A Distributed Optimization Approach for Multi-Agent Systems over Delaying Networks

—This paper investigates a novel method to solve distributed optimization problems in the presence of communication delays between the networked agents that cooperate together to find an optimal solution of a global cost function composed of local ones. In the problem of distributed optimization in a network of multi-agent because of existing phenomena such as communication delay, deriving approaches having appropriate performance so that the states of all agents converge to the same value always has been a substantial challenge. Delay-dependent conditions in the form of linear matrix inequities are derived to analyze the convergence of the introduced scheme to the optimal solution. It is demonstrated that the maximum allowable time delay in the network and convergence rate of the optimization procedure are increased by the suggested strategy. Finally, comparative simulation results are considered to illustrate the superior performance of the introduced scheme compared to a rival one in the literature.