Observer-based adaptive fuzzy controller for nonlinear systems with unknown control directions and input saturation

This paper addresses design of an observer-based adaptive fuzzy controller for a class of single-input-single-output (SISO) nonlinear systems with unknown dynamics subject to input nonlinearity and unknown direction. The proposed controller is singularity free. A high-gain observer is designed to estimate the unmeasured states, and the Lipschitz condition for proving boundedness of the estimated states is relaxed. The Nussbaum function is used to handle the unknown virtual control directions and the backstepping technique has been applied for controller design. It is proved that all closed loop signals are semi-globally uniformly ultimately bounded (SGUUB) and the output tracking error converges to a small neighborhood of the origin by choosing the design parameters appropriately. Numerical example illustrates effectiveness of the proposed method even for the system with a change in control direction.