Robust Adaptive Asymptotic Tracking of Nonlinear Systems in a Semi-strict Feedback Form

For a class of nonlinear systems in a semistrict feedback form with both parametric uncertainty and unknown nonlinearities, a new control design scheme based on backstepping approach is proposed. The Nussbaum gain technique is used as a robust control term to deal with unknown nonlinearities for the first time. This gives a continuous control, in contrast to those schemes using the sign function to obtain zero steady-state tracking error. It is shown that the proposed adaptive scheme can guarantee the global uniform boundedness of all signals and achieve asymptotic tracking property with the continuous control.