Hybrid multi-observer for improving estimation performance

TL;DR

This paper introduces a hybrid multi-observer framework for nonlinear systems that enables online tuning of observer gains to enhance estimation performance, ensuring stability and improved accuracy.

Contribution

It proposes a flexible hybrid multi-observer scheme with proven stability that improves estimation performance compared to nominal observers.

Findings

Enhanced estimation accuracy demonstrated in numerical examples

Proven input-to-state stability of the proposed scheme

Flexible design allowing for various performance properties

Abstract

Various methods are nowadays available to design observers for broad classes of systems, where the primary focus is on establishing the convergence of the estimated states. Nevertheless, the question of the tuning of the observer to achieve satisfactory estimation performance remains largely open. In this context, we present a general design framework for the online tuning of the observer gains. Our starting point is a robust nominal observer designed for a general nonlinear system, for which an input-to-state stability property can be established. Our goal is then to improve the performance of this nominal observer. We present for this purpose a new hybrid multi-observer scheme, whose great flexibility can be exploited to enforce various desirable properties, e.g., fast convergence and good sensitivity to measurement noise. We prove that an input-to-state stability property also holds for the proposed scheme and, importantly, we ensure that the estimation performance in terms of a quadratic cost is (strictly) improved. We illustrate the efficiency of the approach in improving the performance of given nominal observers in two numerical examples (Van der Pol oscillator and Lithium-Ion (Li-Ion) battery model).