Adaptive fuzzy controller for a SISO nonlinear system with state observer

This paper addresses the adaptive fuzzy control problem using the Lyapunov synthesis approach, in which the fuzzy model is viewed as the approximator, which is referred to as fuzzy approximator, to deal with the unknown functions in the plant to be controlled. In order to deal with the case that the system state is unavailable to be used in the system development, state observer involving the fuzzy approximator is proposed. It is shown that the adaptive fuzzy controller presented guarantees the tracking error, between the output of the considered system and the desired value, to be shrunken to an arbitrarily small bound asymptotically, while maintaining all signals involved in the system stable.