On the tightest interval-valued state estimator for linear systems

TL;DR

This paper derives the tightest interval-valued state estimator for linear systems, balancing computational complexity and estimator accuracy through over-approximations.

Contribution

It introduces the theoretically optimal interval estimator as an intersection of all estimators, addressing practical implementation challenges.

Findings

Derived the expression for the tightest interval-valued estimator.

Identified the estimator as an infinite-dimensional dynamic system.

Proposed over-approximation methods for practical implementation.

Abstract

This paper discusses an interval-valued state estimator for linear dynamic systems. In particular, we derive an expression of the tightest possible interval-valued estimator in the sense that it is the intersection of all interval-valued estimators. This estimator appears, in a general setting, to be an infinite dimensional dynamic system. Therefore, practical implementation requires some over-approximations which would yield a good trade-off between computational complexity and tightness.