Modeling and Identification of Dynamical Systems and Time Series Using Fuzzy Logic Type 3

Abstract

This dissertation develops an innovative approach for modeling and identifying complex non-linear dynamical systems and time series (such as real ECG signals and the Mackey Glass chaotic time series) using Type-3 Fuzzy Logic Systems optimized by the Kalman Filter. The research is structured into four chapters: Chapter I covers the theoretical foundations of dynamical systems and temporal dynamics. Chapter II reviews mathematical modeling and system identification procedures. Chapter III focuses on fuzzy logic evolution, showcasing Type-3 fuzzy logic's superior ability to handle high-order uncertainties. Chapter IV details the proposed methodology, which connects a low-resolution primary fuzzy model in parallel with a fuzzy error model to reduce uncertainty. Parameters are optimized via the Kalman filter, achieving outstanding high-resolution tracking and minimal modeling error.