State Observation of Affine-in-the-States Systems with Unknown Time-Varying Parameters and Output Delay

TL;DR

This paper develops an adaptive state observer for affine-in-the-states systems with unknown, time-varying parameters and output delays, leveraging PEBO and DREM techniques for fixed-time convergence under weak excitation.

Contribution

It introduces a novel observer design combining PEBO and DREM for systems with unknown parameters and delays, achieving fixed-time convergence.

Findings

Observer ensures convergence despite output delay.

Fixed-time convergence under weak excitation conditions.

Effective handling of unknown, time-varying parameters.

Abstract

In this paper we address the problem of adaptive state observation of affine-inthe-states time-varying systems with delayed measurements and unknown parameters. The development of the results proposed in the [Bobtsov et al. 2021a] and in the [Bobtsov et al. 2021c] is considered. The case with known parameters has been studied by many researchers (see [Sanz et al. 2019, Bobtsov et al. 2021b] and references therein) where, similarly to the approach adopted here, the system is treated as a linear time-varying system. We show that the parameter estimation-based observer (PEBO) design proposed in [Ortega et al. 2015, 2021] provides a very simple solution for the unknown parameter case. Moreover, when PEBO is combined with the dynamic regressor extension and mixing (DREM) estimation technique [Aranovskiy et al. 2016, Ortega et al. 2019], the estimated state converges in fixed-time with extremely weak excitation assumptions.