Reachable set-based dynamic quantization for the remote state estimation of linear systems

TL;DR

This paper introduces a novel reachability analysis-based dynamic quantization method using zonotopes for remote state estimation of linear systems, improving transmission efficiency and error bounds.

Contribution

It presents the first set-based zonotope method for dynamic quantization in remote state estimation, extending applicability and reducing communication requirements.

Findings

Set-based zonotope method offers larger system class coverage.

Method guarantees bounded quantization and reconstruction errors.

Numerical example confirms theoretical advantages.

Abstract

We employ reachability analysis in designing dynamic quantization schemes for the remote state estimation of linear systems over a finite date rate communication channel. The quantization region is dynamically updated at each transmission instant, with an approximated reachable set of the linear system. We propose a set-based method using zonotopes and compare it to a norm-based method in dynamically updating the quantization region. For both methods, we guarantee that the quantization error is bounded and consequently, the remote state reconstruction error is also bounded. To the best of our knowledge, the set-based method using zonotopes has no precedent in the literature and admits a larger class of linear systems and communication channels, where the set-based method allows for a longer inter-transmission time and lower bit rate. Finally, we corroborate our theoretical guarantees with a numerical example.