Numerical approximation of the data-rate limit for state estimation under communication constraints

TL;DR

This paper develops an algorithm to compute rigorous upper bounds on the minimal communication channel capacity needed for accurate state estimation in networked control systems, extending previous theoretical results.

Contribution

It introduces a novel algorithm that provides rigorous upper bounds on the data-rate limit for state estimation, based on analytical estimates and applicable to time-invariant systems.

Findings

The algorithm computes upper bounds on the data-rate limit.

It extends theoretical estimates of the minimal channel capacity.

The approach is applicable to systems characterized by topological or restoration entropy.

Abstract

In networked control, a fundamental problem is to determine the smallest capacity of a communication channel between a dynamical system and a controller above which a prescribed control objective can be achieved. Often, a preliminary task of the controller, before selecting the control input, is to estimate the state with a sufficient accuracy. For time-invariant systems, it has been shown that the smallest channel capacity $C_0$ above which the state can be estimated with an arbitrarily small error, depending on the precise formulation of the estimation objective, is given by the topological entropy or a quantity named restoration entropy, respectively. In this paper, we propose an algorithm that computes rigorous upper bounds of $C_0$, based on previous analytical estimates.