I. Introduction
Backstepping technique [1] is one of the most powerful tools in nonlinear control, which has been widely applied in different kinds of nonlinear systems [2]–[4]. The standard backstepping control design procedure uses current virtual control function and its time derivative to construct the next virtual control function, and in the end, the control law can be obtained via the last virtual control function and its time derivative. The problem in standard backstepping controller is that the high-order time derivatives of virtual control functions can result in explosive complexity in the controller design. Therefore, it is inappropriate to apply standard backstepping control scheme to high-dimensional nonlinear systems. In order to address the problem of computing the complex derivative of virtual control functions, command filtered backstepping was proposed in [5], which avoids analytic computation of the derivative of virtual control functions and greatly decrease the computation burden compared with standard backstepping. When standard backstepping and command filtered backstepping are applied into strict-feedback nonlinear systems with unmodeled dynamics and external disturbances, both methods need large values of feedback gains to reduce the influence of the system uncertainties, which may cause the saturation of the controller and increase the control cost. Thus, they are only appropriate for strict-feedback nonlinear systems with small uncertainties. As for adaptive backstepping [6]–[8] and command filtered adaptive backstepping [9], they can only deal with the system with unknown parameters that appear linearly related to certain known nonlinear functions, which limits greatly the possible range of their application.