Skip to main content
Springer Nature Link
Log in

Pruning Based Robust Backpropagation Training Algorithm for RBF Network Tracking Controller

  • Published:
Journal of Intelligent and Robotic Systems Aims and scope Submit manuscript

Abstract

A pruning based robust backpropagation training algorithm is proposed for the online tuning of the Radial Basis Function(RBF) network tracking control system. The structure of the RBF network controller is derived using a filtered error approach. The proposed method in this paper begins with a relatively large network, and certain neural units of the RBF network are dropped by examining the estimation error increment. A complete convergence proof is provided in the presence of disturbance.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Suykens, J.A.K., De Moor, B., Vandewalle, J.: NLq theory: a neural control framework with global asymptotic stability criteria. Neural Netw. 10(4), 615–637 (1997)(June)

    Article  Google Scholar 

  2. Suykens, J.A.K., Vandewalle, J., De Moor, B.: Lur’e systems with multilayer perceptron and recurrent neural networks: absolute stability and dissipativity. IEEE Trans. Automat. Contr. 44(4), 770–774 (1999)(April)

    Article  MATH  Google Scholar 

  3. Lee, M.H., Choi, H.S.: A robust neural controller for underwater robot manipulators. IEEE Trans. Neural Netw. 11, 1465–1470 (2000)

    Article  Google Scholar 

  4. Patino, H.D., Carelli, R., Kuchen, B.R.: Neural networks for advanced control of robot manipulators. IEEE Trans. Neural Netw. 13, 343–354 (2002)

    Article  Google Scholar 

  5. Ge, S.S., Wang, C.: Direct adaptive NN control of a class of nonlinear systems. IEEE Trans. Neural Netw. 13, 214–221 (2002)

    Article  Google Scholar 

  6. Jagannathan, S.: Control of a class of nonlinear discrete-time systems using multilayer neural networks. IEEE Trans. Neural Netw. 12, 1113–1120 (2001)

    Article  Google Scholar 

  7. Song, Q., Hu, W.J., Yin, L., Soh, Y.C.: Robust adaptive dead zone technology for fault-tolerant control of robot manipulators. J. Intell Robot. Syst. 33, 113–137 (2002)

    Article  MATH  Google Scholar 

  8. Song, Q., Xiao, J.Z., Soh, Y.C.: Robust backpropagation training algorithm for multilayered neural tracking controller. IEEE Trans. Neural Netw. 10, 1133–1141 (1999)

    Article  Google Scholar 

  9. Lee, S., Kil, R.M.: A Gaussian potential function network with hierarchically self-organizing learning. Neural Netw. 4, 207–224 (1991)

    Article  Google Scholar 

  10. Bors, A.G., Gabbouj, M.: Minimal topology for a radial basis functions neural network for pattern classification. Digit. Signal Process. 4(3), 173–188 (1994)(July)(A Review Journal)

    Article  Google Scholar 

  11. Chen, T.P., Chen, H.: Approxination capability to functions of several variables, nonlinear functionals, and operators by radial basis function neural networks. IEEE Trans. Neural Netw. 6(4), 904–910 (1995)(July)

    Article  Google Scholar 

  12. Lee, C.-C., Chung, P.-C., Tsai, J.-R., Chang, C.-I.: Robust radial basis function neural networks. IEEE Trans. Syst. Man. Cybern. B. 29(4), 674–685 (1999)

    Google Scholar 

  13. Gomm, J.B., Yu, D.L.: Selecting radial basis function network centers with recursive orthogonal least square training. IEEE Trans. Neural Netw. 11, 306–314 (2000)(March)

    Article  Google Scholar 

  14. Geva, S., Malmstrom, K.: Local cluster neural net: architecture, training and applications. Neural Comput. 20, 36–56 (1998)(March)

    Google Scholar 

  15. Park, J.W., Harley, R.G., Venayagamoorthy, G.K.: Comparision of MLP and RBF neural networks using deviation signals for on-line identification of a synchronous generator. IEEE Trans. Neural Netw. 274–279 (2002)

  16. Abido, M.A., Abdel-Magid, Y.L.: Online identification of synchronous machines using radial basis function neural network. IEEE Trans. Power Syst. 12(4), 1500–1506 (1997)(November)

    Article  Google Scholar 

  17. Elanayar, S., Shin, Y.C.: Radial basis function neural network for approximation and estimation of nonlinear stochastic dynamic systems. IEEE Trans. Neural Netw. 5(4), 594–603 (1994)

    Article  Google Scholar 

  18. Ramakrishna, G., Malik, O.P.: RBF identifier and pole-shifting controller for PSS application. In: Proc. IEEE International Electric Machines and Drives Conference, Seattle, Washington, pp. 589–591 (1999)

  19. Baum, E.B., Haussler, D.: What size gives valide generalization. Neural Comput. 1, 151–160 (1989)

    Google Scholar 

  20. Le Cun, Y.: Generalization and Network Design Strategies. Connectionism in Perspective, pp. 143–155. Elsevier, North Holland (1989)

    Google Scholar 

  21. Haykin, S.: Neural Network – A Comprehensive Fundation. Prentice Hall, New Jersey (1999)

    Google Scholar 

  22. Karystinos, G.N., Pados, D.A.: On overfitting, generalization, and randomly expanded training sets. IEEE Trans. Neural Netw. 11, 1050–1057 (2000)

    Article  Google Scholar 

  23. Karayiannis, N.B., Mi, G.W.: Growing radial basis neural networks: merging supervised and unsupervised learning with network growth techniques. IEEE Trans. Neural Netw. 11, 306–314 (2000)(March)

    Article  Google Scholar 

  24. Hassibi, B., Stork, D.G.: Second-order derivatives for network pruning : optimal brain surgeon. Adv. Neural Inf. Process. Syst. 164–171 (1993)

  25. Cun, Y.L., Denker, J.S., Solla, S.A.: Optimal brain damage. Adv. Neural Inf. Process. Syst. 2, 598–605 (1993)

    Google Scholar 

  26. Platt, J.: A resource allocating network for function interpolation. Neural Comput. 3, 213–225 (1991)

    MathSciNet  Google Scholar 

  27. Kadirkamanathan, V., Niranjan, M.: A function estimation approach to sequential learning with neural network. Neural Comput. 5, 954–975 (1993)

    Google Scholar 

  28. Goodwin, G., Sin, K.S.: Adaptive Filtering, Prediction and Control. Prentice-Hall, Englewood Cliffs, NJ (1984)

    MATH  Google Scholar 

  29. Heiss, M.: Error-minimizing deadzone for basis function networks. IEEE Trans. Neural Netw. 7, 39–50 (1996)

    Google Scholar 

  30. Slotine, J.-J.E., Sanner, R.M: Neural networks for adaptive control and recursive identification: a theoretical framework. In: Trentelman, H.L., Willems, J.C. (eds.) Essays on Control: Perspectives in the Theory and its Application, ch. 11, pp. 381–436. Birkhuaser, Boston, MA (1993)

    Google Scholar 

  31. Colub, G.H., Loan, C.F.V.: Matrix Computation. North Oxford Academic, Oxford, U.K (1983)

    Google Scholar 

  32. Stahlberger, A., Riedmiller, M.: Fast network pruning and feature extraction by using the Unit-OBS algorithm. Adv. Neural Inf. Process. Syst. 9, 655–661 (1997)

    Google Scholar 

  33. Polycarpou, M.M., Ioannou, P.A.: Learning and convergence analysis of neural-type structured networks. IEEE Trans. Neural Netw. 3, 39–50 (1992)

    Article  Google Scholar 

  34. Jagannathan, S., Lewis, F.L.: Multilayer discrete-time neural-net controller with guaranteed performance. IEEE Trans. Neural Netw. 7(1), 107–130 (1996)

    Article  Google Scholar 

  35. Jagannathan, S., Lewis, F.L.: Discrete-time neural net controller for a class of nonlinear dynamic systems. IEEE Trans. Automat. Contr. 4(11), 1693–1699 (1996)

    Article  MathSciNet  Google Scholar 

  36. Zhihong, M., Wu, H.R., Palaniswami, M.: An adaptive tracking controller using neural networks for a class of nonlinear systems. IEEE Trans. Neural Netw. 9(5), 947–955 (1998)

    Article  Google Scholar 

  37. Ni, J., Song, Q.: Dynamic pruning algorithm for multilayer perceptron based neural control systems. Neuro Comput. 69, (16–18) (2006)

    Google Scholar 

  38. Ni, J., Song, Q.: Sequential neuron pruning algorithm for RBF network with guaranteed stability. In: International Joint Conference on Neural Networks (IJCNN’2005) Montreal, Canada, July 2005

  39. Guo, C.Y., Song, Q., Cai, W.J.: A neural network assisted cascade control system for air handling unit. IEEE Ind. Electron. (2007) (in press)

Download references

Author information

Authors and Affiliations

  1. School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore

    Jie Ni & Qing Song

Authors
  1. Jie Ni
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Qing Song
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Qing Song.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ni, J., Song, Q. Pruning Based Robust Backpropagation Training Algorithm for RBF Network Tracking Controller. J Intell Robot Syst 48, 375–396 (2007). https://doi.org/10.1007/s10846-006-9093-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10846-006-9093-x

Key words