<i>H</i> <sub>∞</sub> synthesis of unknown input observers for non-linear Lipschitz systems

Pertew, A.M.; Marquez, Horacio J.; Zhao, Qing

doi:10.1080/00207170500155488

Cited by 69 publications

(38 citation statements)

References 24 publications

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“…In turn, the latter is necessary in most unknown-input observers designs -see e.g. [25]; it is also used in Lyapunov-based designs as in e.g., [27] and [16] or in order to decompose the system, as in [30] and [12]. A notable exception (for linear systems) is [14] where the authors propose a method to transform the system into a new canonical form; however, even though the authors of [14] succeed in avoiding the relative degree one assumption, it is assumed that measurements are noise-free i.e., y = C 0 x * .…”

Section: Problem Statementmentioning

confidence: 99%

Continuously-implemented sliding-mode adaptive unknown-input observers under noisy measurements

Dimassi

Lorı́a

Belghith

2012

Systems & Control Letters

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We propose an estimator for nonlinear systems with unmatched unknown inputs and under measurement noise. The estimator design is based on the combination of observer design for descriptor systems, sliding-modes theory and adaptive control. The estimation of the measurement noise is achieved thanks to the transformation of the original system into a singular form where the measurement noise makes part of the augmented state. Two adaptive parameters are updated online, one to compensate for the unknown bounds on the states, the unkown inputs and the measurement noise and a second one to compensate for the effect of the nonlinearities. To join robust state estimation and unknown-inputs reconstruction, our approach borrows inpiration from sliding-mode theory however, all signals are comtinuously implemented. We demonstrate that both state and unknown-inputs estimation are achieved up to arbitrarily small tolerance. The utility of our theoretical results is illustrated through simulation case-studies.

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Section: Problem Statementmentioning

confidence: 99%

Continuously-implemented sliding-mode adaptive unknown-input observers under noisy measurements

Dimassi

Lorı́a

Belghith

2012

Systems & Control Letters

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“…Taking into account the evolution of both state and fault estimation errors (36), it is possible to provide a new observer design procedure, which is comprehensively detailed in the subsequent section.…”

Section: Fault Estimation Strategymentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

“…[42,51]) becomes a usual Lipschitz condition [1,27,37,36] with γ being a Lipschitz constant. This appealing property makes the employed strategy more general than those presented in the literature [1,27,37,36]. Moreover, a significant progress was recently obtained in the observer design for non-linear systems by introducing the so-called one-sided Lipschitz condition [53], which means that a wider spectrum of systems can be tackled with the new approach.…”

Section: Preliminariesmentioning

confidence: 99%

“…It should also be pointed out that the proposed description of non-linearity constitutes an alternative to other approaches presented in the literature [1,27,37,36,33].…”

Section: Introductionmentioning

confidence: 99%

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

Witczak

Buciakowski

Puig

et al. 2015

Int. J. Robust. Nonlinear Control

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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.

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Adaptive sensor and actuator fault estimation for a class of uncertain Lipschitz nonlinear systems

Defoort

Veluvolu

Rath

et al. 2015

Adaptive Control & Signal

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This paper deals with state and fault estimations for a class of uncertain Lipschitz nonlinear systems. The proposed scheme combines a descriptor form observer and an adaptive sliding mode observer. The adaptive descriptor sliding approach is proposed to jointly estimate the state and reconstruct the sensor fault while rejecting the effect of uncertainties and Lipschitz nonlinearities. Using a Lyapunov analysis, the stability condition is analyzed and the observer gains are designed such that the reduced-order system is practically stable. Then, an adaptive super-twisting observer is derived to reconstruct the actuator faults. The main feature of the proposed adaptive scheme is that it does not overestimate the observer gains, which mitigates chattering in the presence of bounded uncertainties, actuator, and sensor faults with unknown boundaries. Simulation results for a robotic manipulator show the effectiveness of the proposed method.constraining the system motion along manifolds of reduced dimensionality in the state space and is applicable to a broad variety of practical applications. Robustness properties against various kinds of uncertainties such as parameter perturbations and external disturbances can be guaranteed.Several SMO-based FDI approaches have been developed recently for linear systems and a class of nonlinear systems. The first-order SMOs in [14][15][16] are designed to directly tackle the actuator faults through the sliding mode terms via some transformations. Unfortunately, the realization of first-order sliding mode implies the undesirable chattering phenomenon, that is, high-frequency vibrations of the closed-loop system, which may excite unmodeled high-frequency dynamics, degrade the system performances, and lead to instability. Other techniques rely on a nonlinear coordinate transformation to obtain a form suite for the design of high-gain observer [17,18]. The gains are designed based on the inverse jacobian of the state transformation. However, this transformation is valid only locally and no sensor fault is considered. Recently, some SMOs have been proposed to reconstruct both the system state, actuator faults, and sensor faults. In [19,20], actuator fault is reconstructed with the so-called equivalent output estimation error injection concept. Then, sensor fault is estimated via a low-pass filter and appropriate secondary SMO. Nevertheless, the sensor fault estimation is very sensitive to the filter parameters, and no uncertainty acting on the system is considered. An SMO is proposed in [21,22] to solve this problem for nonlinear systems without uncertainty assuming some conditions on the fault distribution matrix. Descriptor sliding mode approaches are introduced in [5, 23] to simultaneously reconstruct state, sensor, and actuator faults for linear systems. In [24], a sliding mode unknown input observer is given for linear systems where the same additive perturbation affects both the dynamics and the output. In [25], a H 1 SMO is derived for a class of uncertain nonlinear Lipschitz sy...

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H _∞ synthesis of unknown input observers for non-linear Lipschitz systems

Cited by 69 publications

References 24 publications

Continuously-implemented sliding-mode adaptive unknown-input observers under noisy measurements

Continuously-implemented sliding-mode adaptive unknown-input observers under noisy measurements

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

Adaptive sensor and actuator fault estimation for a class of uncertain Lipschitz nonlinear systems

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H ∞ synthesis of unknown input observers for non-linear Lipschitz systems

Cited by 69 publications

References 24 publications

Continuously-implemented sliding-mode adaptive unknown-input observers under noisy measurements

Continuously-implemented sliding-mode adaptive unknown-input observers under noisy measurements

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

Adaptive sensor and actuator fault estimation for a class of uncertain Lipschitz nonlinear systems

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H _∞ synthesis of unknown input observers for non-linear Lipschitz systems