State Observation of Affine-in-the-States Time-Varying Systems with Unknown Parameters and Delayed Measurements

摘要

In this paper we address the problem of adaptive state observation of affine-in-the-states time-varying systems with delayed measurements and unknown parameters. The case with known parameters has been studied by many researchers—see [Sanz et al. 2019, Bobtsov et al. 2021] 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, 2020] 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.