Fuzzy Identification Based on a Chaotic Particle Swarm Optimization Approach Applied to a Nonlinear Yo-yo Motion System

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The identification of uncertain and nonlinear systems is an important and challenging problem. Fuzzy models, particularly Takagi–Sugeno (TS), have received particular attention in the area of nonlinear identification due to their potentialities to approximate any nonlinear behavior. A method of nonlinear identification based on the TS fuzzy model and optimization procedure is proposed in this paper. Chaotic particle swarm optimization (CPSO) algorithms, based on chaotic Zaslavskii map sequences, combined with efficient Gustafson–Kessel (GK) clustering algorithm are proposed here for the design of the premise part of production rules, while the least-mean-square technique is utilized for the subsequent part of the production rules of the TS fuzzy model. An experimental case study using a nonlinear yo-yo motion control system is analyzed by the proposed algorithms. The numerical results presented here indicate that the traditional particle swarm optimization algorithm and, particularly, the CPSO combined with GK algorithms are effective in building a good TS fuzzy model for nonlinear identification. </para>