Abstract
In general, RBF neural network cannot match nonlinear systems exactly. Unmodeled dynamic leads parameters drift and even instability problem. According to system identification theory, robust modification terms must be included in order to guarantee Lyapunov stability. This paper suggests new learning laws for normal and adjustable RBF neural networks based on Input-to-State Stability (ISS) approach. The new learning schemes employ a time-varying learning rate that is determined from input-output data and model structure. The calculation of the learning rate does not need any prior information such as estimation of the modeling error bounds.
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References
Cybenko, G.: Approximation by Superposition of Sigmoidal Activation Function. Math.Control Sig. Syst. 2, 303–314 (1989)
Egardt, B.: Stability of Adaptive Controllers. Lecture Notes in Control and Information Sciences, vol. 20. Springer, Berlin (1979)
Haykin, S.: Neural Networks- A Comprehensive Foundation. Macmillan College Publ. Co., New York (1994)
Ioannou, P.A., Sun, J.: Robust Adaptive Control. Prentice-Hall, Inc., Upper Saddle River (1996)
Jagannathan, S., Lewis, F.L.: Identification of Nonlinear Dynamical Systems Using Multilayered Neural Networks. Automatica 32, 1707–1712 (1996)
Jin, L., Gupta, M.M.: Stable Dynamic Backpropagation Learning in Recurrent Neural Networks. IEEE Trans. Neural Networks 10, 1321–1334 (1999)
Jiang, Z.P., Wang, Y.: Input-to-State Stability for Discrete-Time Nonlinear Systems. Automatica 37, 857–869 (2001)
Kosmatopoulos, E.B., Polycarpou, M.M., Christodoulou, M.A., Ioannou, P.A.: High-Order Neural Network Structures for Identification of Dynamical Systems. IEEE Trans. on Neural Networks 6, 442–431 (1995)
Mandic, D.P., Hanna, A.I., Razaz, M.A.: Normalized Gradient Descent Algorithm for Nonlinear Adaptive Filters Using a Gradient Adaptive Step Size. IEEE Signal Processing Letters 8, 295–297 (2001)
Peng, H., Ozaki, T., Ozaki, V.H., Toyoda, Y.: A Parameter Optimization Method for Radial Basis Function Type Models. IEEE Trans. Neural Networks 14, 432–438 (2003)
Polycarpou, M.M., Ioannou, P.A.: Learning and Convergence Analysis of Neural-Type Structured Networks. IEEE Trans. Neural Networks 3, 39–50 (1992)
Song, Q., Xiao, J., Soh, Y.C.: Robust Backpropagation Training Algorithm for Multilayered Neural Tracking Controller. IEEE Trans. Neural Networks 10, 1133–1141 (1999)
Suykens, J.A.K., Vandewalle, J., De Moor, B.: NLq Theory: Checking and Imposing Stability of Recurrent Neural Networks for Nonlinear Modelling. IEEE Transactions on Signal Processing 45, 2682–2691 (1997)
Yu, W., Li, X.: Some New Results on System Identification with Dynamic Neural Networks. IEEE Trans. Neural Networks 12, 412–417 (2001)
Yu, W., Poznyak, A.S., Li, X.: Multilayer Dynamic Neural Networks for Nonlinear System On-line Identification. International Journal of Control 74, 1858–1864 (2001)
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© 2004 Springer-Verlag Berlin Heidelberg
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Yu, W., Li, X. (2004). System Identification Using Adjustable RBF Neural Network with Stable Learning Algorithms. In: Yin, FL., Wang, J., Guo, C. (eds) Advances in Neural Networks - ISNN 2004. ISNN 2004. Lecture Notes in Computer Science, vol 3174. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28648-6_33
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DOI: https://doi.org/10.1007/978-3-540-28648-6_33
Publisher Name: Springer, Berlin, Heidelberg
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