Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
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Radial Basis Function Network Based Predictive Control of Chaotic Nonlinear Systems

  • Published : 2003.10.01
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Abstract

As a technical method for controlling chaotic dynamics, this paper presents a predictive control for chaotic systems based on radial basis function networks(RBFNs). To control the chaotic systems, we employ an on-line identification unit and a nonlinear feedback controller, where the RBFN identifier is based on a suitable NARMA real-time modeling method and the controller is predictive control scheme. In our design method, the identifier and controller are most conveniently implemented using a gradient-descent procedure that represents a generalization of the least mean square(LMS) algorithm. Also, we introduce a projection matrix to determine the control input, which decreases the control performance function very rapidly. And the effectiveness and feasibility of the proposed control method is demonstrated with application to the continuous-time and discrete-time chaotic nonlinear system.

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References

  1. E. Ott, C. Grebogi and J. A. York, "Controlling Chaos," Physical Review Letters, Vol. 64, No. 11, pp. 1196-1199, 12 March 1990. https://doi.org/10.1103/PhysRevLett.64.1196
  2. G. Chen and X. Dong, "On Feedback Control of Chaotic Continuous-Time Systems," IEEE Trans. on Circuits and Systems, Vol. 40, No. 9, pp. 591-601, September 1993. https://doi.org/10.1109/81.244908
  3. G. Chen, "Optimal Control of Chaotic Systems," Int'l Jour. Bifurcation and Chaos, Vol. 4, No. 2, pp. 461-463, 1994. https://doi.org/10.1142/S0218127494000320
  4. G. Chen, "Intelligent Identification and Control of Chaotic Dynamics," Proc. of IEEE Symp. Circuits and Systems, pp. 5-8, 1996.
  5. K. B. Kim, J. B. Park, Y. H. Choi and G. Chen, "Control of Chaotic Nonlinear Systems Using Radial Basis Function Network Approximators," Information Sciences, Vol. 130, pp. 165-183, 2000. https://doi.org/10.1016/S0020-0255(00)00074-8
  6. K. S. Park, J. B. Park, Y. H. Choi, G. Chen, "Generalized Preclictive Control of Discrete-Time Chaotic System," Int'l Jour. of Bifurcation and Chaos, Vol. 8, No. 7, 1998.
  7. D. W. Clarke, C. Mohtadi and P. S. Tuffs, "Generalized Predictive Control, Part I and lI, The Basic Algorithm," Automatica, Vol. 23, No. 2, pp. 137-148, 1987. https://doi.org/10.1016/0005-1098(87)90087-2
  8. S. Chen, C. F. N. Cowan and P. M. Grant, "Orthogonal Least Squares Learning Algorithm for Raclial Basis Function Networks," IEEE Trans. on Neural Networks, Vol. 2, No. 2, pp. 302-309, March 1991. https://doi.org/10.1109/72.80341
  9. S. M. Botros and C. G. Atkeson, "Generalization Properties of Radial Basis Functions," Advances in Neural Information Processing Systems Ill, pp. 707-713, Morgan Kaufmann, 1991.
  10. V. Kadirkamanathan, M. Niranjan and F. Fallside, "Sequential Adaptation of Radial Basis Function Neural Networks," Advances in Neural Information Processing Systems Ill, pp. 721-727, Morgan Kaufmann, 1991.
  11. M. T. Musavi, W. Ahmed, K. H. Chan, K. B. Faris and D. M. Hummels, "On the Training of Raclial Basis Function Classifiers," Neural Networks, Vol. 5, pp. 595-603, 1992. https://doi.org/10.1016/S0893-6080(05)80038-3
  12. A. S. Pandya and R. B. Macy, Pattern Recognition with Neural Networks in C++, CRC Press, 1996.
  13. K. S. Narendra and S. Mukhopadhyay, "Adaptive Control Using Neural Networks and Approximate Models," IEEE Trans. on Neural Networks, Vol. 8, pp. 475-485, 1997. https://doi.org/10.1109/72.572089
  14. K. V. Ha, "Hierarchical Raclial Basis Function Networks" Proc. of IEEE International Joint Conf. on Neural Networks, Vol. 3, pp. 1893-1898, 1998.
  15. J. B. Rosen, "The Graclient Projection Method for Nonlinear Programming, Part I, Linear Constraints," SIAM J. Applied Mathematics, Vol. 8, pp. 181-217, 1960. https://doi.org/10.1137/0108011

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