Advertisement

Synchronization of single-degree-of-freedom oscillators via neural network based on fixed-time terminal sliding mode control scheme

  • Haibin Sun
  • Linlin Hou
  • Chaojie Li
Original Article
  • 71 Downloads

Abstract

In this paper, the synchronization problem is investigated for two single-degree-of-freedom oscillators via neural network based on fixed-time terminal sliding mode control. First, a fixed-time terminal sliding mode is constructed. Then, in order to deal with the unknown function in master system, the neural network technique is introduced. Combining fixed-time terminal sliding mode surface and adaptive control scheme plus neural network technique, an adaptive fixed-time terminal sliding mode controller is presented. The stability of the closed-loop system is analyzed. Finally, simulation results are provided to demonstrate the effectiveness of the proposed two control strategies.

Keywords

Oscillators Synchronization Non-singular fixed-time control Sliding mode control Neural network Adaptive control 

Notes

Acknowledgements

This work was supported in part by the National natural Science Foundation of China (Nos. 61773236, 61773235), and the Postdoctoral Science Foundation of China (2017M612236, 2017M611222).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interests.

References

  1. 1.
    Chung SJ, Slotine JJE (2009) Cooperative robot control and concurrent synchronization of Lagrangian systems. IEEE Trans Rob 25(3):686–700CrossRefGoogle Scholar
  2. 2.
    Du HB, Li SH (2014) Attitude synchronization control for a group of flexible spacecraft. Automatica 50(2):646–651MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Zhang Z, Shen H, Li J (2011) Adaptive stabilization of uncertain unified chaotic systems with nonlinear input. Appl Math Comput 218(8):4260–4267MathSciNetzbMATHGoogle Scholar
  4. 4.
    Jia Q (2007) Adaptive control and synchronization of a new hyperchaotic system with unknown parameters. Phys Lett A 362(5–6):424–429CrossRefzbMATHGoogle Scholar
  5. 5.
    Li R, Xu W, Li S (2009) Anti-synchronization on autonomous and non-autonomous chaotic systems via adaptive feedback control. Chaos Solitons Fractals 40(3):1288–1296MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Li HQ, Liao XF, Li CD, Li CJ (2011) Chaos control and synchronization via a novel chatter free sliding mode control strategy. Neurocomputing 74(17):3212–3222CrossRefGoogle Scholar
  7. 7.
    Li HQ, Liao XF, Chen G, Hill DJ, Dong ZY, Huang TW (2015) Event-triggered asynchronous intermittent communication strategy for synchronization in complex dynamical networks. Neural Netw 66:1–10CrossRefGoogle Scholar
  8. 8.
    Li CJ, Gao DY, Liu C, Chen G (2014) Impulsive control for synchronizing delayed discrete complex networks with switching topology. Neural Comput Appl 24(1):59–68CrossRefGoogle Scholar
  9. 9.
    Li CJ, Yu XH, Huang TW, He X (2017) Distributed optimal consensus over resource allocation network and its application to dynamical economic dispatch. IEEE Trans Neural Netw Learn Syst.  https://doi.org/10.1109/TNNLS.2017.2691760 Google Scholar
  10. 10.
    Li CJ, Yu XH, Yu WW, Huang TW, Liu ZW (2016) Distributed event-triggered scheme for economic dispatch in smart grids. IEEE Trans Ind Inf 12(5):1775–1785CrossRefGoogle Scholar
  11. 11.
    Lei Y, Xu W, Shen J, Fang T (2006) Global synchronization of two parametrically excited systems using active control. Chaos Solitons Fractals 28(2):428–436MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Wu XF, Cai JP, Wang MH (2008) Global chaos synchronization of the parametrically excited Duffing oscillators by linear state error feedback control. Chaos Solitons Fractals 36(1):121–128MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Lei Y, Yung KL, Xu Y (2010) Chaos synchronization and parameter estimation of single-degree-of-freedom oscillators via adaptive control. J Sound Vib 329(8):973–979CrossRefGoogle Scholar
  14. 14.
    Zhang Z, Wang Y, Du Z (2012) Adaptive synchronization of single-degree-of-freedom oscillators with unknown parameters. Appl Math Comput 218(12):6833–6840MathSciNetzbMATHGoogle Scholar
  15. 15.
    Yan JJ, Hung ML, Liao TL (2006) Adaptive sliding mode control for synchronization of chaotic gyros with fully unknown parameters. J Sound Vib 298(1–2):298–306MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Yuan J, Shi B, Xiu G (2016) Sliding control for single-degree-of-freedom fractional oscillators. arXiv preprint arXiv:1608.04850
  17. 17.
    Haibo Du, Xinghuo Yu, Michael Z.Q. Chen, Shihua Li, (2016) Chattering-free discrete-time sliding mode control. Automatica 68:87-91MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Du HB, Wen GH, Cheng YY, He YG, Jia RT (2017) Distributed finite-time cooperative control of multiple high-order nonholonomic mobile robots. IEEE Trans Neural Netw Learn Syst 28(12):2998–3006MathSciNetCrossRefGoogle Scholar
  19. 19.
    Du HB, Wen GH, Yu XH, Li SH, Chen MZQ (2015) Finite-time consensus of multiple nonholonomic chained-form systems based on recursive distributed observer. Automatica 62(12):236–242MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Du HB, He YG, Cheng YY (2014) Finite-time synchronization of a class of second-order nonlinear multi-agent systems using output feedback control. IEEE Trans Circuits Syst I Regul Pap 61(6):1778–1788CrossRefGoogle Scholar
  21. 21.
    Sun H, Hou L, Zong G (2016) Continuous finite time control for static var compensator with mismatched disturbances. Nonlinear Dyn 85(4):2159–2169CrossRefzbMATHGoogle Scholar
  22. 22.
    Aghababa MP, Khanmohammadi S, Alizadeh G (2011) Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique. Appl Math Model 35(6):3080–3091MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Li S, Tian YP (2003) Finite time synchronization of chaotic systems. Chaos Solitons Fractals 15(2):303–310MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Filippov AF (1988) Differential equations with discontinuous right-hand sides. Kluwer Academic, New YorkCrossRefzbMATHGoogle Scholar
  25. 25.
    Polyakov A (2012) Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Trans Autom Control 57(8):2106–2110MathSciNetCrossRefzbMATHGoogle Scholar
  26. 26.
    Zuo ZY (2015) Non-singular fixed-time terminal sliding mode control of non-linear systems. IET Control Theory Appl 9(4):545–552MathSciNetCrossRefGoogle Scholar
  27. 27.
    Ni JK, Liu L, Liu CX, Hu XY, Li SL (2017) Fast fixed-time nonsingular terminal sliding mode control and its application to chaos suppression in power system. IEEE Trans Circuits Syst II Express Briefs 64(2):151–155CrossRefGoogle Scholar
  28. 28.
    Park J, Sandberg IW (1991) Universal approximation using radial-basis-function networks. Neural Comput 3(2):246–257CrossRefGoogle Scholar
  29. 29.
    Sanner RM, Slotine JJ (1992) Gaussian networks for direct adaptive control. IEEE Trans Neural Netw 3(6):837–863CrossRefGoogle Scholar
  30. 30.
    Sun H, Guo L (2017) Neural network-based DOBC for a class of nonlinear systems with unmatched disturbances. IEEE Trans Neural Netw Learn Syst 28(2):482–489MathSciNetCrossRefGoogle Scholar
  31. 31.
    Li CJ, Yu XH, Huang TW, Chen G, He X (2016) A generalized Hopfield network for nonsmooth constrained convex optimization: Lie derivative approach. IEEE Trans Neural Netw Learn Syst 27(2):308–321MathSciNetCrossRefGoogle Scholar
  32. 32.
    Bhat SP, Bernstein DS (1995) Lyapunov analysis of finite-time differential equations. In: Proceedings of the American control conference, 1831–1832Google Scholar
  33. 33.
    Bhat SP, Bernstein DS (1998) Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans Autom Control 43(5):678–682MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Feng Y, Yu X, Man Z (2002) Non-singular terminal sliding mode control of rigid manipulators. Automatica 28(11):2159–2167MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Sun HB, Li SH, Sun CY (2013) Finite time integral sliding mode control of hypersonic vehicles. Nonlinear Dyn 73(1–2):229–244MathSciNetCrossRefzbMATHGoogle Scholar
  36. 36.
    Li YK, Sun HB, Zong GD, Hou LL (2017) Composite anti-disturbance resilient control for Markovian jump nonlinear systems with partly unknown transition probabilities and multiple disturbances. Int J Robust Nonlinear Control 27(14):2323–2337MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Xu B, Sun FC (2018) Composite intelligent learning control of strict feedback systems with disturbance. IEEE Trans Cybern 48(2):730–741CrossRefGoogle Scholar
  38. 38.
    Sun HB, Li YK, Zong GD, Hou LL (2018) Disturbance attenuation and rejection for stochastic Markovian jump system with partially known transition probabilities. Automatica 89:349–357MathSciNetCrossRefGoogle Scholar

Copyright information

© The Natural Computing Applications Forum 2018

Authors and Affiliations

  1. 1.School of EngineeringQufu Normal UniversityRizhaoP. R. China
  2. 2.School of Information Science and EngineeringQufu Normal UniversityRizhaoP. R. China
  3. 3.School of EngineeringRMIT UniversityMelbourneAustralia

Personalised recommendations