In collaboration with Payame Noor University and the Iranian Society of Instrumentation and Control Engineers

Document Type : Research Article

Author

Payame Noor University (PNU), Tehran, Iran

Abstract

‎Rough extreme learning machines (RELMs) are rough-neural networks with one hidden layer where the parameters between the inputs and hidden neurons are arbitrarily chosen and never updated‎. ‎In this paper‎, ‎we propose RELMs with a stable online learning algorithm for the identification of continuous-time nonlinear systems in the presence of noises and uncertainties‎, ‎and we prove the global asymptotically convergence of the proposed learning algorithm using the Lyapunov stability theory‎. ‎Then‎, ‎we use the proposed methodology to identify the chaotic systems of Duffing's oscillator and Lorentz system‎. ‎Simulation results show the efficiency of the proposed model.

Keywords

‎bibitem{abdollahi}‎
‎Abdollahi F.‎, ‎Talebi A.‎, ‎Patel R‎. ‎(2006)‎.
‎``Stable identification of nonlinear systems using neural networks‎: ‎Theory and experiments"‎, ‎IEEE/ASME Transactions on Mechatronics‎, ‎11(4)‎, ‎488-495‎.
 
‎bibitem{ahmadi}‎
‎Ahmadi G.‎, ‎Teshnehlab M‎. ‎(2016)‎. ‎``Designing and implementation of stable sinusoidal rough-neural identifier"‎, ‎IEEE Transactions on Neural Networks and Learning Systems‎, ‎28(8)‎, ‎1774-1786‎.
 
 
‎bibitem{ahmadi3}‎
‎Ahmadi G.‎, ‎Teshnehlab M‎. ‎(2020)‎. ‎``Identification of multiple input-multiple output non-linear system cement rotary kiln using stochastic gradient-based rough-neural network"‎, ‎Journal of AI and Data Mining‎, ‎8(3)‎, ‎417-425‎.
 
‎bibitem{ahmadi2}‎
‎Ahmadi G.‎, ‎Teshnehlab M.‎, ‎Soltanian F‎. ‎(2018)‎. ‎``A Higher Order Online Lyapunov-Based Emotional Learning for Rough-Neural Identifiers"‎, ‎Control and Optimization in Applied Mathematics (COAM)‎, ‎3(1)‎, ‎87-108‎.
‎bibitem{alehasher}‎
‎Alehasher S.‎, ‎Teshnehlab M‎. ‎(2012)‎. ‎``Implementation of‎
‎rough neural networks with probabilistic learning for nonlinear system identification"‎,
‎J‎. ‎Control 6(1)‎, ‎41-50‎.
‎bibitem{cellier}‎
‎Cellier F‎. ‎E‎. ‎(1991)‎. ‎``Continuous system modelling"‎, ‎Springer-Verlag‎, ‎New York‎.
‎bibitem{coca}‎
‎Coca D.‎, ‎Billings S‎. ‎(1997)‎. ‎``Continuous-time system identification‎
‎for linear and nonlinear systems using wavelet decompositions"‎, ‎International Journal of‎
‎Biforcation and Chaos 7(1)‎, ‎87-96‎.
 
‎bibitem{feng}‎
‎Feng L.‎, ‎Xu S.‎, ‎Wang F.‎, ‎Liu S.‎, ‎Qiao H‎. ‎(2019)‎. ‎``Rough extreme learning‎
‎machine‎: ‎A new classification method based on uncertainty measure"‎, ‎Neurocomputing‎, ‎325‎, ‎269-282‎.
‎bibitem{garnier}‎
‎Garnier H., Wang L‎. ‎(2008)‎. ‎``Identification of continuous-time models from sampled data"‎, ‎Springer-Verlag‎, ‎London‎.
‎bibitem{hassan}‎
‎Hassan Y‎. ‎(2014)‎. ‎``Rough neural networks in adapting cellular automata rule‎
‎for reducing image noise"‎, ‎International Journal of Computer‎, ‎Information‎, ‎Systems and‎
‎Control Engineering‎, ‎8(1)‎, ‎71-74‎.
‎bibitem{ella}‎
‎Hassanien A.‎, ‎Slezak D‎. ‎(2006)‎. ‎``Rough-neural intelligent approach for image classification‎: ‎A case of patients with suspected breast cancer"‎, ‎International Journal of Hybrid Intelligent Systems‎, ‎3‎, ‎205-218‎.
 
‎bibitem{huang2006}‎
‎Huang G. B‎., ‎Zhu Q.-Y.‎, ‎Siew C.-K‎. ‎(2006)‎. ‎``Extreme learning machine‎: ‎Theory and applications"‎, ‎Neurocomputing‎, ‎70‎, ‎489-501‎.
 
‎bibitem{huang2012}‎
‎Huang G. B.‎, ‎Zhou H.‎, ‎Ding X.‎, ‎Zhang R‎. ‎(2012)‎. ‎``Extreme learning machine for regression and‎
‎multiclass classification"‎, ‎IEEE Transaction on Systems‎, ‎Man‎, ‎and Cybernetics—Part B‎: ‎Cybernetics‎, ‎42(2)‎, ‎513-529‎.
 
 
‎bibitem{hykin}‎
‎{Hykin S‎. ‎(1998)‎. ‎``Neural networks‎: ‎A comprehensive foundation"‎, ‎Prentice Hall International‎, ‎Canada.}‎
 
 
‎bibitem{Ioannou}‎
‎Ioannou P.‎, ‎Sun J‎. ‎(1996)‎. ‎``Robust adaptive control"‎, ‎Prentice Hall‎, ‎New Jersey‎.
 
 
‎bibitem{jahangir}‎
‎Jahangir H.‎, ‎Golkar M‎. ‎A.‎, ‎Alhameli F.‎, ‎Mazouz A.‎,
‎Ahmadian A.‎, ‎Elkamel A‎. ‎(2020)‎. ‎``Short-term wind speed forecasting framework based on stacked denoising‎
‎auto-encoders with rough ANN"‎, ‎Sustainable Energy Technologies and Assessments‎, ‎38‎, ‎100601‎.
 
‎bibitem{jahangir2}‎
‎Jahangir H.‎, ‎Tayarani H.‎, ‎Baghali S.‎, ‎Ahmadian A.‎, ‎Elkamel A.‎, ‎Golkar M‎. ‎A‎. ‎(2020)‎. ‎``A novel electricity price forecasting approach based on dimension reduction‎
‎strategy and rough artificial neural networks"‎, ‎IEEE Transactions on Industrial Informatics‎, ‎16(4)‎, ‎2369-2381‎.
‎bibitem{janakiraman}‎
‎Janakiraman V‎. ‎M.‎, ‎Assanis D‎. ‎(2012)‎. ‎``Lyapunov method based online‎
‎identification of nonlinear systems using extreme learning machines"‎,
‎Computing Research Repository (CoRR):1211.1441‎, ‎pp 1-8‎.
‎bibitem{vijay3}‎
‎Janakiraman V‎. ‎M.‎, ‎Nguyen X.‎, ‎Assanis D.‎, ‎(2016)‎. ‎``Stochastic gradient based extreme‎
‎learning machines for stable online learning of advanced combustion engines"‎, ‎Neurocomputing‎, ‎177‎, ‎304-316‎.
‎bibitem{lamamra}‎
‎Lamamra K.‎, ‎Vaidyanathan S.‎,
‎Azar A‎. ‎T.‎, ‎Ben Salah C‎. ‎(2017)‎.
‎``Chaotic system modelling using a neural‎
‎network with optimized structure"‎, ‎in‎:
‎Azar A‎. ‎T‎. ‎et al‎. ‎(eds.)‎, ‎Fractional order control and synchronization‎
‎of chaotic systems‎, ‎Studies in Computational Intelligence 688‎, ‎Springer International Publishing AG‎.
 
‎bibitem{lingras}‎
‎Lingras P‎. ‎(1996)‎. ‎``Rough neural networks"‎, ‎in‎: ‎Proceedings of the 6th international conference on information processing and management of uncertainty (IPMU)‎,
‎Granada‎, ‎1445-1450‎.
‎bibitem{GPLiu}‎
‎Liu G.‎, ‎Kadirkamanathan V.‎, ‎Billings S‎.
‎(1994)‎. ‎``Stable sequential identification of continuous nonlinear dynamical systems by‎
‎growing RBF networks"‎, ‎PhD thesis‎, ‎Research Report No‎. ‎547‎, ‎Depatment of Automatic‎
‎Control and System Engineering‎, ‎University of Sheffild‎, ‎UK‎.
‎bibitem{narendra}‎
‎Narendra K.‎, ‎Parthasarathy K‎. ‎(1990)‎. ‎``Identification‎
‎and control of dynamical systems using neural networks"‎, ‎IEEE Trans‎. ‎Neural Networks‎,
‎1(1)‎, ‎4-27‎.
‎bibitem{nelles}‎
‎Nelles O‎. ‎(2001)‎. ‎``Nonlinear system identification‎: ‎From classical approaches to‎
‎neural networks and fuzzy models"‎, ‎Springer-Verlag‎, ‎Berlin‎.
‎bibitem{paw}‎
‎Pawlack Z‎. ‎(1982)‎. ‎``Rough sets"‎, ‎International Journal of Computer and Information Sciences‎, ‎11(5)‎, ‎341-356‎.
‎bibitem{poznyak}‎
‎Poznyak A‎. ‎S.‎, ‎Yu W.‎, ‎Sanchez E‎. ‎N‎. ‎(1982)‎. ‎``Identification and control of unknown chaotic‎
‎systems via dynamic neural networks"‎, ‎IEEE Transactions on Circuits and Systems—I‎: ‎Fundamental Theories and Applications‎, ‎46(12)‎.
 
‎bibitem{rao}‎
‎Rao G.‎, ‎Unbehauen H‎. ‎(2006)‎. ‎``Identification of continuous-time‎
‎systems"‎, ‎IEE Proc.-Control Theory Appl.‎, ‎153(2)‎, ‎185-220‎.
 
‎bibitem{ren} Ren X.‎, ‎Rad A.‎, ‎Chan P.‎, ‎Lo W‎. ‎(2003)‎. ‎``Identification and control of continuous-time nonlinear systems via dynamic neural networks"‎,
‎IEEE Transactions on Industrial Electronics‎, ‎50(3)‎, ‎478-486‎.
‎bibitem{pan}‎
‎Pan S. T.‎, ‎Lai C. C‎. ‎(2008)‎. ‎``Identification of chaotic systems by neural network with‎
‎hybrid learning algorithm"‎,
‎Chaos‎, ‎Solitons and Fractals‎, ‎37‎, ‎233-244‎.
‎bibitem{wang}‎
‎Wang Z.‎, ‎Li M.‎, ‎Wang H.‎, ‎Jiang H.‎, ‎Yao Y.‎, ‎Zhang H.‎, ‎Xin J‎. ‎(2019)‎. ‎``Breast cancer detection using extreme learning machine‎
‎based on feature fusion with CNN deep features"‎, ‎IEEE Access‎, ‎105146-105158‎.
 
‎bibitem{yama}‎
‎Yamaguchi‎
‎D.‎, ‎Katayama F.‎, ‎Takahashi M.‎, ‎Arai M.‎, ‎Mackin K‎. ‎(2008)‎. ‎``The medical diagnostic‎
‎support system using extended rough neural network and multiagent"‎, ‎Artificial Life and‎
‎Robotics‎, ‎13(1)‎, ‎184-187‎.
‎bibitem{zhang}‎
‎Zhang B.‎, ‎Billings S‎. ‎(2015)‎. ‎``Identification of continuous-time non‎-
‎linear systems‎: ‎The nonlinear difference equation with moving average noise (ndema)‎
‎framework"‎, ‎Mechanical Systems and Signal Processing‎, ‎60‎, ‎810-835‎.