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Adaptive Nonlinear Systems Identification via Discrete Multi-Time Scales Dynamic Neural Networks



In this paper, we extend our previous results on continuous multi-time scales dynamic neural networks identification to the discrete domain. A robust on-line identification algorithm is proposed for nonlinear systems identification via discrete multi-time scales dynamic neural networks. The main contribution of the paper is that the input-to-state stability (ISS) approach is used to tune the weights of the discrete multi-time scales dynamic neural networks in the sense of L1. The commonly used robustifying techniques, such as dead-zone or s-modification in the weight tuning, are not necessary for the proposed identification algorithm. The stability of the proposed identifier is proved by Lyapunov function and ISS theory. Two examples are given to demonstrate the correctness of the theoretical results.



Total Pages: 13
Pages: 111-123


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Volume: 22
Issue: 1
Year: 2015

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Alanis A. Y. Advances in Neural Networks

De Jesús Rubio, J., and W. Yu. "A New Discrete-Time Sliding-Mode Control with Time-Varying Gain and Neural Identification." International Journal of Control 79.4 (2006): 338-348. Crossref. Web.

Feldkamp, Lee A., Danil V. Prokhorov, and Timothy M. Feldkamp. "Simple and Conditioned Adaptive Behavior from Kalman Filter Trained Recurrent Networks☆." Neural Networks 16.5-6 (2003): 683-689. Crossref. Web.

Fu Z.-J. IEEE Transactions on Neural Networks and Learning Systems

Fu, Zhi-Jun, Wen-Fang Xie, and Wei-Dong Luo. "Robust on-Line Nonlinear Systems Identification Using Multilayer Dynamic Neural Networks with Two-Time Scales." Neurocomputing 113 (2013): 16-26. Crossref. Web.

Grover R. Introduction to random signals and applied kalman filtering

Han, Xuan et al. "Nonlinear Systems Identification Using Dynamic Multi-Time Scale Neural Networks." Neurocomputing 74.17 (2011): 3428-3439. Crossref. Web.

Haykin, Simon, ed. "Kalman Filtering and Neural Networks." (2001): n. pag. Crossref. Web.

Jagannathan S. Neural network control of nonlinear discrete-time systems

Jagannathan, S., and F.L. Lewis. "Identification of Nonlinear Dynamical Systems Using Multilayered Neural Networks." Automatica 32.12 (1996): 1707-1712. Crossref. Web.

Jiang, Zhong-Ping, and Yuan Wang. "Input-to-State Stability for Discrete-Time Nonlinear Systems." Automatica 37.6 (2001): 857-869. Crossref. Web.

Kokotovic P. V. Singular perturbation methods in control: Analysis and design

Yu, W., and X. Li. "Discrete-Time Neuro Identification Without Robust Modification." IEE Proceedings - Control Theory and Applications 150.3 (2003): 311-316. Crossref. Web.

Lou, Xuyang, and Baotong Cui. "Synchronization of Competitive Neural Networks with Different Time Scales." Physica A: Statistical Mechanics and its Applications 380 (2007): 563-576. Crossref. Web.

Meyer-Bäse, Anke, Guillermo Botella, and Liliana Rybarska-Rusinek. "Stochastic Stability Analysis of Competitive Neural Networks with Different Time-Scales." Neurocomputing 118 (2013): 115-118. Crossref. Web.

Meyer-Baese, Anke et al. "Global Stability Analysis and Robust Design of Multi-Time-Scale Biological Networks Under Parametric Uncertainties." Neural Networks 22.5-6 (2009): 658-663. Crossref. Web.

Meyer-Bäse, Anke, Frank Ohl, and Henning Scheich. "Singular Perturbation Analysis of Competitive Neural Networks with Different Time Scales." Neural Computation 8.8 (1996): 1731-1742. Crossref. Web.

Meyer-Bäse, A., R. Roberts, and V. Thümmler. "Local Uniform Stability of Competitive Neural Networks with Different Time-Scales Under Vanishing Perturbations." Neurocomputing 73.4-6 (2010): 770-775. Crossref. Web.

Narendra, K.S., and K. Parthasarathy. "Identification and Control of Dynamical Systems Using Neural Networks." IEEE Transactions on Neural Networks 1.1 (1990): 4-27. Crossref. Web.

Rovithakis, George A., and Manolis A. Christodoulou. "Adaptive Control with Recurrent High-Order Neural Networks." Advances in Industrial Control (2000): n. pag. Crossref. Web.

Sandoval A. C. International Joint Conf. on Neural Networks 16.3 (2006)

Sontag, Eduardo D., and Yuan Wang. "On Characterizations of the Input-to-State Stability Property." Systems & Control Letters 24.5 (1995): 351-359. Crossref. Web.

SUCKLEY, REBECCA, and VADIM N. BIKTASHEV. "THE ASYMPTOTIC STRUCTURE OF THE HODGKIN-HUXLEY EQUATIONS." International Journal of Bifurcation and Chaos 13.12 (2003): 3805-3825. Crossref. Web.

Xie, W.F. et al. "Nonlinear System Identification Using Optimized Dynamic Neural Network." Neurocomputing 72.13-15 (2009): 3277-3287. Crossref. Web.

Yu, W. "Nonlinear System Identification Using Discrete-Time Recurrent Neural Networks with Stable Learning Algorithms." Information Sciences 158 (2004): 131-147. Crossref. Web.

Yu, Wen, and Xiaoou Li. "Passivity Analysis of Dynamic Neural Networks with Different Time-Scales." Neural Processing Letters 25.2 (2007): 143-155. Crossref. Web.

Wen Yu, and Xiaoou Li. "Some New Results on System Identification with Dynamic Neural Networks." IEEE Transactions on Neural Networks 12.2 (2001): 412-417. Crossref. Web.

Yu, W., and A.S. Poznyak. "Indirect Adaptive Control via Parallel Dynamic Neural Networks." IEE Proceedings - Control Theory and Applications 146.1 (1999): 25-30. Crossref. Web.


ISSN PRINT: 1079-8587
ISSN ONLINE: 2326-005X
DOI PREFIX: 10.31209
10.1080/10798587 with T&F
IMPACT FACTOR: 0.652 (2017/2018)
Journal: 1995-Present


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