Consistent event-triggered consensus on complete graphs

This paper starts by considering an optimal control formulation of the consensus problem on complete graphs with a cost capturing disagreement and agents modeled by integrators. An optimal control policy for this problem is shown to be the well-known consensus algorithm by which each agent resets its state to the average of its and other agents' state values received at every time step. The framework is extended to the case where agents can only exchange information periodically, with a period larger than one. Then an event-triggered control strategy is proposed that results in a better cost than that of the optimal periodic one with the same average transmission rate, that is, it is consistent. According to this strategy, each agent distributedly transmits its state if the error between its current state and a common consensus estimate based on previously transmitted agents' data exceeds a threshold. Simulation results are presented to illustrate the proposed strategy.