Smooth control design for adaptive leader

In this paper, we investigate the distributed adaptive leader-following consensus control for high-order nonlinear multi-agent systems with a time-varying reference trajectory under directed topology, subjected to mismatched unknown parameters and unknown control directions. By introducing local estimators for the bounds of the reference trajectory and a filter for each agent, a new backstepping-based smooth distributed adaptive control protocol is proposed. Meanwhile, a Nussbaum-type function is applied to address the consensus control with unknown control directions. It is shown that global uniform boundedness of all the closed-loop signals and asymptotic output consensus tracking can be achieved. Simulation results are provided to verify the effectiveness of our scheme