Output regulation for uncertain nonlinear constrainted systems with a novel root-type barrier Lyapunov function

This article deals with the output regulation problem with output constraint for uncertain nonlinear systems with unknown control directions. An output feedback backstepping control and an internal model integrating root-type barrier Lyapunov function are designed. The root-type barrier Lyapunov function is used for the first time in designing an adaptive controller to deal with the output constraint of the output regulation problem, which ensures that the system output cannot violate the given boundary. Compared with other barrier Lyapunov functions, the key advantage lies in its polynomial-form derivatives, which avoid singularity issues near constraint boundaries. Nussbaum functions are utilised to address the problem of unknown directions. It is proven that under the adaptive controller via a novel algorithm, all signals of the closed-loop system are ultimately uniformly bounded(UUB), and the tracking error remains strictly within pre-given constraint intervals. Finally, the effectiveness of the proposed method is shown by two simulation examples.