Event-triggered distributed optimisation for multi-agent systems with transmission delay

In this study, the authors discuss the event-triggered distributed optimisation algorithm for multi-agent systems with sampled-data and transmission delay. Each agent only knows its local objective function and exchanges information with its connected neighbours through the network. Firstly, they present sufficient conditions of exponential stability for a class of hybrid non-linear systems by using continuous and discrete analysis. Then, based on these conditions, a distributed optimisation algorithm is proposed such that a multi-agent system achieves consensus and optimality. Finally, a simulation example is provided to verify the effectiveness of the theoretical results.