Regularized data-driven construction of fuzzy controllers
-
M. Burger
,
U. Bodenhofer
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.
© 2013 by Walter de Gruyter GmbH & Co.
Articles in the same Issue
- Contents
- Regularized data-driven construction of fuzzy controllers
- Stable identification of piecewise-constant potentials from fixed-energy phase shifts
- Several remarks on numerical solution of the one-dimensional coefficient inverse problem
- Reconstruction of the potential from I-function
- Some inverse problems for Schrödinger operator with Kato potential
- Inverse spectral problems for higher-order differential operators with a singularity
Articles in the same Issue
- Contents
- Regularized data-driven construction of fuzzy controllers
- Stable identification of piecewise-constant potentials from fixed-energy phase shifts
- Several remarks on numerical solution of the one-dimensional coefficient inverse problem
- Reconstruction of the potential from I-function
- Some inverse problems for Schrödinger operator with Kato potential
- Inverse spectral problems for higher-order differential operators with a singularity
