Hierarchical parameter estimation for distributed networked systems: a dynamic consensus approach

TL;DR

This paper proposes a two-stage distributed estimation framework using dynamic consensus for networked systems, ensuring exponential convergence and adaptability to various network conditions.

Contribution

It introduces a novel hierarchical approach combining dynamic consensus and local estimation, with extensions to switched topologies and relaxed excitation conditions.

Findings

Achieves exponential convergence of the local Gradient Estimator (GE).

Supports extension to switched network topologies and quantization.

Allows substitution of GE with DREM estimator for relaxed excitation requirements.

Abstract

This work introduces a novel two-stage distributed framework to globally estimate constant parameters in a networked system, separating shared information from local estimation. The first stage uses dynamic average consensus to aggregate agents' measurements into surrogates of centralized data. Using these surrogates, the second stage implements a local estimator to determine the parameters. By designing an appropriate consensus gain, the persistence of excitation of the regressor matrix is achieved, and thus, exponential convergence of a local Gradient Estimator (GE) is guaranteed. The framework facilitates its extension to switched network topologies, quantization, and the heterogeneous substitution of the GE with a Dynamic Regressor Extension and Mixing (DREM) estimator, which supports relaxed excitation requirements.