Distributed Optimization of Average Consensus Containment with Multiple Stationary Leaders

TL;DR

This paper addresses distributed algorithms for multi-agent systems to achieve average consensus of stationary leaders' states over directed networks, optimizing convergence rates using ADMM, with numerical validation.

Contribution

It introduces a distributed algorithm for followers to reach average consensus of multiple stationary leaders and optimizes convergence speed via distributed weight adjustment using ADMM.

Findings

The proposed algorithm successfully achieves average consensus.

Optimized weights improve convergence rate.

Numerical examples validate the effectiveness of the approach.

Abstract

In this paper, we consider the problem of containment control of multi-agent systems with multiple stationary leaders, interacting over a directed network. While, containment control refers to just ensuring that the follower agents reach the convex hull of the leaders states, we focus on the problem where the followers achieve a consensus to the average values of the leaders states. We propose an algorithm that can be implemented in a distributed manner to achieve the above consensus among followers. Next we optimize the convergence rate of the followers to the average consensus by proper choice of weights for the interaction graph. This optimization is also performed in a distributed manner using Alternating Direction Method of Multipliers (ADMM). Finally, we complement our results by illustrating them with numerical examples.