Improved fuzzy approximation accuracy using a linear TSK approach

We propose a new Takagi-Sugeno-Kang (TSK) approach for fuzzy function approximation. We use a novel linear TSK design to define the rule base and obtain the membership functions for the inputs and outputs of a given system. Unlike traditional TSK, the output is obtained as a weighted sum of linear functions of the inputs. We provide an upper bound on the approximation error for this class of fuzzy systems achievable using a reduced number of membership functions. To demonstrate the new approach, we apply it to a numerical example.

I. Introduction

The goal of control system design is to achieve a desired time response. Thus, a controller can be specified in terms of desired input-output pairs. The control problem can then be recast as the design of a fuzzy approximation that realizes the desired behavior with specified accuracy. In addition, fuzzy approximation based on input-output pairs provides a solution to difficult system identification problems. Fuzzy identification is especially useful where the model structure is vaguely understood or highly complex so that traditional statistical methods are unattractive.