Inductive Reasoning Supports the Design of Fuzzy Controllers

François E. Cellier
Institute of Computational Science
ETH Zürich
CH-8092 Zürich
Switzerland
Email: FCellier@Inf.ETHZ.CH
Francisco Mugica Alvarez
Instituto Latinoamericano de la Comunicación Educativa
Calle del Puente, 45
Col. Ejidos de Huipulco, Delegación Tlalpan
14380, México, D.F.
México
Email: FMugica@ILCE.Edu.MX

Abstract

In this paper, a new systematic design methodology for fuzzy controllers is presented. For any desired plant output, it is possible to find off-line the optimal plant input that will produce a plan output that is as close as possible to the desired one. However, this constitutes an open-loop design. In this paper, a new methodology is introduced that allows to compute on-line a signal that is close to the optimal plant input as a function of system inputs and plant outputs. To this end, an inductive reasoning model is created that estimates the optimal plant input from given system inputs and plant outputs. The inductive reasoning model can be interpreted and realized as a fuzzy controller. Thereby, a large portion of the controller is realized through feedback, and the previous open-loop design is converted to an equivalent and more robust closed-loop design. The inductive reasoning technique is described in detail in the first part of this paper. An example is shown in the second part of the paper in order to demonstrate the validity of the chosen approach.

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