Model Identification Using Fuzzy Neural Networks and T-S Models with Input-Output Membership Functions

In this article, we explore the concept of model identification and demonstrate how fuzzy neural networks and Takagi-Sugeno (T-S) models can be employed for system identification. Model identification refers to the process of constructing mathematical models of system dynamics from experimental data. This process requires defining system inputs and outputs, along with their corresponding membership functions. Fuzzy neural networks and T-S models represent two widely-used modeling techniques that enable more precise characterization of system dynamics.

From an implementation perspective, fuzzy neural networks typically combine fuzzy logic systems with neural network architectures, where membership functions can be implemented using Gaussian or triangular functions coded through parameters like center points and widths. The T-S model employs a fuzzy rule structure where consequent parts are linear functions of input variables, often implemented through linear regression techniques. Key implementation steps include: defining input-output variables using MATLAB's fisvar function, configuring membership functions through gaussmf or trimf functions, and establishing fuzzy rule bases using the addrule method.

We will provide detailed explanations of both modeling approaches, discuss their comparative advantages and limitations, and illustrate practical applications for model identification. The article will include code snippets demonstrating how to configure membership functions and implement rule-based reasoning mechanisms for dynamic system characterization.