Fuzzy models within orthonormal basis function framework

Presents a framework for fuzzy modeling of dynamic systems using orthonormal basis functions in the representation of the model input signals. The main objective of using orthonormal bases is to overcome the task of estimating the order and time delay of the process. The result is a nonlinear moving average fuzzy model which, consequently, has no feedback of prediction errors. Although any technique of fuzzy modeling can be used in the proposed framework, a relational approach is considered. The performance of fuzzy models with orthonormal basis functions is illustrated by examples and the results are compared with those provided by conventional fuzzy models and Volterra models.

[1]  M. Sugeno,et al.  Fuzzy modeling and control of multilayer incinerator , 1986 .

[2]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[3]  Witold Pedrycz.  Identification in fuzzy systems , 1984, IEEE Transactions on Systems, Man, and Cybernetics.

[4]  Leon O. Chua,et al.  Fading memory and the problem of approximating nonlinear operators with volterra series , 1985 .

[5]  L. Ljung,et al.  Hard frequency-domain model error bounds from least-squares like identification techniques , 1992 .

[6]  C. Hwang,et al.  A Combined Approach to Fuzzy Model Identification , 1994, IEEE Trans. Syst. Man Cybern. Syst..

[7]  Bo Wahlberg,et al.  On approximation of stable linear dynamical systems using Laguerre and Kautz functions , 1996, Autom..

[8]  Stephen A. Billings,et al.  Identi cation of nonlinear systems-A survey , 1980 .

[9]  W. Pedrycz,et al.  An introduction to fuzzy sets : analysis and design , 1998 .

[10]  A. C. Tsoi,et al.  Nonlinear system identification using discrete Laguerre functions , 1996 .

[11]  Michio Sugeno,et al.  A fuzzy-logic-based approach to qualitative modeling , 1993, IEEE Trans. Fuzzy Syst..

[12]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[13]  Pertti M. Mäkilä,et al.  Approximation of stable systems by laguerre filters , 1990, Autom..

[14]  Witold Pedrycz,et al.  Fuzzy control and fuzzy systems (2nd, extended ed.) , 1993 .

[15]  Yong-Zai Lu,et al.  Fuzzy Model Identification and Self-Learning for Dynamic Systems , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[16]  D. Willaeys,et al.  THE USE OF FUZZY SETS FOR THE TREATMENT OF FUZZY INFORMATION BY COMPUTER , 1993 .

[17]  Shyh Hwang,et al.  An identification algorithm in fuzzy relational systems , 1996, Soft Computing in Intelligent Systems and Information Processing. Proceedings of the 1996 Asian Fuzzy Systems Symposium.

[18]  P. V. D. Hof,et al.  System identification with generalized orthonormal basis functions , 1994, Proceedings of 1994 33rd IEEE Conference on Decision and Control.

[19]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1971 .

[20]  Alfredo C. Desages,et al.  Approximate models for nonlinear process control , 1996 .

[21]  Kazuo Tanaka,et al.  Successive identification of a fuzzy model and its applications to prediction of a complex system , 1991 .

[22]  Paul W. Broome,et al.  Discrete Orthonormal Sequences , 1965, JACM.

[23]  R. Tong.  SYNTHESIS OF FUZZY MODELS FOR INDUSTRIAL PROCESSES-SOME RECENT RESULTS , 1978 .

[24]  Guy A. Dumont,et al.  Non-linear adaptive control via Laguerre expansion of Volterra kernels , 1993 .

[25]  B. Wahlberg.  System identification using Laguerre models , 1991 .

[26]  Bo Wahlberg.  Identification of resonant systems using Kautz filters , 1991, [1991] Proceedings of the 30th IEEE Conference on Decision and Control.

[27]  M. Sugeno,et al.  Structure identification of fuzzy model , 1988 .

[28]  W. Pedrycz,et al.  Fuzzy relational modeling of dynamic systems with regenerative I/O interfaces , 1994, Proceedings of 1994 IEEE 3rd International Fuzzy Systems Conference.

[29]  G. Dumont,et al.  Deterministic adaptive control based on Laguerre series representation , 1988 .