Fuzzy control for uncertainty nonlinear systems with dual fuzzy equations

Issue title: Dedicated to Professor Lotfi A. Zadeh and Fifty Years of Fuzzy Logic

Article type: Research Article

Authors: Jafari, Raheleh | Yu, Wen^*

Affiliations: Departamento de Control Automático, CINVESTAV-IPN (National Polytechnic Institute), Mexico City, Mexico

Correspondence: [*] Corresponding author. Wen Yu, Departamento de Control Automático, CINVESTAV-IPN (National Polytechnic Institute), Mexico City, Mexico. Tel.: +52 55 57473734; Fax: +52 55 57473982; E-mail: yuw@ctrl.cinvestav.mx.

Abstract: Many uncertain nonlinear systems can be modeled by the linear-in-parameter model, and the parameters are uncertain in the sense of fuzzy numbers. Fuzzy equations can be used to model these nonlinear systems. The solutions of the fuzzy equations are the controllers. In this paper, we give the controllability condition for the fuzzy control via dual fuzzy equations. Two types of neural networks are applied to approximate the solutions of the fuzzy equations. These solutions are then transformed into the fuzzy controllers. The novel methods are validated with five benchmark examples.

Keywords: Fuzzy equation, fuzzy number, fuzzy control

DOI: 10.3233/IFS-151731

Journal: Journal of Intelligent & Fuzzy Systems, vol. 29, no. 3, pp. 1229-1240, 2015