Observer-based indirect adaptive fuzzy sliding mode control with state variable filters for unknown nonlinear dynamical systems

This paper proposes an observer-based indirect adaptive fuzzy sliding mode controller with state variable filters for a certain class of unknown nonlinear dynamic systems in which not all the states are available for measurement. To design the proposed controller, we first construct the fuzzy models to describe the input/output behavior of the nonlinear dynamic system. Then, an observer is employed to estimate the tracking error vector. Based on the observer, a fuzzy sliding model controller is developed to achieve the tracking performance. Then, a filtered observation error vector is obtained by passing the observation error vector to a set of state variable filters. Finally, on the basis of the filtered observation error vector, the adaptive laws are proposed to adjust the free parameters of the fuzzy models. The stability of the overall control system is analyzed based on the Lyapunov method. Simulation results illustrate the design procedures and demonstrate the tracking performance of the proposed controller.