Publication

Addressing the relative degree restriction in nonlinear adaptive observers: A high-gain observer approach

Journal Article (2022)

Journal

Journal of the Franklin Institute

Doc link

https://doi.org/10.1016/j.jfranklin.2022.03.020

File

Download the digital copy of the doc pdf document

Abstract

The design of adaptive observers is a common approach for the joint state and parameter-estimation problem. Nonetheless, there are still some obstacles that have to be solved to improve the design of adaptive observers and extend its implementability to a larger class of systems. First, the separation of the state-estimation and the parameter-estimation requires a relative degree one or zero between some known signal and the parameters to be estimated. Second, standard stability proofs for adaptive observers cannot be easily extended to consider the unavoidable presence of sensor noise and unmodelled system uncertainty. Consequently, on the one hand, this work proposed a methodology to relax the relative degree condition through the use of a high-gain observer that will be coupled with the adaptive observer. On the other hand, the stability and performance of the proposed observer scheme will be analysed by the use of a strict Lyapunov function based on the Mazenc construction, which allows to have provable convergence and to study the effect of sensor noise and model uncertainty through common Lyapunov theory. Finally, the proposed approach is validated in a compartmental epidemiology model.

Categories

control theory, observability.

Author keywords

Robust estimation, Adaptive systems, Nonlinear observer design, parameter-estimation, Compartmental model, strict Lyapunov functions

Scientific reference

A. Cecilia and R. Costa. Addressing the relative degree restriction in nonlinear adaptive observers: A high-gain observer approach. Journal of the Franklin Institute, 2022, to appear.