Robust adaptive finite-time containment control for nonlinear multi-agent systems with unknown input saturations

In this article, the distributed adaptive finite-time containment control problem is investigated for nonlinear multi-agent systems with unknown input saturations. Since the leaders are only available to partial subsystems, a distributed estimator is designed to estimate the local reference signals. The saturated function is converted to the combination of a linear part and a nonlinear part, thus overcomes the difficulties caused by unknown saturated bounds. By utilising the command filtered and backstepping control techniques, a two-step method is adopted to construct the controller, under which the effect of unknown input saturations can be compensated well. It is proved that the closed-loop system is practical finite-time stable, and the output of each follower can converge to the dynamic convex hull spanned by the leaders in finite time. Finally, a group of four one-link manipulator systems is used to support the feasibility of the developed control scheme.