An LMI approach to robust fault estimation for a class of nonlinear systems

Abstract

SUMMARYThe paper presents a robust fault estimation approach for a class of non-linear discrete-time systems. In particular, two sources of uncertainty are present in the considered class of systems, i.e., an unknown input and an exogenous external disturbance. Thus, apart from simultaneous state and fault estimation, the objective is to decouple the effect of an unknown input while minimizing the influence of the exogenous external disturbance within the H∞ framework. The resulting design procedure guarantees that a prescribed disturbance attenuation level is achieved with respect to the state and fault estimation error while assuring the convergence of the observer. The core advantage of the proposed approach is its simplicity by reducing the fault estimation problem to matrix inequalities formulation. In addition, the design conditions ensure the convergence of the observer with guaranteed H∞ performance. The effectiveness of the proposed approach is demonstrated by its application to a Twin Rotor MIMO System.

Robust adaptive simultaneous state and fault estimation for nonlinear systems: Application to an aerodynamical system

“…Although some approaches for nonlinear systems have been proposed as high gain observer for Lipschitz systems [9], geometric approach [10] however, the fault estimation for problem nonlinear system is still an open issue of paramount importance. This paper extends the approach developed by the authors in [11] where the objective was to determine an optimal state and fault estimation in the sense of H ∞ norm. In this work, a design strategy that additionally provides confidence intervals overbounding the estimates are consistent with the disturbances and measurement noises.…”

“…FAULT ESTIMATION STRATEGY To make the paper self contained, this section presents the design procedure [11] of the robust observer that will estimate simultaneously the state x k , and the fault f k , and decouple the effect of the unknown input d k . To this purpose, the following structure is proposed…”

“…Subsequently, according to (20), firstly matrix T is determined to satisfy T D = 0 and then matrix G is calculated such that G = T B as follows (for further details see [11]). …”

“…The detailed description of the model is given in [11] and is omitted due the lack of space. Let the initial condition for the system and the observer be Moreover, let us consider the following fault scenarios i.e., additive faults in the tail motor f h (k) and additive faults in the main motor f v (k), described as follows:…”

Simultaneous actuator and sensor fault estimation for discrete‐time Lipschitz nonlinear systems in finite‐frequency domain

“…However, the sliding-mode observer method requires several state transformations, rank condition, and a priori knowledge of the upper bounds of the faults. In the work of Witczak et al, 25 a robust actuator fault estimation approach for discrete-time nonlinear systems based on the general idea of unknown input observer and the H ∞ technique is proposed. Qian et al 26 developed a framework of reduced-order observer-based robust actuator fault estimation and accommodation for discrete-time Lipschitz systems.…”