Hopfield Neural Network Identification for Prandtl-Ishlinskii Hysteresis Nonlinear System

  • Xuehui GaoEmail author
  • Shubo Wang
  • Ruiguo Liu
  • Bo Sun
Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 528)


A new Hopfield Neural Network (HNN) identification approach is proposed for a Prandtl-Ishlinskii (P-I) hysteresis nonlinear system. Firstly, The P-I hysteresis nonlinear system is transformed into canonical form by linear state transformation with \(B^\perp \) to suit the identification design. Then, we define a energy function E which is constituted by the transformed canonical state space system coefficients. Another suitable energy function \(E_n\) is proposed with HNN to identify the hysteresis system. Finally, simulation results have verified the performance of the proposed identification.


HNN Identification Hysteresis P-I model 



This work is Supported by the National Natural Science Foundation of China (61433003), Shandong Natural Science Foundation of China(ZR2017MF048), Shandong Key Research and Development Programme (2016GGX105013), Shandong Science and technology program of higher education (J17KA214), Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents (2016RCJJ035), Tai’an Science and Technology development program (2017GX0017).


  1. 1.
    J. Na, A.S. Chen, G. Herrmann, R. Burke, C. Brace, Vehicle engine torque estimation via unknown input observer and adaptive parameter estimation. IEEE Transactions on Vehicular Technology 67(1), 409–422 (2018). JanCrossRefGoogle Scholar
  2. 2.
    S. Wang, J.Na, X. Ren, Rise-based asymptotic prescribed performance tracking control of nonlinear servo mechanisms. IEEE Trans. Syst. Man Cybern. Syst. (99), 1–12 (2017)Google Scholar
  3. 3.
    D. Zhang, M. Jia, Y. Liu, Z. Ren, C.S. Koh, Comprehensive improvement of temperature-dependent jiles-atherton model utilizing variable model parameters. IEEE Trans. Mag. 54(3), 1–4 (2018). MarchGoogle Scholar
  4. 4.
    X. Gao, X. Ren, C. Zhu, C. Zhang, Identification and control for hammerstein systems with hysteresis non-linearity. IET Control Theory Appl. 9(13), 1935–1947 (2015)MathSciNetCrossRefGoogle Scholar
  5. 5.
    X. Gao, R. Liu, B. Sun, D. Shen, Neural Network Adaptive Control for Hysteresis Hammerstein System, vol. 459 (China, Mudanjiang, 2018), pp. 259–269Google Scholar
  6. 6.
    G. Xuehui, S. Bo, Identification for Bouc-Wen hysteresis system with hopfield neural network, in 2017 9th International Conference on Modelling, Identification and Control (ICMIC), July 2017, pp. 248–253Google Scholar
  7. 7.
    P. Cheng, R. Szewczyk, Modified Description of Magnetic Hysteresis in Jiles-Atherton Model, vol. 743 (Warsaw, Poland, 2018), pp. 648–654Google Scholar
  8. 8.
    N. Pop, O. Caltun, Jiles-atherton magnetic hysteresis parameters identification. Acta Phys. Polon. A 120(3), 491–496 (2011)CrossRefGoogle Scholar
  9. 9.
    J. Zou, G. Gu, Modeling the viscoelastic hysteresis of dielectric elastomer actuators with a modified rate-dependent Prandtl-Ishlinskii model. Polymers 10(5) (2018)Google Scholar
  10. 10.
    M. Al Janaideh, O. Aljanaideh, Further results on open-loop compensation of rate-dependent hysteresis in a magnetostrictive actuator with the Prandtl-Ishlinskii model. Mech. Syst. Signal Process. 104, 835–850 (2018)Google Scholar
  11. 11.
    M. Atencia, G. Joya, F. Sandoval, Identification of noisy dynamical systems with parameter estimation based on hopfield neural networks. Neurocomputing 121, 14–24 (2013)CrossRefGoogle Scholar
  12. 12.
    C.-H. Wang, K.-N. Hung, Dynamic system identification using high-order hopfield-based neural network (HOHNN). Asian J. Control 14(6), 1553–1566 (2012)MathSciNetCrossRefGoogle Scholar
  13. 13.
    S. Liu, C.-Y. Su, Inverse error analysis and adaptive output feedback control of uncertain systems preceded with hysteresis actuators. Control Theory Appl. IET 8(17), 1824–1832 (2014)MathSciNetCrossRefGoogle Scholar
  14. 14.
    P.V.N.M. Vidal, E.V.L. Nunes, L. Hsu, Output-feedback multivariable global variable gain super-twisting algorithm. IEEE Trans. Autom. Control 62(6), 2999–3005 (2017). JuneMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Department of Mechanical and Electrical EngineeringShandong University of Science and TechnologyTai’anChina
  2. 2.College of Automation and Electrical EngineeringQingdao UniversityQingdaoPeople’s Republic of China

Personalised recommendations