Command filtered adaptive backstepping

As the order of the system increases, implementation of adaptive backstepping controllers becomes increasingly complex due to the necessity to calculate analytically the partial derivatives of certain stabilizing functions with respect to the system state. To remove the burden of computation, in this paper we propose a command filtered adaptive backstepping design method. In the proposed controller design method, analytic calculation of partial derivatives is not required. The control law and the update law become succinct. The stability properties of the controllers is analyzed through a sequence of theorems. Effectiveness of the proposed method is shown by simulation results.