A direct PI adaptive fuzzy controller design with state observer

A direct PI adaptive fuzzy control scheme with the state observer is presented for a class of uncertain multiple-input-multiple- output (MIMO) nonlinear systems. Because the states are assumed to be unavailable, an observer is designed to estimate the unavailable states. Due to a PI control architecture to be designed, it improves robustness in the closed-loop system and avoids affection of uncertainties and external disturbances. In addition, this scheme enhances speed of the convergence. Based on the stability Lyapunov theory, it can be ensured that all signals of closed-loop system are bounded, and the tracking errors converge to a small neighborhood around zero.