Distributed Consensus of Layered Multi-Agent Systems Subject to Attacks on Edges

This paper addresses the consensus problem for two-layered MASs (multi-agent systems) subject to attacks on communication edges. Unlike most existing two-layered MAS models, the considered MASs are allowed to have heterogeneous inner communication topologies between the different layers. By using the linear transformation technique, some sufficient criteria are first given to achieve consensus among the leaders within the leader layer where the condition that the interaction topology has directed spanning trees with a fixed root required in most existing works has been removed. Furthermore, based on the relative outputs, observer-based controllers are designed to achieve node-to-node consensus among the two layers. By developing a new kind of multiple Lyapunov function (MLF) based on a bisection search method, some criteria are established under which the node-to-node consensus error will converge into a bounded set asymptotically. It is interestingly found that a less conservative average dwell time (ADT) constraint is obtained for achieving node-to-node consensus by utilizing the proposed MLF compared with that yielded by the traditional MLF constructed from nonsingular M matrix theory. Moreover, we show that consensus can be achieved asymptotically in the layered MASs with the same inner topology subject to synchronous attacks under some suitable conditions. Finally, the effectiveness of the criteria is verified by simulation on networking linear oscillators.