Regularized data-driven construction of fuzzy controllers

Authors Martin Burger
Josef Haslinger
Ulrich Bodenhofer
Heinz W. Engl
Title Regularized data-driven construction of fuzzy controllers
Type article
Journal Journal of Inverse Ill-Posed Probl
Number 4
Volume 10
Year 2002
Pages 319-344
SCCH ID# 256

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.