Distributed zero-gradient-sum optimisation algorithm with an edge-based adaptive event-triggered mechanism

This paper addresses the continuous-time distributed optimisation problem over networks, where the global objective function is formed by a sum of convex local objective functions. To avoid continuous communication among agents, a distributed adaptive Zero-Gradient-Sum (ZGS) optimisation algorithm under a dynamic event-triggered scheme is proposed. This is achieved by dynamically adjusting the coupling strengths of adjacent agents within the network. Our analysis confirms that the proposed algorithm will exponentially converge to the optimal solution provided that the underlying communication graph is undirected and connected. Additionally, we demonstrate that our event-triggered scheme is not subject to Zeno behaviour, which is a theoretical concern in systems with frequent event triggers.