Barrier Lyapunov Functions-based adaptive control for a class of nonlinear pure-feedback systems with full state constraints

In this study, an adaptive control technique is developed for a class of uncertain nonlinear parametric systems. The considered systems can be viewed as a class of nonlinear pure-feedback systems and the full state constraints are strictly required in the systems. One remarkable advantage is that only less adjustable parameters are used in the design. This advantage is first to take into account the pure-feedback systems with the full state constraints. The characteristics of the considered systems will lead to a difficult task for designing a stable controller. To this end, the mean value theorem is employed to transform the pure-feedback systems to a strict-feedback structure but non-affine terms still exist. For the transformed systems, a novel recursive design procedure is constructed to remove the difficulties for avoiding non-affine terms and guarantee that the full state constraints are not violated by introducing Barrier Lyapunov Function (BLF) with the error variables. Moreover, it is proved that all the signals in the closed-loop system are global uniformly bounded and the tracking error is remained in a bounded compact set. Two simulation studies are worked out to show the effectiveness of the proposed approach.