Sample-based detectability and moving horizon state estimation of continuous-time systems

TL;DR

This paper introduces a new detectability condition for nonlinear continuous-time systems with infrequent measurements, linking it to observability and proposing a stable moving horizon estimation method demonstrated via a biomedical example.

Contribution

It develops a sample-based detectability condition for nonlinear systems, relates it to linear observability, and presents a robust moving horizon estimation scheme.

Findings

Established a sufficient condition for sample-based i-iIOSS.

Linked sample-based i-iIOSS with linear observability.

Demonstrated the estimation scheme's applicability in biomedical simulation.

Abstract

In this paper we propose a detectability condition for nonlinear continuous-time systems with irregular/infrequent output measurements, namely a sample-based version of incremental integral input/output-to-state stability (i-iIOSS). We provide a sufficient condition for an i-iIOSS system to be sample-based i-iIOSS. This condition is also exploited to analyze the relationship between sample-based i-iIOSS and sample-based observability for linear systems, such that previously established sampling strategies for linear systems can be used to guarantee sample-based i-iIOSS. Furthermore, we present a sample-based moving horizon estimation scheme, for which robust stability can be shown. Finally, we illustrate the applicability of the proposed estimation scheme through a biomedical simulation example.