Asymptotic Tracking Control for a Class of Uncertain High-order Nonlinear Systems

In this paper, asymptotic tracking control of uncertain high-order nonlinear systems with time-varying desired signals is achieved for the first time. A novel asymptotic tracking controller is constructed with Nussbaum functions. Some compact sets are introduced to analysis the bounds of system uncertainties on these sets, and the stability analysis is presented by using these bounds in view of quadratic Lyapunov functions (QLF). This new controller allows the output of high-order nonlinear systems to track arbitrary bounded time-varying signals. The boundedness of all closed-loop signals is proved using Lyapunov stability theorem and invariant set theory. Moreover guaranteed by the Barbalat’s Lemma, the tracking error is further ensured to approach zero asymptotically. Simulation results demonstrate the claims.