Adaptive secure output consensus tracking of linear multi-agent systems via dynamic event-triggered impulsive control under DoS attack

In this paper, the adaptive secure output consensus tracking (ASOCT) problem for general linear multi-agent systems (MASs) with denial-of-service (DoS) attacks via novel dynamic event-triggered impulsive control (DETIC) protocols is considered. An observer-based distributed impulsive control scheme is proposed, where the designed control protocols and event-triggered mechanisms (ETMs) use the estimated value of the observer instead of the sampled information. The DoS attack considered in this paper appears aperiodically with an unknown attack strategy, which interrupts all communication links between agents, and further damages the controllers of agents. To handle the ASOCT under the DoS attack, some sufficient conditions for attack duration and attack frequency are derived. Moreover, the ETM considered in this paper is pull-based dynamic event-triggered mechanism (DETM), that is, the controllers of each agent merely are updated at its own triggering time while its neighbors will not be affected, as well each agent dynamically regulates its event-triggering threshold with the help of auxiliary parameters, which can effectively reduce controllers updates and allow larger triggering intervals. Furthermore, rigorous mathematical proofs are given, and some sufficient conditions are obtained to guarantee ASOCT of the linear MASs. The Zeno behavior is also proved theoretically to be precluded. Finally, the validity of the proffered control schemes is demonstrated by provided simulations.