Simplifying Nonlinear Control Design with Reduced-Complexity T-S Fuzzy System

Abstract

This work introduces a new method to decrease the complexity of Takagi-Sugeno (TS) representations with sector nonlinearity. Takagi-Sugeno (TS) fuzzy control is a structured method deal with managing non-linear systems, first introduced in 1985. It depends on the utilization of fuzzy system, which represent a collection of If-Then fuzzy regulations with regional linear descriptions in the consequent parts. The proposed method uses linear interconnections among submodels to simplify the TS fuzzy model, resulting in fewer rules and maintaining equivalence to the original model. The simplified model is demonstrated as a combination of $(p + 1)$ matrices that are affine, with stability analysis and controller design performed using linear matrix inequalities. The suggested technique has been shown on inverted pendulum model, showing the benefits of reduced complexity for of nonlinear control systems. The reduced-complexity model may result in conservative stability conditions compared to the classical TS fuzzy approach, but offers a significant reduction in numerical complexity and increased computational efficiency for complex systems.