Matrix-Scaled Consensus over Undirected Networks

TL;DR

This paper introduces matrix-scaled consensus algorithms for undirected networks of linear agents, providing new methods for achieving state agreement with matrix weights, including nonlinear, finite-time, and observer-based variants, supported by rigorous analysis and simulations.

Contribution

The paper develops novel matrix-scaled consensus algorithms for linear agents, analyzing their properties and extending to nonlinear, finite-time, and observer-based methods with proven convergence.

Findings

Algorithms achieve asymptotic consensus with matrix scaling.

Nonlinear and finite-time consensus algorithms are effective.

Rigorous mathematical analysis confirms convergence.

Abstract

In this paper, we propose matrix-scaled consensus algorithms for linear dynamical agents interacting over an undirected network. Under the proposed algorithms, the state vectors of all agents to asymptotically agree up to some matrix scaling weights. First, the algebraic properties of the matrix-scaled Laplacian and the geometry of the matrix-scaled consensus space are studied. Second, we examine matrix-scaled consensus algorithms for networks of single-integrators with or without constant parametric uncertainties. Nonlinear and finite-time matrix-scaled consensus algorithms are also proposed. Third, observer-based matrix-scaled consensus algorithms for homogeneous or heterogeneous linear-time invariant agents are designed. The convergence of the proposed algorithms is asserted by rigorous mathematical analysis and supported by numerical simulations.