State and parameter estimation: a nonlinear Luenberger observer approach

TL;DR

This paper introduces a nonlinear Luenberger observer for parametrized linear SISO systems, providing a new low-dimensional, Lyapunov-stable identification algorithm with practical implementation on a third-order system.

Contribution

It presents a novel, low-dimensional nonlinear observer with a strict Lyapunov function for system identification, improving upon existing adaptive observers.

Findings

Successful implementation on a third-order system

Observer guarantees stability via Lyapunov function

Reduced complexity compared to traditional adaptive observers

Abstract

The design of a nonlinear Luenberger observer for a parametrized linear SISO (single-input single-output) system is studied. From an observability assumption of the system, the existence of such an observer is concluded. In a second step, a novel algorithm for the identification of such systems is suggested and is implemented on a third order system. Compared to the adaptive observer available in the litterature, it has the advantage to be of low dimension and to admit a strict Lyapunov function. This is a long version of a paper which is published in IEEE TAC 2017.