Delay-dependent LMI-based stability criterion for distributed optimization problem in heterogeneous linear multi-agent systems over random digraphs

TL;DR

This paper develops delay-dependent stability criteria using LMIs for distributed optimization in heterogeneous multi-agent systems over unreliable, randomly connected communication networks, ensuring convergence despite delays and network randomness.

Contribution

It introduces a novel delay-dependent LMI-based stability criterion for distributed optimization over random digraphs in heterogeneous multi-agent systems.

Findings

The proposed approach guarantees convergence under communication delays.

Numerical simulations confirm the effectiveness of the stability criterion.

The method handles unreliable, randomly switching network topologies.

Abstract

This work studies the problem of distributed optimization in heterogeneous linear multi-agent systems. Instead of relying on a perfect communication network as in many existing distributed optimization approaches, we considered two important issues related to communication networks. First, assumed that communication delays exist when each agent receives information from its neighbors. Further, since communications networks are generally unreliable, we assumed each agent interacted with the other agents through random digraphs. Finally, to prove convergence to optimal solutions, delay-dependent sufficient conditions are derived in the form of linear matrix inequality. An analysis of numerical simulation results is presented to demonstrate the effectiveness of the introduced approach.