Design of non-singular adaptive terminal backstepping controllers with perturbation estimation for non-linear systems in semi-strict feedback form

An adaptive non-singular backstepping control with perturbation estimation scheme is designed for a class of multi-input systems with matched and mismatched perturbations to solve the regulation problems. The design procedure of this control scheme mainly contains two parts. The first part is the design of the virtual control inputs, the second part is the design of control input functions and perturbation estimation mechanism. The main advantage of the proposed control scheme is that, without knowing the upper bounds of perturbations, the controlled system is still capable of suppressing the perturbations so that the controlled states are able to reach zero within a finite time. Another advantage is that there is no singular problem at all. Finally, a numerical example and a practical application are given for demonstrating the feasibility of the proposed control strategy.