A New Exact Inversion Approach for Takagi-Sugeno Fuzzy Systems Representing SISO Nonlinear Systems

Inversion of Takagi-Sugeno (TS) fuzzy systems has significant applications in nonlinear control systems. In this study, a new approach is presented for the exact inversion of TS fuzzy systems representing affine-in-control Single-Input-Single-Output (SISO) nonlinear systems. The proposed approach provides exact inverse solutions for TS fuzzy systems whose rule consequents are in the form of linear state-space models. Although this type of fuzzy system is widely used in control applications to represent SISO nonlinear dynamical systems, there is currently no existing inversion method in the literature for a fuzzy system with a similar structure. In the proposed method, the inverse model is obtained by using a rule-by-rule inversion approach. In order to show the exactness of the proposed inversion approach, a simulation example is given for a TS fuzzy model of a single link manipulator. Simulation results validate the exactness of the proposed inversion method.