Almost fast finite-time adaptive tracking control for a class of full-state constrained pure-feedback nonlinear systems

In this article, a novel almost fast finite-time adaptive tracking control scheme is proposed for a class of full-state constrained pure-feedback nonlinear systems based on barrier Lyapunov functions (BLFs). First, by employing the mean value theorem, the pure-feedback systems are converted to the strict-feedback structure with nonaffine terms. Then, by fusing adaptive backstepping technique and BLFs, the design difficulties caused by the nonaffine terms and full-state constraints are overcome. Furthermore, according to the predeveloped almost fast finite-time stability criterion, it is proved that the tracking error can converge to a small compact set and all signals of the closed-loop system can be bounded in an almost fast finite time. Finally, a simulation example of a single-link robot is presented to verify the effectiveness of the proposed control scheme.