Distributed optimization of first-order discrete-time multi-agent systems with event-triggered communication

This paper focuses on the event-triggered distributed subgradient algorithms for solving a class of convex optimization problems based on first-order discrete-time multi-agent systems over undirected networks. The communication process of the whole network is controlled by a set of trigger conditions monitored by each agent. The trigger condition and event-triggered distributed subgradient optimization algorithm for each agent are completely decentralized and just rest with each agent's and its neighboring agents' individual states at the event-triggered sequence of themselves as well as each agent's local objective function. At each time instant, each agent updates its state by employing its own objective function and the states collected from itself and its neighboring agents at their separate event-triggered time instants. A sufficient condition for ensuring the consensus and reaching the optimization solution is established under the condition that the undirected network topology is connected and the design parameters are properly designed. Theoretical analysis shows that the event-triggered distributed subgradient algorithm is capable of steering the whole network of agents asymptotically converge to an optimal solution of the convex optimization problem. Simulation results validate effectiveness of the introduced algorithm and demonstrate feasibility of the theoretical analysis.