  This paper considers self-triggered consensus control of unknown linear
multi-agent systems (MASs). Self-triggering mechanisms (STMs) are widely used
in MASs, thanks to their advantages in avoiding continuous monitoring and
saving computing and communication resources. However, existing results require
the knowledge of system matrices, which are difficult to obtain in real-world
settings. To address this challenge, we present a data-driven approach to
designing STMs for unknown MASs building upon the model-based solutions. Our
approach leverages a system lifting method, which allows us to derive a
data-driven representation for the MAS. Subsequently, a data-driven
self-triggered consensus control (STC) scheme is designed, which combines a
data-driven STM with a state feedback control law. We establish a data-based
stability criterion for asymptotic consensus of the closed-loop MAS in terms of
linear matrix inequalities, whose solution provides a matrix for the STM as
well as a stabilizing controller gain. In the presence of external
disturbances, a model-based STC scheme is put forth for
$\mathcal{H}_{\infty}$-consensus of MASs, serving as a baseline for the
data-driven STC. Numerical tests are conducted to validate the correctness of
the data- and model-based STC approaches. Our data-driven approach demonstrates
a superior trade-off between control performance and communication efficiency
from finite, noisy data relative to the system identification-based one.
