Plug-and-play distributed state estimation for linear systems

TL;DR

This paper introduces a plug-and-play distributed state estimation method for large-scale linear systems, enabling local estimators to be designed independently and ensuring bounded estimation errors under disturbances.

Contribution

It presents a novel LSE design framework that is modular, scalable, and guarantees error bounds, suitable for large interconnected systems with minimal information exchange.

Findings

Estimation errors are confined within prescribed polyhedral sets.

Estimation errors converge to zero in the absence of disturbances.

The method is validated through numerical experiments on a mechanical system.

Abstract

This paper proposes a state estimator for large-scale linear systems described by the interaction of state-coupled subsystems affected by bounded disturbances. We equip each subsystem with a Local State Estimator (LSE) for the reconstruction of the subsystem states using pieces of information from parent subsystems only. Moreover we provide conditions guaranteeing that the estimation errors are confined into prescribed polyhedral sets and converge to zero in absence of disturbances. Quite remarkably, the design of an LSE is recast into an optimization problem that requires data from the corresponding subsystem and its parents only. This allows one to synthesize LSEs in a Plug-and-Play (PnP) fashion, i.e. when a subsystem gets added, the update of the whole estimator requires at most the design of an LSE for the subsystem and its parents. Theoretical results are backed up by numerical experiments on a mechanical system.