  In this chapter we look at one of the canonical driving examples for
multi-agent systems: average consensus. In this scenario, a group of agents
seek to agree on the average of their initial states. Depending on the
particular application, such states might correspond to sensor measurements,
estimates about the position of a target, or some other data that needs to be
fused. Due to its numerous applications in networked systems, many algorithmic
solutions exist to the multi-agent average consensus problem; however, a
majority of them rely on agents having continuous or periodic availability of
information from other agents. Unfortunately, this assumption leads to
inefficient implementations in terms of energy consumption, communication
bandwidth, network congestion, and processor usage. Motivated by these
observations, our main goal here is the design of provably correct distributed
event-triggered strategies that autonomously decide when communication and
control updates should occur so that the resulting asynchronous network
executions still achieve average consensus.
