Robust adaptive backstepping control for an uncertain nonlinear system with input constraint based on Lyapunov redesign

This paper presents the control problem for a class of n-order semi-strict nonlinear system subjects to unknown parameters, uncertainty, and input constraint. The controller is designed via combining backstepping control and Lyapunov redesign. Firstly, based on the Lyapunov function, a composite adaptive law is constructed to estimate the unknown parameters. To sequel, a robust term is designed to handle the matched and unmatched uncertainties on the basis of Lyapunov redesign technique. The “explosion of terms” problem that inherent in backstepping control is avoided by the robust second-order filters. Thirdly, an auxiliary signal provided by the auxiliary system is employed to handle the influence of the input constraint. It is proved that the closed-loop system is stable in a Lyapunov framework theory and the semi-global uniformly ultimate boundedness of all signals is achieved. Finally, numerical simulations are carried out to evaluate the performance of the proposed control strategy. Numerical example and the application of the hypersonic vehicle (HSV) tracking control are simulated to demonstrate the effectiveness of the proposed control scheme.