D.Swaroop put forward the design method of dynamic surface (DSC) in his paper in 2000, which solved the problem of item explosion in reverse design for the first time. The design idea is to filter the virtual control law with a first-order low-pass filter instead of complex differential operation.

However, DSC does not compensate the filtering error, so in order to make the error as small as possible, the filtering parameter t can only be as small as possible, which increases the difficulty of implementation. Dong Wenjie and others proved the stability of instruction filtering in 2009 and 12 respectively, and proposed an adaptive backstepping design method for instruction filtering, which not only avoided the derivation of virtual control law, but also realized the compensation of filtering error.

Backstepping control is not new.

Backstepping is a method to design nonlinear system controllers. Through the recursion of the subsystem, the input that makes the system stable can be easily obtained. However, most related literatures do not consider the controllability of the system itself, so we first assume that the controlled system is controllable.