Dynamic periodic event-triggered control for nonlinear multi-agent systems under DoS attacks

This article investigates the consensus issue for nonlinear multi-agent systems (MASs) under denial-of-service (DoS) attacks, where the connectivity of topology graph can be destroyed by attacks. Compared with the existing results, the connectivity-maintained attacks and connectivity-broken attacks are both considered, and the corresponding consensus control schemes based on a novel dynamic periodic event-triggered mechanism are respectively presented. Specifically, for the connectivity-maintained attacks, a time-varying and a time-invariant consensus control schemes based on the designed event-triggered mechanism are presented for the known and unknown attacks, respectively. Furthermore, to achieve consensus even though the connectivity of communication network is broken, a dynamic periodic event-triggered controller based on periodic sampling observer is presented for the connectivity-broken attacks. It can be proved that all the proposed control schemes can solve the consensus issues under different types of DoS attacks. In addition, the provided event-triggered conditions can avoid zeno-behavior and have the less conservatism than traditional static event-triggered conditions. Finally, the numerical examples are given to illustrate the proposed controllers.