An energy-gain bounding approach to robust fuzzy identification

A novel method for the robust identification of interpretable fuzzy models, based on the criterion that identification errors are least sensitive to data uncertainties and modelling errors, is suggested. The robustness of identification errors towards unknown disturbances (data uncertainties, modelling errors, etc.) is achieved by bounding (i.e. minimizing) the maximum possible value of energy-gain from disturbances to the identification errors. The solution of energy-gain bounding problem, being robust, shows an improved performance of the identification method. The flexibility of the proposed framework is shown by designing the variable learning rate identification algorithms in both deterministic and stochastic frameworks.

[1]  Norbert Stoll,et al.  A robust design criterion for interpretable fuzzy models with uncertain data , 2006, IEEE Transactions on Fuzzy Systems.

[2]  Xia Hong,et al.  Robust neurofuzzy rule base knowledge extraction and estimation using subspace decomposition combined with regularization and D-optimality , 2004, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[3]  Martin Burger,et al.  Regularized data-driven construction of fuzzy controllers , 2002 .

[4]  Joos Vandewalle,et al.  Constructing fuzzy models with linguistic integrity from numerical data-AFRELI algorithm , 2000, IEEE Trans. Fuzzy Syst..

[5]  Ali H. Sayed,et al.  Variable step-size NLMS and affine projection algorithms , 2004, IEEE Signal Processing Letters.

[6]  T. A. Johansen,et al.  Robust identification of Takagi-Sugeno-Kang fuzzy models using regularization , 1996, Proceedings of IEEE 5th International Fuzzy Systems.

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

[8]  Norbert Stoll,et al.  Robust Adaptive Identification of Fuzzy Systems with Uncertain Data , 2004, Fuzzy Optim. Decis. Mak..

[9]  Wen Yu,et al.  Fuzzy identification using fuzzy neural networks with stable learning algorithms , 2004 .

[10]  Norbert Stoll,et al.  Regularized Adaptation of Fuzzy Inference Systems. Modelling the Opinion of a Medical Expert about Physical Fitness: An Application , 2003, Fuzzy Optim. Decis. Mak..

[11]  Norbert Stoll,et al.  Robust Solution to Fuzzy Identification Problem with Uncertain Data by Regularization , 2004, Fuzzy Optim. Decis. Mak..

[12]  Ramesh C. Jain,et al.  A robust backpropagation learning algorithm for function approximation , 1994, IEEE Trans. Neural Networks.

[13]  Dimiter Driankov,et al.  Fuzzy model identification - selected approaches , 1997 .

[14]  T. Kailath,et al.  Linear estimation in Krein spaces. I. Theory , 1996, IEEE Trans. Autom. Control..

[15]  Norbert Stoll,et al.  Robust Adaptive Fuzzy Identification of Time-Varying Processes with Uncertain Data. Handling Uncertainties in the Physical Fitness Fuzzy Approximation with Real World Medical Data: An Application , 2003, Fuzzy Optim. Decis. Mak..

[16]  Thomas Kailath,et al.  2. Linear Estimation in Krein Spaces , 1999 .

[17]  Ulrich Bodenhofer,et al.  Towards an Axiomatic Treatment of "Interpretability" , 2000 .

[18]  Magne Setnes,et al.  Rule-based modeling: precision and transparency , 1998, IEEE Trans. Syst. Man Cybern. Part C.

[19]  Robert Babuška.  Construction of Fuzzy Systems - Interplay between Precision and Transparency , 2000 .

[20]  Ali H. Sayed,et al.  H∞ optimality of the LMS algorithm , 1996, IEEE Trans. Signal Process..

[21]  Chi-Hsu Wang,et al.  Function approximation using fuzzy neural networks with robust learning algorithm , 1997, IEEE Trans. Syst. Man Cybern. Part B.

[22]  T. Kailath,et al.  Linear estimation in Krein spaces. II. Applications , 1996, IEEE Trans. Autom. Control..

[23]  P. Lindskog.  Fuzzy identification from a grey box modeling point of view , 1997 .