Adaptive observer for a nonlinear system with partially unknown state matrix and delayed measurements

TL;DR

This paper develops an adaptive observer for nonlinear systems with partially unknown state matrices and delayed measurements, enabling the reconstruction of unknown states and parameters despite measurement delays.

Contribution

It introduces a novel adaptive observer design that handles unknown time-varying parameters, partially unknown state matrices, and measurement delays in nonlinear systems.

Findings

Successfully reconstructs unknown states and parameters

Handles measurement delays in the observer design

Builds on and extends recent theoretical results

Abstract

Problem of an adaptive state observer design for nonlinear system with unknown time-varying parameters and under condition of delayed measurements is considered. State observation problem was raised by many researchers (see for example Sanx et al. (2019)). In this paper the results proposed in Bobtsov et al. (2021b), Bobtsov et al. (2021a), Bobtsov et al. (2022a), Bobtsov et al. (2022b) are developed. The problem is solved under assumption that the state matrix can be represented as sum of known and unknown parts. The output vector is measured with a known constant delay. An adaptive observer which reconstructs unknown state and unknown time-varying parameter is proposed.