Implementation of the Takagi-Sugeno model-based fuzzy control using an adaptive gain controller

Abstract

A fuzzy controller of the type of the Takagi–Sugeno model is investigated. The proposed adaptive gain controller for Takagi–Sugeno fuzzy control, which results from the direct adaptive approach, is employed to directly adapt the appended gain parameters in the THEN-part of the Takagi–Sugeno model. Then, the constructed Takagi–Sugeno fuzzy controller can be best approximated to a given optimal control. Generally speaking, a complicated design procedure is necessary to determine the parameters in the Takagi–Sugeno fuzzy controller, but the number of parameters in THEN-part is proportional to the number of rules and states. However, in this study, the THEN-part of each rule with only an injected parameter could be adapted to determine the control action of each rule. The best merits of the proposed method are that the number of regulated parameters depends on the number of rules, and the design algorithm is implemented more easily than existing approaches. In addition, a maximum control is established to guarantee the system robust stability. The derivation shows that the proposed controller is stable in the sense of Lyapunov. Finally, a nonlinear system simulation example is applied to verify the effectiveness and ability of the proposed controller.