High‐order robust command filtered backstepping design for strict‐feedback systems: A high‐order fully actuated system approach

A high‐order fully actuated (HOFA) system approach is invoked to construct a high‐order robust command filtered backstepping (HORCFB) controller to track a feasible desired output trajectory for the second‐ and high‐order strict‐feedback systems (SFSs) subjected simultaneously to nonlinear uncertainties, where the subsystems of the SFSs possess a common full‐actuation structure. Unlike the existing classical first‐order state‐space approach, the proposed HORCFB scheme avoids converting the high‐order systems into first‐order ones, and thus simpler to implement and needs fewer steps. Moreover, the presented result avoids the complexity arising due to repeatedly differentiating, namely, the problem of “explosion of complexity.” Stability analysis of the closed‐loop system shows that all the states of the closed‐loop system are kept uniformly ultimately bounded, and the output is driven to track a feasible desired output trajectory with an arbitrarily small error by proper selection of the design parameters. Finally, the effectiveness of the proposed scheme is demonstrated by the trajectory tracking control problem of a single‐link robot arm with the elastic revolute joint.