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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.


IMPACT FACTOR 2018: 0.881
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1569-3945
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Volume 10, Issue 4

Issues

Regularized data-driven construction of fuzzy controllers

M. Burger
  • Industrial Mathematics Institute, Johannes Kepler Universität Linz, Altenbergerstr. 69, A-4040 Linz, Austria.
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ J. Haslinger / U. Bodenhofer / H. W. Engl
  • Industrial Mathematics Institute, Johannes Kepler Universität Linz, Altenbergerstr. 69, A-4040 Linz, Austria.
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2013-09-07 | DOI: https://doi.org/10.1515/jiip.2002.10.4.319

Abstract

- This paper is devoted to the mathematical analysis and the numerical solution of data-driven construction of fuzzy controllers. We show that for a special class of controllers (so-called Sugeno controllers), the design problem is equivalent to a nonlinear least squares problem, which turns out to be ill-posed. Therefore we investigate the use of regularization in order to obtain stable approximations of the solution. We analyze a smoothing method, which is common in spline approximation, as well as Tikhonov regularization with respect to stability and convergence.

In addition, we develop an iterative method for the regularized problems, which uses the special structure of the problem and test it in some typical numerical examples. We also compare the behavior of the iterations for the original and the regularized least squares problems. It turns out that the regularized problem is not only more robust but also favors solutions that are interpretable easily, which is an important criterion for fuzzy systems.

About the article

Published Online: 2013-09-07

Published in Print: 2002-08-01


Citation Information: Journal of Inverse and Ill-posed Problems, Volume 10, Issue 4, Pages 319–344, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip.2002.10.4.319.

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