Learning-Based Dynamic Takagi-Sugeno Fuzzy Modeling of Nonlinear Systems

Abstract

Dynamic Takagi-Sugeno fuzzy systems are characterized by their use of linear state-space models as their rule consequents. Thanks to their ease of use during the controller design procedure, they are extensively utilized in nonlinear control applications. Generally, analytical models of nonlinear systems are used to obtain the dynamic TS fuzzy models. This requirement limits their application to the control of nonlinear systems for which mathematical modeling is laborious, expensive, or even not possible. In this study, we propose a learning-based dynamic TS fuzzy modeling method for nonlinear systems. In the proposed method, only the input-output measurements of the nonlinear system are used to identify the parameters of the dynamic TS fuzzy model, that is the membership function coefficients of the premise part and the state-space matrix elements of the consequent part. By combining the least-squares estimation method with gradient descent, a hybrid learning algorithm carries out the identification step. The performance of the aforementioned method is tested through simulation studies, which consists of modeling three nonlinear systems. These were first, a second-order nonlinear system, second, a spherical tank system, and lastly, a single-degree-of-freedom flexible joint system. Results of the simulation indicate that the method provides effective dynamic TS fuzzy models for nonlinear systems without requiring a prior mathematical model.