Distributed optimization for multi-agent systems with communication delays and external disturbances under a directed network

This article studies the distributed optimization problem for multi-agent systems with communication delays and external disturbances in a directed network. Firstly, algorithm is proposed based on internal model principle which term can effectively compensate environmental disturbances. Secondly, relationship between optimal solution equilibrium point of system discussed through properties Laplacian matrix graph theory. Some sufficient conditions are derived by using Lyapunov–Razumikhin theory, ensures all agents asymptotically reach value problem. Moreover, an aperiodic sampled-data control protocol proposed, be well transformed into time-varying delay analyzed Finally, example given to verify effectiveness results.