$\mathcal{H}_\infty$ Network Optimization for Edge Consensus

TL;DR

This paper develops $_ ext{infty}$-norm bounds for edge consensus protocols in multi-agent networks with disturbances, enabling optimized network design considering agent time scales and edge weights.

Contribution

It introduces new $_ ext{infty}$-norm bounds for networks with heterogeneous agent time scales and edge weights, and formulates a convex optimization approach for network parameter tuning.

Findings

Derived explicit $_ ext{infty}$-norm bounds for disturbed networks.

Formulated convex optimization for time scale and edge weight selection.

Validated bounds and optimization through numerical and formation control examples.

Abstract

This paper examines the $\mathcal{H}_\infty$ performance problem of the edge agreement protocol for networks of agents operating on independent time scales, connected by weighted edges, and corrupted by exogenous disturbances. $\mathcal{H}_\infty$-norm expressions and bounds are computed that are then used to derive new insights on network performance in terms of the effect of time scales and edge weights on disturbance rejection. We use our bounds to formulate a convex optimization problem for time scale and edge weight selection. Numerical examples are given to illustrate the applicability of the derived $\mathcal{H}_\infty$-norm bound expressions, and the optimization paradigm is illustrated via a formation control example involving non-homogeneous agents.