article  Google Scholar 

  34. Yang X, He H (2018) Adaptive critic designs for event-triggered robust control of nonlinear systems with unknown dynamics. IEEE Trans Cybern 49(6):2255–2267

    Article  Google Scholar 

  35. Yu W, Li X (2001) Some new results on system identification with dynamic neural networks. IEEE Trans Neural Netw 12(2):412–417

    Article  Google Scholar 

  36. Wang D, He H, Liu D (2017) Adaptive critic nonlinear robust control: a survey. IEEE Trans Cybern 47(10):3429–3451

    Article  Google Scholar 

  37. Hassan Z, Travis D, Sarangapani J (2018) Optimal control of nonlinear continuous-time systems in strict-feedback form. IEEE Trans Neural Netw Learn Syst 29(10):37–50

    MathSciNet  Google Scholar 

  38. Ha M, Wang D, Liu D (2020) Event-triggered adaptive critic control design for discrete-time constrained nonlinear systems. IEEE Trans Syst Man Cybern Syst 50(9):3158–3168

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the National Key Research and Development Project of China under Grant 2018AAA0100101, in part by Chongqing Social Science Planning Project under Grant 2019BS053, in part by Fundamental Research Funds for the Central Universities under Grant XDJK2020B009, in part by Chongqing Basic and Frontier Research Project under Grant cstc2019jcyj-msxm2105 and cstc2020jcyj-msxmX0139, in part by the Chongqing Technological Innovation and Application Project under Grant cstc2018jszx-cyzdX0171, in part by the Science and Technology Research Program of Chongqing Municipal Education Commission under Grant KJQN201900816, in part by Chongqing Social Science Planning Project under Grant 2019BS053.

Author information

Authors and Affiliations

  1. School of Business Administration, Chongqing Technology and Business University, Chongqing, 400067, P.R. China

    Wenjie Hu

  2. College of Electronics and Information Engineering, Southwest University, Chongqing, 400715, P.R. China

    Luli Gao & Tao Dong

Authors
  1. Wenjie Hu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Luli Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tao Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tao Dong.

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.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, W., Gao, L. & Dong, T. Event-Based Projective Synchronization for Different Dimensional Complex Dynamical Networks with Unknown Dynamics by Using Data-Driven Scheme. Neural Process Lett 53, 3031–3048 (2021). https://doi.org/10.1007/s11063-021-10515-9

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11063-021-10515-9

Keywords

Search

Navigation