Distributed Optimisation with Stochastic Event-Triggered Multi-Agent Control Algorithm

In this paper, we study the distributed optimisation problem in which multiple agents cooperatively and distributively solve an optimisation problem. In order to avoid continuous communication among agents, we propose a stochastic distributed dynamic event-triggering law to schedule the communication. We show that the optimisation problem can be solved with exponential rate and arbitrarily small optimisation error. We further prove that Zeno behaviour does not exist in the proposed stochastic event-triggering law by constructing a lower bound on the inter-event interval which is essential for the feasibility of proposed algorithm. A numerical simulation is presented to illustrate the effectiveness of the proposed algorithm when compared with some existing event-triggered distributed optimisation algorithms.