Distributed Dynamic Event-triggered Optimization Algorithm for MASs Subject to Cyber Attacks and Its Applications*

In this paper, the distributed optimization problem (DOP) for multi-agent systems (MASs) is addressed. Unlike the existing results, the present problem faces with some demands, named, the existence of persistent cyber attacks on communication edges, the discrete communication among agents and some devices. To solve such an optimization problem while satisfying the mentioned demands, a distributed dynamic event-triggered optimization algorithm is proposed. Only the information at the triggering time instants is used in the algorithm. Under assumptions on the local functions, the communication graph and attacks, sufficient conditions for the exponentially convergence of the proposed algorithm are derived. It is also proved that the Zeno-behavior is excluded for the triggering time sequences. Finally, the proposed algorithm is applied to the economic dispatch problem to illustrate and validate the efficiency of it.