The problem of neural network-based robust identification of nonlinear dynamic objects in the presence of non-Gaussian noise is considered. To solve this problem, a radial basis network was chosen whose structure is specified and training is provided with the help of a genetic algorithm. The simulation results are presented that confirm the efficiency of the proposed approach.
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I. J. Leontaritis and S. A. Billings, “Input-output parametric models for non-linear systems. Part I: Deterministic non-linear systems,” Inf. J. of Control., 41, 303–308 (1985).
I. J. Leontaritis and S. A. Billings, “Input-output parametric models for non-linear systems. Part II: Stochastic non-linear systems,” Int. J. of Control, 41, 309–344 (1985).
S. Chen and S. A. Billings, “Representations of nonlinear systems: The NARMAX model,” Int. J. of Control, 49(3), 1013–1032 (1983).
K. S. Narendra and K. Parthasarathy, “Identification and control of dynamical systems using neural networks,” IEEE Trans. on Neural Networks, 1, No. 1, 4–26 (1990).
S. Chen, S. A. Billings, and P. M. Grant, “Recursive hybrid algorithm for non-linear system identification using radial basis function networks,” Int. J. of Control., 55, 1051–1070 (1992).
S. Khaikin, Neural Networks: A Complete Course [in Russian], Izd. Dom “Williams,” Moscow (2006).
J. T. Spooner and K. M. Passino, “Decentralized adaptive control of nonlinear systems using radial basis neural networks,” IEEE Trans. on Automatic Control, 44, No. 11, 2050–2057 (1999).
R. J. Shilling, J. J. Carroll, and A. F. Al-Ajlouni, “Approximation of nonlinear systems with radial basis function neural networks,” IEEE Trans. on Neural Networks, 12, No. 6, 1–15 (2001).
O. G. Rudenko and A. A. Bessonov, “Real-time identification of nonlinear time-varying systems using radial basis function network,” Cybernetics and Systems Analysis, 39, No. 6, 927–934 (2003).
Y. Li, N. Sundararajan, and P. Saratchandran, “Analysis of minimal radial basis function network algorithm for real-time identification of nonlinear dynamic systems,” IEEE Proc., Control Theory Appl., 147, No. 4, 476–484 (2000).
D. L. Yu and D. W. Yu, “A new structure adaptation algorithm for RBF networks and its application,” Neural Comput. & Appl., 16, 91–100 (2007).
E. P. Maillard and D. Gueriot, “RBF neural network, basis functions and genetic algorithm,” in: Proc. Int. Conf. on Neural Networks, 4, Houston, TX (1997), pp. 2187–2192.
S. Ding, L. Xu, and H. Zhu, “Studies on optimization algorithms for some artificial neural networks based on genetic algorithm (GA),” J. Computers, 6, No. 5, 939–946 (2011).
O. Buchtala, M. Klimek, and B. Sick, “Evolutionary optimization of radial basis function classifiers for data mining applications,” IEEE Trans. on Systems, Man, and Cybernetics, Part B, 35, No. 5, 928–947 (2005).
P. Huber, Robustness in Statistics [Russian translation], Mir, Moscow (1984).
F. R. Hampel, E. M. Ronchetti, P. J. Rousseeuw, and W. A. Stahel, Robust Statistics: The approach Based on Influence Functions, Wiley, N.Y. (1986).
D. S. Chen, and R. C. Jain, “A robust back-propagation learning algorithm for function approximation,” IEEE Trans. on Neural Networks, 5, 467–479 (1994).
K. Liano, “A robust approach to supervised learning in neural network,” in: Proc. ICNN, 1 (1994), pp. 513–516.
Ch.-Ch. Lee, P.-Ch. Chung, J.-R. Tsai, and Ch.-I. Chang, “Robust radial basis function neural networks. Part B: Cybernetics,” IEEE Trans. on Systems, Man, and Cybernetics, 29, No. 6, 674–685 (1999).
O. G. Rudenko and A. A. Bessonov, “Robust training of wavelet neural networks,” Probl. Upravl. Inf., No. 5, 66–79 (2010).
O. G. Rudenko and A. A. Bessonov, “Robust training of radial basis networks,” Cybernetics and Systems Analysis, 47, No. 6, 863–870 (2011).
O. Rudenko and O. Bezsonov, “Function approximation using robust radial basis function networks,” J. of Intelligent Learning Systems and Appl., 3, 17–25 (2011).
O. G. Rudenko and A. A. Bessonov, “M-training of radial basis networks using asymmetric influence functions,” Probl. Upravl. Inf., No. 1, 79–93 (2012).
Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 15–26, March–April 2013.
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Rudenko, O.G., Bezsonov, O.O. & Rudenko, S.O. Robust identification of nonlinear objects with the help of an evolving radial basis network. Cybern Syst Anal 49, 173–182 (2013). https://doi.org/10.1007/s10559-013-9497-0
- neural network
- evolutionary algorithm