Learning fuzzy control rules by α‐constrained Simplex method

Abstract

AbstractThe learning of fuzzy control rules can be defined as a constrained nonlinear optimization problem so that its objective function is indifferentiable. As an optimization method of this problem, “α‐constrained Powell method,” which optimizes a given initial rule, is proposed. However, the difficulty with the learning by the α‐constrained Powell method is that it is necessary to have initial rules of certain accuracy formulated by human experts, thus requiring a very large number of control experiments. In this study, we propose an α‐constrained Simplex method, in which the α‐level comparison is added to the Simplex method, which is a nonlinear optimization method. The α‐constrained Simplex method is an optimization method for constrained problems using the α‐level comparison that takes account of the constraint satisfaction instead of ordinary order relation used in the Simplex method, which is a direct search method based only on values of the objective function. In order to demonstrate the effectiveness of this method, we carried out computer simulation of the fuzzy control rules for a pole‐cart system. We have shown that this method makes it possible to achieve a fast learning of highly accurate rules from mechanically created rules based on a relatively small number of experiments, without relying on any existing rules. © 2003 Wiley Periodicals, Inc. Syst Comp Jpn, 34(6): 80–90, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.1207