High-Order Neural Network Structure Selection for Function Approximation Applications Using Genetic Algorithms

IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics

Volumn 34, Issue 1, 2004, Pages 150-158

  Rovithakis, G A ^a   Chalkiadakis, I ^b   Zervakis, M E ^b  

^a ARISTOTLE UNIVERSITY OF THESSALONIKI   (Greece)

^b TECHNICAL UNIVERSITY OF CRETE   (Greece)

Author keywords

Genetic algorithms; Neural networks; Nonlinear function approximation; Structure determination

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; DIFFERENCE EQUATIONS; ERROR ANALYSIS; GENETIC ALGORITHMS; LEARNING SYSTEMS; LYAPUNOV METHODS; MULTIVARIABLE SYSTEMS; NONLINEAR EQUATIONS; OPTIMIZATION; POLYNOMIALS; PROBLEM SOLVING;

NONLINEAR FUNCTION APPROXIMATION; STRUCTURE DETERMINATION;

NEURAL NETWORKS;

EID: 0742272570     PISSN: 10834419     EISSN: None     Source Type: Journal    
DOI: 10.1109/TSMCB.2003.811767     Document Type: Article

References (22)

1. N. E. Cotter, "The Stone-Weierstrass theorem and its applications to neural networks," IEEE Trans. Neural Networks, vol. 1, pp. 290-295, 1990.
2. G. Cybenko, "Approximations by superpositions of a sigmoidal function," Math. Contr., Signals, Syst., vol. 2, pp. 303-314, 1989.
3. A. R. Barron, "Universal approximation bounds for superpositions of a sigmoidal function," IEEE Trans. Inform. Theory, vol. 39, pp. 930-945, 1993.
4. G. A. Rovithakis, "Tracking control of multi input affine nonlinear dynamical systems with unknown nonlinearities using dynamical neural networks," IEEE Trans. Syst., Man, Cybern. B, vol. 29, pp. 179-189, 1999.
5. _, "Robust neural adaptive stabilization of unknown systems with measurement noise," IEEE Trans. Syst., Man, Cybern. B, vol. 29, pp. 453-458, 1999.
6. G. A. Rovithakis and M. A. Christodoulou, Adaptive Control With Recurrent High-Order Neural Networks. Berlin, Germany: Springer-Verlag, 2000.
7. G. A. Rovithakis, "Performance of a neural adaptive tracking controller for multi-input nonlinear dynamical systems in the presence of additive and multiplicative external disturbances," IEEE Trans. Syst., Man, Cybern. A, vol. 30, pp. 720-730, 2000.
8. J. Yen, J. C. Liao, B. Lee, and D. Randolph, "A hybrid approach to modeling metabolic systems using a genetic algorithm and simplex approach, " IEEE Trans. Syst., Man, Cybern. B, vol. 28, no. 2, pp. 173-191, 1998.
9. J. H. Holland, "Genetic algorithms," Sci. Amer., pp. 66-72, July 1992.
10. M. R. Azimi-Sadjadi, S. Sheedvash, and F. O. Trujillo, "Recursive dynamic node creation in multilayer neural networks," IEEE Trans. Neural Networks, vol. 4, no. 2, pp. 242-256, 1993.
11. D. Chen, C. Giles, G. Sun, H. Chen, Y. Less, and M. Goudreau, "Constructive learning of recurrent neural networks," in Proc. IEEE In. Conf. Neural Networks, vol. 3, 1993, pp. 1196-1201.
12. B. Hassibi and D. G. Strork, "Second order derivatives for network pruning: optimal brain surgeon," in Advances in Neural Information Processing Systems 5, S. J. Hanson, J. D. Cowan, and C. L. Giles, Eds. San Mateo, CA: Morgan Kaufmann, 1993, pp. 164-171.
13. G. P. Liu and V. Kardirkamanathan, "Multi-objective criteria for neural network structure selection and identification of nonlinear systems using genetic algorithms," Proc. Inst. Elect. Eng., vol. 146, no. 5, 1999.
14. D. Katie and M. Vubratovic, "A neural network based classification of environment dynamic models for compliant control of manipulator robots, " IEEE Trans. Syst., Man, Cybern. B, vol. 28, no. 1, pp. 58-69, 1998.
15. A. Blanco, M. Delgado, and M. Pegalajar, "A genetic algorithm to obtain the optimal recurrent neural network," Int. J. Approx. Reas., vol. 23, no. 1, pp. 67-83, 2000.
16. P. Angeline, G. Saunders, and J. Pollack, "An evolutionary algorithm that constructs recurrent neural networks," IEEE Trans. Neural Networks, vol. 5, no. 1, pp. 54-65, 1994.
17. H. K. Khalil, Nonlinear Systems, Singapore: Maxwell Macmillan Int., 1992.
18. K. S. Tang, C. Y. Chan, K. F. Man, and S. Kwon, "Genetic structure for neural network topology and weights optimization," Proc. Inst. Elect. Eng., 1995.
19. M. M. Gupta and D. H. Rao, Eds., Neuro-Control Systems: Theory and Applications. New York: IEEE Press, 1994.
20. Handbook of Intelligent Control: Neural, Fuzzy and Adaptive Approaches. D. A. White and D. A. Sofge, Eds., Van Nostrand and Reinhold, New York, 1993.
21. T. Poggio and F. Girosi, "Regularization algorithms for learning that are equivalent to multilayer networks," Science, vol. 247, pp. 978-982, 1990.
22. S. H. Lane, D. A. Handelman, and J. J. Gelfand, "Theory and development of higher-order CMAC neural networks," IEEE Contr. Syst. Mag., pp. 23-30, 1992.