Robust Adaptive Control of High-Order Fully-Actuated Systems: Command Filtered Backstepping With Concurrent Learning

This paper investigates the problem of tracking control for high-order strict-feedback systems (HOSFSs) with both parametric uncertainties and nonlinear function uncertainties. Based on the high-order fully-actuated (HOFA) system approach, a direct high-order robust adaptive command filtered backstepping (HORACFB) design is proposed. We adopt the concurrent learning (CL) technique to identify the unknown parameters through the examination of linear independence within the recorded data. To do so, we have introduced a novel parametric model for constructing the parameter update law under the presence of both parametric uncertainties and nonlinear function uncertainties. This is achieved by introducing new filtering variables to avoid utilizing high-order derivative information of system states required by the existing CL technique. The proposed framework can guarantee both reference tracking and unknown parameter estimation convergence (to their true values) with arbitrary accuracy that can be tuned by the designer. The closed-loop system proves to be uniformly ultimately bounded. Last but not the least, the proposed control framework avoids converting the high-order systems into first-order ones, thereby reducing unnecessary backstepping steps.