Takagi–Sugeno fuzzy model based indirect adaptive fuzzy observer and controller design

This paper proposes the design scheme of the alternative adaptive observer and controller based on the Takagi–Sugeno (T–S) fuzzy model. The T–S fuzzy modeling and the state feedback control technique are adopted for the simple structure. The proposed method maintains consistent performance in the presence of parameter uncertainties and incorporates linguistic fuzzy information from human operators. In addition, with the simple adaptive state feedback controller, it solves the singularity problem, which occurs in the inverse dynamics based on the feedback linearization method. Using Lyapunov theory and Lipschitz condition, the stability analysis is conducted, and the adaptive law is derived. The proposed method is applied to the stabilization problem of a flexible joint manipulator in order to guarantee its performance.