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Learning Convergence of CMAC Algorithm

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Abstract

CMAC convergence properties both in batch and in incremental learning are analyzed. The previous conclusions about the CMAC convergence, which are deduced under the condition that the articulation matrix is positive definite, are improved into the new less limited and more general conclusions in which no additive conditions are needed. An improved CMAC algorithm with self-optimizing learning rate is proposed from the new conclusions. Simulation results show the correctness of the new conclusions and the advantages of the improved algorithm.

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References

  1. Albus, J. S.: A new approach to manipulator control: the cerebellar model articulation controller (CMAC), Trans. of ASME Journal of Dynamic Systems, Measurements, and Control, 97(3) (1975) 220–227.

    Google Scholar 

  2. Albus, J. S.: Data storage in the cerebellar model articulation controller (CMAC), Trans. of ASME Journal of Dynamic Systems, Measurements, and Control, 97(3) (1975) 228–233.

    Google Scholar 

  3. Miller, W. T., Glanz, F. H., and Kraft, L. G.: CMAC: An associative neural network alternative to backpropagation, Proc. IEEE, 78(10) (1990) 1561–1567.

    Google Scholar 

  4. Cetinkunt, S. and Donmez, A.: CMAC learning controller for servo control of high precision machine tools, Proc. of American Control Conference, San Francisco, CA (1993) pp. 1976–1980.

  5. Larsen, G. A., Ku, S. S., and Cetinkunt, S.: Low speed motion control experiments on a single point diamond turning machine usin CMAC learning control algorithm, Proc. of ASME Dynamic Systems and Control Division, DSC57(1) (1995) 497–501.

    Google Scholar 

  6. Larsen, G. A., Cetinkunt, S., and Donmez, A.: CMAC neural network control for high precision motion control in the presence of large friction, Journal of Dynamic Systems, Measurement, and Control, 117 (1995) 415–420.

    Google Scholar 

  7. Ku, S.-S, Larsen, G., and Cetinkunt, S.: Fast tool servo control for ultra-precision machining at extremely low feed rates, Mechatronics, 8 (1998) 381–393.

    Google Scholar 

  8. Trouretzky, D. S. (ed.), Neural Information Processing Systems 1, Morgan Kaufmann, Los Altos, CA, 1989.

    Google Scholar 

  9. Wong, Y.-F. and Sideris, A.: Learning convergence in the cerebellar model articulation controller, IEEE Trans. Neural Networks, 3(1) (1992) 115–121.

    Google Scholar 

  10. Zhang, L. and Zhang, B.: Theories and Applications of the Artificial Neural Networks, Zhejiang Science and Technology Publishing House, Hangzhou, China, 1997.

    Google Scholar 

  11. Luo, Z, Xie, Y., and Zhu, C.: A study of the convergence of the CMAC learning process, Acta Automatica Sinica, 23(4) (1997) 455–461.

    Google Scholar 

  12. Liu, H., Xu, X., and Zhang, Z.: An improved CMAC neural network algorithm, Acta Automatica Sinica 23(4) (1997) 482–488.

    Google Scholar 

  13. Ding, L.: Numerical Calculation Methods, Beijing Institute of Technology Publisher, Beijing, China, 1997.

    Google Scholar 

  14. Shi, R.: Matrix Analysis, Beijing Institute of Technology Publisher, Beijing, China, 1996.

    Google Scholar 

  15. Xi, M.: Numerical Analysis Methods, Chinese science and Technology Publisher, Hefei, China, 1995.

    Google Scholar 

  16. Li, B.: The combination of chaos search and stochastic search, Proc. of 1999 Chinese Conference on Artificial Intelligence and Automation, Tsinghua University Publisher, Beijing, China (1999) pp. 823–826.

    Google Scholar 

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He, C., Xu, L. & Zhang, Y. Learning Convergence of CMAC Algorithm. Neural Processing Letters 14, 61–74 (2001). https://doi.org/10.1023/A:1011382225296

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