Adaptive Fuzzy Control for a Class of Nonlinear Systems with State Observer

This paper addresses the fuzzy control problem using the Lyapunov synthesis approach. In order to deal with cases where the system state is unavailable, a state observer is proposed. Consequently, the whole system behavior can be attributed to a kind of standard singularly perturbed form. At the same time, to deal with the gap, if any, between the real state and its estimated value from the state observer, we view it as a part of system disturbance, and propose a unique way to deal with the disturbance, i.e., adopt a switching function with an alterable coefficient, which is tuned by adaptive law based on the tracking error between the output of the considered system and the desired value. Finally, it is shown that the fuzzy controller proposed guarantees the tracking error will shrink to zero, while maintaining the stability of all signals involved in the system.