On Optimal Test Signal Design and Parameter Identification Schemes for Dynamic Takagi-Sugeno Fuzzy Models Using the Fisher Information Matrix

Abstract

This paper is concerned with the analysis of optimization procedures for optimal experiment design for locally affine Takagi-Sugeno (TS) fuzzy models based on the Fisher Information Matrix (FIM). The FIM is used to estimate the covariance matrix of a parameter estimate. It depends on the model parameters as well as the regression variables. Due to the dependency on the model parameters good initial models are required. Since the FIM is a matrix, a scalar measure of the FIM is optimized. Different measures and optimization goals are investigated in three case studies.

An optimized excitation signal design for identification of PWA model and application to automotive throttles

“…15,16 Typical methods of excitation signal design can be categorized as model-based and model-free approaches. [16][17][18] In most of these methods, the main task of excitation signal design is to optimize the parameters of a pre-defined excitation signal according to different criteria. Model-based approaches are often called optimal experiment designs (OED), which utilize pre-defined model structures to optimize the variance of model output or model parameters.…”

“…The main drawback of both works is that this method demands prior knowledge of the target system. In Himmelsbach and Kroll 18 and Kroll and Du¨rrbaum, 22 a scalar measure of FIM was used to determine the optimum experimental design to identify TS (Takagi-Sugeno) fuzzy models. These works are limited due to the choice of FIM measure, which impacts the computational cost.…”