Autosoft Journal

Online Manuscript Access


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


Authors



Abstract

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.


Keywords


Pages

Total Pages: 13
Pages: 111-123

DOI
10.1080/10798587.2015.1058469


Manuscript ViewPdf Subscription required to access this document

Obtain access this manuscript in one of the following ways


Already subscribed?

Need information on obtaining a subscription? Personal and institutional subscriptions are available.

Already an author? Have access via email address?


Published

Volume: 22
Issue: 1
Year: 2015

Cite this document


References

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. https://doi.org/10.1080/00207170600566188

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. https://doi.org/10.1016/S0893-6080(03)00127-8

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. https://doi.org/10.1016/j.neucom.2012.11.041

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. https://doi.org/10.1016/j.neucom.2011.06.007

Haykin, Simon, ed. "Kalman Filtering and Neural Networks." (2001): n. pag. Crossref. Web. https://doi.org/10.1002/0471221546

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. https://doi.org/10.1016/S0005-1098(96)80007-0

Jiang, Zhong-Ping, and Yuan Wang. "Input-to-State Stability for Discrete-Time Nonlinear Systems." Automatica 37.6 (2001): 857-869. Crossref. Web. https://doi.org/10.1016/S0005-1098(01)00028-0

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. https://doi.org/10.1049/ip-cta:20030204

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. https://doi.org/10.1016/j.physa.2007.02.088

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. https://doi.org/10.1016/j.neucom.2013.02.020

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. https://doi.org/10.1016/j.neunet.2009.06.051

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. https://doi.org/10.1162/neco.1996.8.8.1731

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. https://doi.org/10.1016/j.neucom.2009.10.003

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. https://doi.org/10.1109/72.80202

Rovithakis, George A., and Manolis A. Christodoulou. "Adaptive Control with Recurrent High-Order Neural Networks." Advances in Industrial Control (2000): n. pag. Crossref. Web. https://doi.org/10.1007/978-1-4471-0785-9

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. https://doi.org/10.1016/0167-6911(94)00050-6

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. https://doi.org/10.1142/S0218127403008764

Xie, W.F. et al. "Nonlinear System Identification Using Optimized Dynamic Neural Network." Neurocomputing 72.13-15 (2009): 3277-3287. Crossref. Web. https://doi.org/10.1016/j.neucom.2009.02.004

Yu, W. "Nonlinear System Identification Using Discrete-Time Recurrent Neural Networks with Stable Learning Algorithms." Information Sciences 158 (2004): 131-147. Crossref. Web. https://doi.org/10.1016/j.ins.2003.08.002

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. https://doi.org/10.1007/s11063-007-9034-0

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. https://doi.org/10.1109/72.914535

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. https://doi.org/10.1049/ip-cta:19990368

JOURNAL INFORMATION


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




CONTACT INFORMATION


TSI Press
18015 Bullis Hill
San Antonio, TX 78258 USA
PH: 210 479 1022
FAX: 210 479 1048
EMAIL: tsiepress@gmail.com
WEB: http://www.wacong.org/tsi/