Distributed robust estimation over randomly switching networks using $H_\infty$ consensus

TL;DR

This paper develops a method for distributed robust estimation in networks with randomly changing topology, using $H_ fty$ consensus to ensure reliable estimates despite network variations.

Contribution

It introduces sufficient and necessary conditions for $H_ fty$ consensus in switching networks, enabling local gain computation via LMIs and addressing partial topology knowledge.

Findings

Guarantees suboptimal $H_ abla$ level of disagreement.

Allows gain computation through LMIs when global network info is available.

Establishes conditions linking graph Laplacian properties to detectability.

Abstract

The paper considers a distributed robust estimation problem over a network with Markovian randomly varying topology. The objective is to deal with network variations locally, by switching observer gains at affected nodes only. We propose sufficient conditions which guarantee a suboptimal $H_\infty$ level of relative disagreement of estimates in such observer networks. When the status of the network is known globally, these sufficient conditions enable the network gains to be computed by solving certain LMIs. When the nodes are to rely on a locally available information about the network topology, additional rank constraints are used to condition the gains, given this information. The results are complemented by necessary conditions which relate properties of the interconnection graph Laplacian to the mean-square detectability of the plant through measurement and interconnection channels.