Linear Fault Estimators for Nonlinear Systems: An Ultra-Local Model Design

TL;DR

This paper introduces a robust fault estimation method for nonlinear systems using an augmented linear model and ultra-local models, enabling effective fault reconstruction without restrictive nonlinear assumptions.

Contribution

It proposes a novel ultra-local model-based linear filter for fault estimation in nonlinear systems, avoiding traditional Lipschitz conditions and optimizing performance via mixed H2/Hinf design.

Findings

Effective fault reconstruction demonstrated in nonlinear systems

Avoids restrictive Lipschitz assumptions in filter design

Optimized for disturbance rejection and noise performance

Abstract

This paper addresses the problem of robust process and sensor fault reconstruction for nonlinear systems. The proposed method augments the system dynamics with an approximated internal linear model of the combined contribution of known nonlinearities and unknown faults -- leading to an approximated linear model in the augmented state. We exploit the broad modeling power of ultra-local models to characterize this internal dynamics. We use a linear filter to reconstruct the augmented state (simultaneously estimating the state of the original system and the sum of nonlinearities and faults). Having this combined estimate, we can simply subtract the analytic expression of nonlinearities from that of the corresponding estimate to reconstruct the fault vector. Because the nonlinearity does not play a role in the filter dynamics (it is only used as a static nonlinear output to estimate the fault), we can avoid standard restrictive assumptions like globally (one-sided) Lipschitz nonlinearities and/or the need for Lipschitz constants to carry out the filter design. The filter synthesis is posed as a mixed H2/Hinf optimization problem where the effect of disturbances and model mismatches is minimized in the Hinf sense, for an acceptable H2 performance with respect to measurement noise.