Distributed Event-Triggered Consensus with Non-Identical Bernoulli Packet Dropout

Distributed event-triggered control for discrete-time stochastic multi-agent systems with non-uniform Bernoulli packet loss is investigated in this paper. An event-triggered strategy is proposed to reduce the load on the communication network, which can be an issue when the bandwidth is small. The proposed trigger condition requires only locally available information, thus enabling a distributed control scheme. To enhance the performance, a co-design of event-triggered strat-egy and controller gains is proposed. Agent dynamics (single integrators) are modeled in discrete time. The network is represented as a Markovian Jump Linear System, and sufficient conditions for mean-square consensus are given in the form of a linear matrix inequality. Since this LMI condition can be of a potentially huge size (when the network is large), we show how the synthesis condition can be turned into a robust synthesis problem with a complexity that is independent of the network size and corresponds to the size of a single agent. A numerical example illustrates the approach and shows how the trigger level can be chosen to trade performance against data transmission rate.