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/H∞ optimization problem where the effect of disturbances and model mismatches is minimized in the H∞ sense, for an acceptable H2 performance with respect to measurement noise.@en

In this paper, we present a methodology for actuator and sensor fault estimation in nonlinear systems. The method consists of 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 ℒ 2 -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.@en