Asymptotic Tracking Control for a Class of Pure-Feedback Nonlinear Systems

This paper studies the adaptive asymptotic tracking problem for a class of unknown nonlinear systems in pure-feedback form. Different from the traditional literatures which only tackle the bounded tracking problem for pure-feedback systems, this paper investigates the asymptotic tracking problem by developing a novel controller design method. Moreover, the differentiable assumption on nonaffine functions is canceled, and only a mild semi-bounded assumption is required as the controllability condition. By utilizing Lyapunov theorem, it is proved that all the variables of the resulting closed-loop system are semi-globally uniformly ultimately bounded, and the output tracking error can converge to zero asymptotically by choosing design parameters appropriately. Finally, a simulation result is presented to verify the effectiveness of the proposed control scheme.