Distributed Smooth Optimisation With Event-Triggered Proportional-Integral Algorithms

In this paper, we consider the distributed smooth optimisation problem of multi-agent systems over undirected connected communication topologies. The objective is to minimise the global objective function, which is the sum of local private objective functions, by exchanging and computing local information among each agent or with its neighbourhoods. To avoid continuous communication among agents and reducing communication overheads, we propose an event-triggered distributed optimisation algorithm based on a proportional-integral control strategy. We first show that the developed algorithm does not exhibit Zeno behaviour. Then, it is shown that the proposed algorithm exponentially converges to an exact global minimiser under the restricted secant inequality condition. This condition admits a more general class of the global objective function since it does not require the convexity of the global objective function and the global minimisers are not required to be unique. Theoretical results are illustrated by numerical simulations.