Nonlinear Dynamics

, Volume 73, Issue 3, pp 1631–1643 | Cite as

Nonlinear system control using a self-organizing functional-linked neuro-fuzzy network

Original Paper


This study presents a self-organizing functional-linked neuro-fuzzy network (SFNN) for a nonlinear system controller design. An online learning algorithm, which consists of structure learning and parameter learning of a SFNN, is presented. The structure learning is designed to determine the number of fuzzy rules and the parameter learning is designed to adjust the parameters of membership function and corresponding weights. Thus, an adaptive self-organizing functional-linked neuro-fuzzy control (ASFNC) system, which is composed of a computation controller and a robust compensator, is proposed. In the computation controller, a SFNN observer is utilized to approximate the system dynamic and the robust compensator is designed to eliminate the effect of the approximation error introduced by the SFNN observer upon the system stability. Finally, to show the effectiveness of the proposed ASFNC system, it is applied to a chaotic system. The simulation results demonstrate that favorable control performance can be achieved by the proposed ASFNC scheme without any knowledge of the control plants and without requiring preliminary offline tuning of the SFNN observer.


Adaptive control Neural control Chaotic system Neural-fuzzy network Functional-linked neural network 



The authors are grateful to the reviewers for their valuable comments. The authors appreciate the partial financial support from the National Science Council of Republic of China under grant NSC 100-2628-E-032-003.


  1. 1.
    Slotine, J.J.E., Li, W.P.: Applied Nonlinear Control. Prentice-Hall, Englewood Cliffs (1991) MATHGoogle Scholar
  2. 2.
    Chen, C.L., Chang, C.W., Yau, H.T.: Terminal sliding mode control for aeroelastic systems. Nonlinear Dyn. 70(3), 2015–2026 (2012) MathSciNetCrossRefGoogle Scholar
  3. 3.
    Liang, C.Y., Su, J.P.: A new approach to the design of a fuzzy sliding mode controller. Fuzzy Sets Syst. 139(1), 111–124 (2003) MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Lin, C.T., Lee, C.S.G.: Neural Fuzzy Systems: A Neuro-Fuzzy Synergism to Intelligent Systems. Prentice-Hall, Englewood Cliffs (1996) Google Scholar
  5. 5.
    Li, C., Lee, C.Y., Cheng, K.H.: Pseudo-error-based self-organizing neuro-fuzzy system. IEEE Trans. Fuzzy Syst. 12(6), 812–819 (2004) CrossRefGoogle Scholar
  6. 6.
    Lin, C.J., Hsu, Y.C.: Reinforcement hybrid evolutionary learning for recurrent wavelet-based neuro-fuzzy systems. IEEE Trans. Fuzzy Syst. 15(4), 729–745 (2007) CrossRefGoogle Scholar
  7. 7.
    Elmas, C., Ustun, O., Sayan, H.H.: A neuro-fuzzy controller for speed control of a permanent magnet synchronous motor drive. Expert Syst. Appl. 34(1), 657–664 (2008) CrossRefGoogle Scholar
  8. 8.
    Chen, C.H., Lin, C.J., Lin, C.T.: Using an efficient immune symbiotic evolution learning for compensatory neuro-fuzzy controller. IEEE Trans. Fuzzy Syst. 17(3), 668–682 (2009) CrossRefGoogle Scholar
  9. 9.
    Orlowska-Kowalska, T., Dybkowski, M., Szabat, K.: Adaptive sliding-mode neuro-fuzzy control of the two-mass induction motor drive without mechanical sensors. IEEE Trans. Ind. Electron. 57(2), 553–564 (2010) CrossRefGoogle Scholar
  10. 10.
    Juang, C.F.: A TSK-type recurrent fuzzy network for dynamic systems processing by neural network and genetic algorithms. IEEE Trans. Fuzzy Syst. 10(2), 155–170 (2002) MathSciNetCrossRefGoogle Scholar
  11. 11.
    Lin, C.J.: An efficient immune-based symbiotic particle swarm optimization learning algorithm for TSK-type neuro-fuzzy networks design. Fuzzy Sets Syst. 159(21), 2890–2909 (2008) CrossRefGoogle Scholar
  12. 12.
    Juang, C.F., Lo, C.: Zero-order TSK-type fuzzy system learning using a two-phase swarm intelligence. Fuzzy Sets Syst. 159(21), 2910–2926 (2008) MathSciNetCrossRefGoogle Scholar
  13. 13.
    Patra, J.C., Kot, A.C.: Nonlinear dynamic system identification using Chebyshev functional link artificial neural networks. IEEE Trans. Syst. Man Cybern., Part B, Cybern. 32(4), 505–511 (2002) CrossRefGoogle Scholar
  14. 14.
    Toh, K.A., Yau, W.Y.: Fingerprint and speaker verification decisions fusion using a functional link network. IEEE Trans. Syst. Man Cybern., Part C, Appl. Rev. 35(3), 357–370 (2005) CrossRefGoogle Scholar
  15. 15.
    Lin, C.J., Wu, C.F.: An efficient symbiotic particle swarm optimization for recurrent functional neural fuzzy network design. Int. J. Fuzzy Syst. 11(4), 262–271 (2009) Google Scholar
  16. 16.
    Chen, C.H., Lin, C.J., Lin, C.T.: A functional-link-based neuro-fuzzy network for nonlinear system control. IEEE Trans. Fuzzy Syst. 16(5), 1362–1378 (2008) CrossRefGoogle Scholar
  17. 17.
    Lin, F.J., Chen, S.Y., Teng, L.T., Chu, H.: A recurrent FL-based fuzzy neural network controller with improved particle swarm optimization for linear synchronous motor drive. IEEE Trans. Magn. 45(8), 3151–3165 (2009) CrossRefGoogle Scholar
  18. 18.
    Lin, F.J., Hsieh, H.J., Chou, P.H., Lin, Y.S.: Digital signal processor-based cross-coupled synchronous control of dual linear motors via functional link radial basis function network. IET Control Theory Appl. 5(4), 552–564 (2011) MathSciNetCrossRefGoogle Scholar
  19. 19.
    Hsu, C.F.: Self-organizing adaptive fuzzy neural control for a class of nonlinear systems. IEEE Trans. Neural Netw. 18(4), 1232–1241 (2007) CrossRefGoogle Scholar
  20. 20.
    Juang, C.F., Wang, C.Y.: A self-generating fuzzy system with ant and particle swarm cooperative optimization. Expert Syst. Appl. 36(3), 5362–5370 (2009) CrossRefGoogle Scholar
  21. 21.
    Cheng, K.H.: Auto-structuring fuzzy neural system for intelligent control. J. Franklin Inst. 346(3), 267–288 (2009) MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Chen, C.S.: Dynamic structure adaptive neural fuzzy control for MIMO uncertain nonlinear systems. Inf. Sci. 179(15), 2676–2688 (2009) MATHCrossRefGoogle Scholar
  23. 23.
    Rubio, J.J.: SOFMLS: online self-organizing fuzzy modified least-squares network. IEEE Trans. Fuzzy Syst. 17(6), 1296–1309 (2009) MathSciNetCrossRefGoogle Scholar
  24. 24.
    Han, H., Qiao, J.: A self-organizing fuzzy neural network based on a growing-and-pruning algorithm. IEEE Trans. Fuzzy Syst. 18(6), 1129–1143 (2010) CrossRefGoogle Scholar
  25. 25.
    Chen, G., Dong, X.: On feedback control of chaotic continuous-time systems. IEEE Trans. Circuits Syst. I 40(9), 591–601 (1993) MathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    Lin, C.M., Chen, C.H.: CMAC-based supervisory control for nonlinear chaotic systems. Chaos Solitons Fractals 35(1), 40–58 (2008) MathSciNetMATHCrossRefGoogle Scholar
  27. 27.
    Peng, Y.F.: Robust intelligent sliding model control using recurrent cerebellar model articulation controller for uncertain nonlinear chaotic systems. Chaos Solitons Fractals 39(1), 150–167 (2009) MathSciNetMATHCrossRefGoogle Scholar
  28. 28.
    Chen, C.S., Chen, H.H.: Robust adaptive neural-fuzzy-network control for the synchronization of uncertain chaotic systems. Nonlinear Anal., Real World Appl. 10(3), 1466–1479 (2009) MathSciNetMATHCrossRefGoogle Scholar
  29. 29.
    Lin, D., Wang, X.: Observer-based decentralized fuzzy neural sliding mode control for interconnected unknown chaotic systems via network structure adaptation. Fuzzy Sets Syst. 161(15), 2066–2080 (2010) MATHCrossRefGoogle Scholar
  30. 30.
    Lin, F.J., Hwang, J.C., Chou, P.H., Hung, Y.C.: FPGA-based intelligent-complementary sliding-mode control for PMLSM servo-drive system. IEEE Trans. Power Electron. 25(10), 2573–2587 (2010) CrossRefGoogle Scholar
  31. 31.
    Hsu, C.F., Chen, G.M., Lee, T.T.: Robust intelligent tracking control with PID-type learning algorithm. Neurocomputing 71(1), 234–243 (2007) CrossRefGoogle Scholar
  32. 32.
    Xu, D., Huang, J.: Robust adaptive control of a class of nonlinear systems and its applications. IEEE Trans. Circuits Syst. I 57(3), 691–702 (2010) MathSciNetCrossRefGoogle Scholar
  33. 33.
    Li, Z., Li, J., Kang, Y.: Adaptive robust coordinated control of multiple mobile manipulators interacting with rigid environments. Automatica 46(12), 2028–2034 (2010) MathSciNetMATHCrossRefGoogle Scholar
  34. 34.
    Wong, C.C., Huang, C.L., Huang, K.H., Hu, Y.Y., Cheng, C.T.: Design and implementation of vision-based fuzzy obstacle avoidance method on humanoid robot. Int. J. Fuzzy Syst. 13(1), 45–54 (2011) Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Department of Electrical EngineeringTamkang UniversityNew Taipei CityTaiwan

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