Online data-driven composite adaptive backstepping control with exact differentiators

This paper presents an online data-driven composite adaptive backstepping control for a class of parametric strict-feedback nonlinear systems with mismatched uncertainties, where both tracking errors and prediction errors are utilized to update parametric estimates. Hybrid exact differentiators are applied to obtain the derivatives of virtual control inputs such that the complexity problem of integrator backstepping can be avoided. Closed-loop tracking error equations are integrated in a moving-time window to generate prediction errors such that online recorded data can be utilized to improve parameter adaptation. Semiglobal asymptotic stability of the closed-loop system is rigorously established by the time-scales separation and Lyapunov synthesis. The proposed composite adaptation can not only avoid the application of identification models and linear filters resulting in a simpler control structure, but also suppress parametric uncertainties and external perturbations via the time-interval integral. Simulation results have demonstrated that the proposed approach possesses superior control performances under both noise-free and noisy-measurement environments. Copyright © 2015 John Wiley & Sons, Ltd.