Prescribed performance backstepping control of nonlinear systems with input saturation

The tracking problem of the nonlinear system with input saturation is investigated by using a backstepping approach based on fuzzy state observer, where the underline system contains immeasurable states and unknown control directions. Firstly, a fuzzy state observer is designed to estimate the immeasurable states. Then, the Hyperbolic tangent function with smooth property and a Nussbaum function are used to handle the input saturation. The bound of the output tracking error is set by the prescribed performance methodology. A robust controller is designed combining the backstepping approach and the dynamic surface method. The Lyapunov theory is applied to analyze the stability of the system. It is proved that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded(SGUUB). Finally, the longitudinal dynamics as the simulation model is given to show the effectiveness of the proposed control approach.