Ultra Local Nonlinear Unknown Input Observers for Robust Fault Reconstruction

TL;DR

This paper introduces a robust nonlinear unknown input observer approach using ultra-local models for accurate actuator and sensor fault estimation in nonlinear systems, ensuring stability and minimizing estimation error.

Contribution

The paper develops a novel ultra-local nonlinear unknown input observer framework with stability guarantees and an SDP-based gain synthesis for fault reconstruction.

Findings

Successful simulation results demonstrate effective fault estimation.

The method guarantees asymptotic stability and ISS properties.

Minimized L2-gain improves robustness against model mismatch.

Abstract

In this paper, we present a methodology for actuator and sensor fault estimation in nonlinear systems. The method consists in augmenting the system dynamics with an approximated ultra-local model (a finite chain of integrators) for the fault vector and constructing a Nonlinear Unknown Input Observer (NUIO) for the augmented dynamics. Then, fault reconstruction is reformulated as a robust state estimation problem in the augmented state (true state plus fault-related state). We provide sufficient conditions that guarantee the existence of the observer and stability of the estimation error dynamics (asymptotic stability of the origin in the absence of faults and ISS guarantees in the faulty case). Then, we cast the synthesis of observer gains as a semidefinite program where we minimize the L2-gain from the model mismatch induced by the approximated fault model to the fault estimation error. Finally, simulations are given to illustrate the performance of the proposed methodology.