A subgradient algorithm for data-rate optimization in the remote state estimation problem

TL;DR

This paper introduces a subgradient algorithm to estimate the minimal communication rate needed for accurate remote state estimation of dynamical systems, leveraging the concept of restoration entropy.

Contribution

It proposes a novel subgradient method to compute restoration entropy using Riemannian metrics, aiding in optimal data-rate selection for remote observers.

Findings

The algorithm effectively estimates restoration entropy from system dynamics.

It applies to both discrete-time maps and continuous-time vector fields.

Provides a practical tool for designing communication-efficient remote estimation systems.

Abstract

In the remote state estimation problem, an observer tries to reconstruct the state of a dynamical system at a remote location, where no direct sensor measurements are available. The observer only has access to information sent through a digital communication channel with a finite capacity. The recently introduced notion of restoration entropy provides a way to determine the smallest channel capacity above which an observer can be designed that observes the system without a degradation of the initial observation quality. In this paper, we propose a subgradient algorithm to estimate the restoration entropy via the computation of an appropriate Riemannian metric on the state space, which allows to determine the approximate value of the entropy from the time-one map (in the discrete-time case) or the generating vector field (for ODE systems), respectively.