Robust Adaptive Backstepping Control of Second-Order Nonlinear Systems with Non-Triangular Structure Uncertainties

In this paper, we consider a class of second-order uncertain nonlinear systems. Besides parametric uncertainties, a non-parametric uncertainty may exist in every state equation or channel with its effects bounded by a known function. Such a bounding function is allowed to depend on all system states which means that the actual system does not need to meet the triangular structure. Therefore the currently available backstepping technique cannot be used to design controllers. To overcome such difficulty, a new backatepping-based robust adaptive control scheme is proposed. It is shown that the proposed scheme can ensure all signals in the closed-loop system bounded.