System Identification of Stochastic Nonlinear Dynamic Systems using Takagi-Sugeno Fuzzy Models

Some novel approaches to estimate Nonlinear Output Error (NOE) models using TS fuzzy models for a class of nonlinear dynamic systems having variability in their outputs is presented in this dissertation. Instead of using unrealistic assumptions about uncertainty, the most common of which is normality, the proposed methodology tends to capture effects caused by the real uncertainty observed in the data. The methodology requires that the identification method must be repeated offline a number of times under similar conditions. This leads to multiple inputoutput time series from the underlying system. These time series are preprocessed using the techniques of statistics and probability theory to generate the envelopes of response at each time instant. By incorporating interval data in fuzzy modelling and using the theory of symbolic interval-valued data, a TS fuzzy model with interval antecedent and consequent parameters is obtained. The proposed identification algorithm provides for a model for predicting the center-valued response as well as envelopes as the measure of uncertainty in system output.