Adaptive Fuzzy Control for a Discrete-Time Nonlinear Systems

This paper, deals with an indirect adaptive fuzzy control of discrete-time MIMO nonlinear systems with parametric variations. The synthesis of the state feedback control law is based on the T-S fuzzy models developed by a local description of the considered system. In the first step, gradient method is used to adjust model parameters locally estimated by the fuzzy model. The state feedback control law based on pole placement is applied to the nonlinear system in the second step. Based on the Lyapunov stability theory, the asymptotic stability of the proposed state feedback adaptive fuzzy control method is studied. Two links robot manipulator arm is used to illustrate the performance of the proposed controller. Keywords— Adaptive control, T-S fuzzy system, nonlinear systems, discrete-time model, stability analysis