An indirect adaptive fuzzy sliding-mode control for decoupled nonlinear systems

In this paper, a decoupled fuzzy sliding-mode control design scheme is presented through width adaptation for a class of fourth-order nonlinear systems. Each subsystem, which is decoupled into two second-order systems, is said to have main and sub control purpose. Two sliding surfaces are constructed. through the state variables of the decoupled subsystem. We define main and sub target condition for these sliding surfaces, and introduce an intermediate variable from the sub sliding surface condition. The proposed adaptation law, which results from the indirect adaptive approach, is used to appropriately determine the width of the unknown system variables. And the membership functions in the THEN part will vary with the width adaptation. An adaptive law is then used to tune the width in the THEN part to appropriately determine the distribution of each membership function. The main advantage of the proposed method is that the structure of fuzzy controller dose not need to be changed while using a common design procedure and the computing time may be reduced considerably. Finally, a nonlinear system simulation example is shown to verify the effectiveness of the proposed adaptive fuzzy-sliding mode controller.