Self-triggered Consensus Control of Multi-agent Systems from Data

Abstract: 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.