Runge-Kutta neural network for identification of dynamical systems in high accuracy

IEEE Transactions on Neural Networks

Volumn 9, Issue 2, 1998, Pages 294-307

  Wang, Yi Jen ^b   Lin, Chin Teng ^a,b  

^a IEEE

^b NATIONAL CHIAO TUNG UNIVERSITY   (Taiwan)

Author keywords

Contraction mapping; Gradient descent; Nonlinear recursive least square; Radial basis function; Runge Kutta method; Vander Pol's equation

Indexed keywords

COMPUTER SIMULATION; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; INTERPOLATION; LEARNING ALGORITHMS; LEAST SQUARES APPROXIMATIONS; STATE ESTIMATION;

RUNGE KUTTA NEURAL NETWORKS (RKNN); VANDER POL'S EQUATION;

NEURAL NETWORKS;

EID: 0032027745     PISSN: 10459227     EISSN: None     Source Type: Journal    
DOI: 10.1109/72.661124     Document Type: Article

References (23)

1. W. T. Miller, R. S. Sutton, and P. J. Werbos, Neural Networks for Control. Cambridge, MA: MIT Press, 1990.
2. K. J. Hunt, D. Sbarbaro, R. Zbikowski, and P. J. Gawthrop, "Neural networks for control systems: A survey," Automatica, vol. 28, no. 6, pp. 1083-1112, Nov. 1992.
3. K. S. Narendra and K. Parthasarathy, "Identification and control of dynamical system using neural networks," IEEE Trans. Neural Networks, vol. 1, pp. 4-27, 1990.
4. Y. Ichikawa and T. Sawa, "Neural network application for direct feedback controllers," IEEE Trans. Neural Networks, vol. 3, pp. 224-231, 1992.
5. P. S. Sastry, G. Santharam, and K. P. Unnikrishnan, "Memory neural networks for identification and control of dynamical systems," IEEE Trans. Neural Networks, vol. 5, pp. 306-319, 1994.
6. R. J. Williams, "Adaptive state representation and estimation using recurrent connectionist networks," in Neural Networks for Control, W. T. Miller, R. S. Sutton, and P. J. Werbos, Eds. Cambridge, MA: MIT Press, 1990.
7. A. G. Parlos, K. T. Chong, and A. F. Atiya, "Application of recurrent multilayer perceptron in modeling complex process dynamics," IEEE Trans. Neural Networks, vol. 5, pp. 255-266, 1994.
8. P. J. Werbos, "Backpropagation through time: What it does and how to do it," in Proc. IEEE, vol. 78, no. 10, pp. 1550-1560, 1990.
9. S. W. Piche, "Steepest descent algorithms for neural network controllers and filters," IEEE Trans. Neural Networks, vol. 5, pp. 198-212, 1994.
10. J. D. Lambert, Computation Methods in O.D.E. New York: Wiley, 1973, ch. 4.
11. F. Caller and C. Desoer, Linear System Theory. New York: Spring-Verlag, 1992.
12. K. Hornik, M. Stinchcombe, and H. White, "Multilayer feedforward networks are universal approximators," Neural Networks, vol. 3, pp. 551-560, 1989.
13. J. Park and I. W. Sandberg, "Universal approximation using radial-basis-fünction networks," Neural Computa., vol. 3, pp. 246-257, 1991.
14. I. G. Petrovski, Ordinary Differential Equations. Englewood Cliffs, NJ: Prentice-Hall, 1966.
15. E. D. Sontag, Mathematical Control Theory: Deterministic Finite-Dimensional Systems. New York: Spring-Verlag, 1990.
16. E. B. Kosmatopoulos, M. M. Polycarpou, M. A. Christodoulou, and P. A. Ioannou, "High-order neural-network structures for identification of dynamical systems," IEEE Trans. Neural Networks, vol. 6, pp. 422-431, 1995.
17. J. Stoer and R. Bulirsch, Introduction to Numerical Analysis, 2nd ed. New York: Springer-Verlag, 1993.
18. V. Lakshmikantham and D. Trigiante, Theory of Difference Equations: Numerical Methods and Applications. Boston, MA: Academic, 1988.
19. R. Fletcher, Practical Methods of Optimization, 2nd ed. Chichester, U.K.: Wiley, 1987.
20. S. Haykin, Neural Networks. New York: Macmillan, 1994, ch. 7.
21. G. C. Goodwin and K. S. Sin, Adaptive Filtering Prediction and Control. Englewood Cliffs, NJ: Prentice-Hall, 1984, ch. 3.
22. P. Linz, Theoretical Numerical Analysis. New York: Wiley, 1979, pp. 126-136.
23. A. Weinmann, Uncertain Models and Robust Control. New York: Springer-Verlag, 1991, ch. 4 and 5.