Takagi-Sugeno-based robust and adaptive fuzzy sliding-mode control systems

A nonlinear dynamic system with bounded disturbance is approximated by N fuzzy-based linear state-space subsystems. Most approaches using a Takagi-Sugeno fuzzy model with linear state-feedback control must solve N linear matrix inequalities for a common positive definite matrix to guarantee the stability of the overall system. Although the iteration design for a common positive definite matrix can be achieved, it is time-consuming. We use the same fuzzy sets of the system rule to establish a reference model for the trajectory tracking. Then the same fuzzy sets of the system rule are employed to design two fuzzy-based robust and adaptive sliding-mode controls. Each includes an equivalent control and a switching control. If the approximation error of the fuzzy-model is not very large, a robust fuzzy sliding mode control is applied to stabilize the nonlinear system and track a bounded reference input. Its performance can be better than that of a fuzzy linear state-feedback control and the approximation error is huge, a simple network is used to model the approximation error and then an adaptive fuzzy sliding-mode control is employed to improve the system performance. Due to the above advantageous features, the proposed control is simple and effective. The stability of the overall system is verified by Lyapunov stability theory. An illustrative example of a two-joint robot is given to explain the design procedure