Abstraction of Linear Consensus Networks with Guaranteed Systemic Performance Measures

TL;DR

This paper introduces a framework and efficient algorithms for creating simplified abstractions of large-scale linear consensus networks, ensuring performance guarantees and reducing communication costs.

Contribution

The paper develops a nearly-linear time algorithm for constructing abstractions of linear consensus networks with guaranteed performance bounds.

Findings

Existence of network abstractions is proven.

Efficient algorithm for abstraction computation is proposed.

Numerical simulations demonstrate effectiveness.

Abstract

A proper abstraction of a large-scale linear consensus network with a dense coupling graph is one whose number of coupling links is proportional to its number of subsystems and its performance is comparable to the original network. Optimal design problems for an abstracted network are more amenable to efficient optimization algorithms. From the implementation point of view, maintaining such networks are usually more favorable and cost effective due to their reduced communication requirements across a network. Therefore, approximating a given dense linear consensus network by a suitable abstract network is an important analysis and synthesis problem. In this paper, we develop a framework to compute an abstraction of a given large-scale linear consensus network with guaranteed performance bounds using a nearly-linear time algorithm. First, the existence of abstractions of a given network is proven. Then, we present an efficient and fast algorithm for computing a proper abstraction of a given network. Finally, we illustrate the effectiveness of our theoretical findings via several numerical simulations.