Autosoft Journal

Online Manuscript Access

Fuzzy functions with function expansion model for nonlinear system identification



In this study, the structure of fuzzy functions is improved by function expansion. Unlike fuzzy conventional if-then rules, classical fuzzy function structure includes fuzzy bases and linear inputs. Membership functions of fuzzy bases are set using fuzzy C-means (FCM) algorithm, and the linear parameters are computed using the least-square estimation (LSE). This study has two main contributions. First, conventional 201Cfuzzy functions201D structure is powered by the expansion of orthogonal 201Ctrigonometric functions201D where the approximation capabilities of the fuzzy functions are increased. Second, the widths of the normalized membership functions determined for the fuzzy function model are optimized using the Nelder-Mead simplex algorithm that provides further enhancement on the identification performance. The advantages of the proposed model are shown via offline identification of a benchmark nonlinear system and online identification of two real-time nonlinear systems.



Total Pages: 8
Pages: 87-94


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?


Volume: 23
Issue: 1
Year: 2016

Cite this document


Aadaleesan, P. et al. "Nonlinear System Identification Using Wiener Type Laguerre-Wavelet Network Model." Chemical Engineering Science 63.15 (2008): 3932-3941. Crossref. Web.

Alci, Musa. "Fuzzy Rule-Base Driven Orthogonal Approximation." Neural Computing and Applications 17.5-6 (2007): 501-507. Crossref. Web.

Anton H. Elementary linear algebra

Beyhan, Selami, and Musa Alci. "Fuzzy Functions Based ARX Model and New Fuzzy Basis Function Models for Nonlinear System Identification." Applied Soft Computing 10.2 (2010): 439-444. Crossref. Web.

Beyhan, Selami, and Musa Alci. "Extended Fuzzy Function Model with Stable Learning Methods for Online System Identification." International Journal of Adaptive Control and Signal Processing 25.2 (2010): 168-182. Crossref. Web.

Dehuri, Satchidananda, and Sung-Bae Cho. "A Comprehensive Survey on Functional Link Neural Networks and an Adaptive PSO-BP Learning for CFLNN." Neural Computing and Applications 19.2 (2009): 187-205. Crossref. Web.

Gelbukh, Alexander, and Carlos Alberto Reyes-Garcia, eds. "MICAI 2006: Advances in Artificial Intelligence." Lecture Notes in Computer Science (2006): n. pag. Crossref. Web.

Lagarias, Jeffrey C. et al. "Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions." SIAM Journal on Optimization 9.1 (1998): 112-147. Crossref. Web.

Yang-Yin Lin, Jyh-Yeong Chang, and Chin-Teng Lin. "Identification and Prediction of Dynamic Systems Using an Interactively Recurrent Self-Evolving Fuzzy Neural Network." IEEE Transactions on Neural Networks and Learning Systems 24.2 (2013): 310-321. Crossref. Web.

Ljung L. System identification theory for the user

Patra J.C. IEEE International Conference on

Patra, J.C. et al. "Identification of Nonlinear Dynamic Systems Using Functional Link Artificial Neural Networks." IEEE Transactions on Systems, Man and Cybernetics, Part B (Cybernetics) 29.2 (1999): 254-262. Crossref. Web.

Purwar, S., I.N. Kar, and A.N. Jha. "On-Line System Identification of Complex Systems Using Chebyshev Neural Networks." Applied Soft Computing 7.1 (2007): 364-372. Crossref. Web.

Söderström, T., P. Stoica, and Rolf Johansson. "System Identification." Journal of Dynamic Systems, Measurement, and Control 115.4 (1993): 739. Crossref. Web.

Türkşen I.B. International Journal of Fuzzy Systems

TürkÅŸen, I. Burhan. "Fuzzy Functions with LSE." Applied Soft Computing 8.3 (2008): 1178-1188. Crossref. Web.

Wang, L.-X., and J.M. Mendel. "Fuzzy Basis Functions, Universal Approximation, and Orthogonal Least-Squares Learning." IEEE Transactions on Neural Networks 3.5 (1992): 807-814. Crossref. Web.

Wang L.-X. A course in fuzzy systems and control

Zarandi, M.H. Fazel et al. "A New Fuzzy Functions Model Tuned by Hybridizing Imperialist Competitive Algorithm and Simulated Annealing. Application: Stock Price Prediction." Information Sciences 222 (2013): 213-228. 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


TSI Press
18015 Bullis Hill
San Antonio, TX 78258 USA
PH: 210 479 1022
FAX: 210 479 1048