Adaptive Backstepping Control for a Class of Nonlinear Systems With Non-Triangular Structural Uncertainties

In this technical note, a robust adaptive control scheme is proposed based on backstepping techniques for a class of nonlinear systems with unknown parameters. A modeling error may also exist in every state equation or channel and it is bounded by a known function which is allowed to depend on all system states. It is shown that the proposed adaptive control scheme can ensure all signals in the closed-loop system bounded, if the strength of system modeling errors is sufficiently weak. Transient performance is also established. Thus stabilizing systems in classical strict-feedback forms with sufficiently small non-triangular structural perturbations is successfully addressed. In the case that system parameters are known, a non-adaptive robust controller is designed to globally exponentially stabilize such a class of nonlinear systems. Finally simulation studies are used to verify the effectiveness of the proposed scheme.