Estimating tolerable communication delays for distributed optimization problems in control of heterogeneous multi‐agent systems

Abstract

This study addresses the problem of distributed optimization in control of heterogeneous linear multi‐agent systems. Instead of assuming a perfect communication medium as in many existing approaches, two important issues arising from communication networks are considered. First, the existence of communication delays is assumed when each agent receives information from its neighbors. Second, since communication networks are generally unreliable, it is assumed that each agent interacts with other agents through random digraphs. Finally, delay‐dependent sufficient conditions are derived in the form of linear matrix inequalities (LMIs) to prove convergence to optimal solutions. Numerical simulation results are analyzed to demonstrate the effectiveness of the proposed approach.