An Adaptive Observer for Uncertain Linear Time-Varying Systems with Unknown Additive Perturbations

TL;DR

This paper introduces a globally convergent adaptive observer for uncertain linear time-varying systems with unknown parameters and additive perturbations, requiring only weak excitation conditions.

Contribution

It presents a novel adaptive observer design that guarantees convergence despite uncertainties and unknown initial conditions in LTV systems.

Findings

The observer achieves global convergence under weak excitation.

It effectively estimates states despite additive perturbations.

The method handles unknown initial conditions in parameters.

Abstract

In this paper we are interested in the problem of adaptive state observation of linear time-varying (LTV) systems where the system and the input matrices depend on unknown time-varying parameters. It is assumed that these parameters satisfy some known LTV dynamics, but with unknown initial conditions. Moreover, the state equation is perturbed by an additive signal generated from an exosystem with uncertain constant parameters. Our main contribution is to propose a globally convergent state observer that requires only a weak excitation assumption on the system.