High-order command filtered adaptive backstepping control for second- and high-order fully actuated strict-feedback systems

Abstract

In this paper, a high-order command filtered adaptive backstepping (HOCFAB)-based approach is proposed in order to track a given reference signal for the second- and high-order strict-feedback systems (SFSs) with parametric uncertainties, where both their subsystems hold a common full-actuation structure, namely, high-order fully actuated (HOFA) SFSs. Unlike the prevailing traditional first-order state-space backstepping approach which suffers from the problem of “explosion of terms”, the proposed HOCFAB approach circumvents the complexity arising owing to differentiating the virtual controllers repeatedly, and does not need to convert the high-order systems into first-order forms which is easier to carry out and demands fewer steps. Meanwhile, an error-compensating mechanism is constructed to reduce filtering errors. A critical analysis is theoretically proven which indicates that in both cases the entire system states are uniformly ultimately bounded under the proposed high-order controller, and the tracking error could be made arbitrarily small with predesigned parameters. Finally, the effectiveness of the proposed scheme is verified by a benchmark application in the robotic manipulator.