Event-triggered scheme for zero-gradient-sum optimisation under directed networks with time delay

The paper investigates the distributed convex optimisation problem of multi-agent systems over strongly connected and balanced digraph with time delay. To reduce the traffic among agents and the control inputs' update frequency, a sample-based distributed event-triggered zero-gradient-sum optimisation algorithm has been proposed. A sufficient stability condition with respect to the related parameters and time delay is derived via the Lyapunov function approach. Moreover, it is proved that the states of agents asymptotically converge to the global optimal point. Since the sampling control is adopted, Zeno behaviour can be naturally excluded. The results of the numerical simulation illustrate the effectiveness of the proposed algorithm.