  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.
