  This paper addresses distributed robust learning-based control for consensus
formation tracking of multiple underwater vessels, in which the system
parameters of the marine vessels are assumed to be entirely unknown and subject
to the modeling mismatch, oceanic disturbances, and noises. Towards this end,
graph theory is used to allow us to synthesize the distributed controller with
a stability guarantee. Due to the fact that the parameter uncertainties only
arise in the vessels' dynamic model, the backstepping control technique is then
employed. Subsequently, to overcome the difficulties in handling time-varying
and unknown systems, an online learning procedure is developed in the proposed
distributed formation control protocol. Moreover, modeling errors,
environmental disturbances, and measurement noises are considered and tackled
by introducing a neurodynamics model in the controller design to obtain a
robust solution. Then, the stability analysis of the overall closed-loop system
under the proposed scheme is provided to ensure the robust adaptive performance
at the theoretical level. Finally, extensive simulation experiments are
conducted to further verify the efficacy of the presented distributed control
protocol.
