Adaptive Backstepping Control for a Class of Non-Triangular Structure Nonlinear Systems

In this paper, an adaptive control scheme is proposed based on backstepping approach for a class of second-order nonlinear systems with non-triangular uncertainties. The triangular form of the control system is destroyed by such uncertainties and the traditional backstepping can not be directly used in the controller design. Compared with the existing results, nonlinear terms and unknown parameters appear in every channel. Thus the linear type of relation between the state vector x and z is difficult to maintain. To overcome such difficulty, a new backatepping-based adaptive control scheme is proposed. A significance of our new scheme is to introduce the feedback gain term l
_i
z
_i
x
_i
²
in virtual control signals. Under the proposed control scheme, not only the non-triangular uncertainties can be restrained effectively but also the estimation of parameter has been realized successfully. Finally simulation studies are used to verify the effectiveness of the proposed scheme.