Fault Detection and Isolation Based on Adaptive Observers for Linear Time Varying Systems

Parameter fault detection and estimation of a class of nonlinear systems using observers

“…Inequality (24) implies the stability of the origin e x ¼ 0, e y ¼ 0 and the uniform boundedness of e x and e y with e x 2 L 2 . On the other hand, from (18), _ e x is uniformly bounded as well. According to Barbalat's Lemma (see [29]), one can get lim t!1 e x ðtÞ ¼ 0.…”

“…In such cases, it is important to carry out fault estimation in addition to detection. Some recent results based on adaptive or robust observers can be found in [16][17][18][19][20]; see [21,22] for methods using learning approach.…”

Parameter fault detection and estimation of a class of nonlinear systems using observers

“…Inequality (24) implies the stability of the origin e x ¼ 0, e y ¼ 0 and the uniform boundedness of e x and e y with e x 2 L 2 . On the other hand, from (18), _ e x is uniformly bounded as well. According to Barbalat's Lemma (see [29]), one can get lim t!1 e x ðtÞ ¼ 0.…”

“…In such cases, it is important to carry out fault estimation in addition to detection. Some recent results based on adaptive or robust observers can be found in [16][17][18][19][20]; see [21,22] for methods using learning approach.…”

H∞Fault Detection for Linear Discrete Time-Varying Descriptor Systems with Missing Measurements

“…In practice, time variability is the inherent characteristic of most systems. Recently, research on fault diagnosis of linear systems with time-varying parameters has attracted more and more attention; see, for example, [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. By dividing the filter gain matrix into two sections, an unknown input decoupling optimal filter for linear stochastic systems has been designed in [7], and its application on fault diagnosis has also been addressed.…”

“…By solving a min-max problem with a generalized least-squares cost criterion, a generalized least-squares fault detection filter has been designed in [9,12]. By using an adaptive observer method, a fault diagnosis technique for linear time-varying systems has been developed in [14,17,18]. However, to the best of authors' knowledge, few reports on fault diagnosis problem of linear discrete time-varying descriptor systems have been published, which motivates the present study.…”

Fault Detection Filter for Nonlinear Systems Using Linear Approximations

“…On the other hand, there are well-known approaches in the study of FDI for linear time invariant systems, such as the residual generation approach and the unknown-input observer approach, which separates the faults into a target fault and several nuisance faults which are unobservable to the residual. There are also some attempts at studying fault detection methods for linear time-varying systems (LTV), such as (Edelmayer et al, 1997) based on a time-invariant representation of a LTI system corrupted by linear time-varying parametric perturbations and (Xu and Zhang, 2002) based on the design of an adaptive observer. Recently, a design which extends the unknown input observer to the time-varying case by designing a fault detection filter has been proposed (Chen et al, 2003).…”

Parameter fault detection and estimation of a class of nonlinear systems using observers

“…Inequality (24) implies the stability of the origin e x ¼ 0, e y ¼ 0 and the uniform boundedness of e x and e y with e x 2 L 2 . On the other hand, from (18), _ e x is uniformly bounded as well. According to Barbalat's Lemma (see [29]), one can get lim t!1 e x ðtÞ ¼ 0.…”

“…In such cases, it is important to carry out fault estimation in addition to detection. Some recent results based on adaptive or robust observers can be found in [16][17][18][19][20]; see [21,22] for methods using learning approach.…”

H∞Fault Detection for Linear Discrete Time-Varying Descriptor Systems with Missing Measurements

“…In practice, time variability is the inherent characteristic of most systems. Recently, research on fault diagnosis of linear systems with time-varying parameters has attracted more and more attention; see, for example, [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. By dividing the filter gain matrix into two sections, an unknown input decoupling optimal filter for linear stochastic systems has been designed in [7], and its application on fault diagnosis has also been addressed.…”

“…By solving a min-max problem with a generalized least-squares cost criterion, a generalized least-squares fault detection filter has been designed in [9,12]. By using an adaptive observer method, a fault diagnosis technique for linear time-varying systems has been developed in [14,17,18]. However, to the best of authors' knowledge, few reports on fault diagnosis problem of linear discrete time-varying descriptor systems have been published, which motivates the present study.…”

Fault Detection Filter for Nonlinear Systems Using Linear Approximations

“…On the other hand, there are well-known approaches in the study of FDI for linear time invariant systems, such as the residual generation approach and the unknown-input observer approach, which separates the faults into a target fault and several nuisance faults which are unobservable to the residual. There are also some attempts at studying fault detection methods for linear time-varying systems (LTV), such as (Edelmayer et al, 1997) based on a time-invariant representation of a LTI system corrupted by linear time-varying parametric perturbations and (Xu and Zhang, 2002) based on the design of an adaptive observer. Recently, a design which extends the unknown input observer to the time-varying case by designing a fault detection filter has been proposed (Chen et al, 2003).…”

Parameter fault detection and estimation of a class of nonlinear systems using observers

“…Inequality (24) implies the stability of the origin e x ¼ 0, e y ¼ 0 and the uniform boundedness of e x and e y with e x 2 L 2 . On the other hand, from (18), _ e x is uniformly bounded as well. According to Barbalat's Lemma (see [29]), one can get lim t!1 e x ðtÞ ¼ 0.…”

“…In such cases, it is important to carry out fault estimation in addition to detection. Some recent results based on adaptive or robust observers can be found in [16][17][18][19][20]; see [21,22] for methods using learning approach.…”

H∞Fault Detection for Linear Discrete Time-Varying Descriptor Systems with Missing Measurements

“…In practice, time variability is the inherent characteristic of most systems. Recently, research on fault diagnosis of linear systems with time-varying parameters has attracted more and more attention; see, for example, [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. By dividing the filter gain matrix into two sections, an unknown input decoupling optimal filter for linear stochastic systems has been designed in [7], and its application on fault diagnosis has also been addressed.…”

“…By solving a min-max problem with a generalized least-squares cost criterion, a generalized least-squares fault detection filter has been designed in [9,12]. By using an adaptive observer method, a fault diagnosis technique for linear time-varying systems has been developed in [14,17,18]. However, to the best of authors' knowledge, few reports on fault diagnosis problem of linear discrete time-varying descriptor systems have been published, which motivates the present study.…”

Fault Detection Filter for Nonlinear Systems Using Linear Approximations

“…On the other hand, there are well-known approaches in the study of FDI for linear time invariant systems, such as the residual generation approach and the unknown-input observer approach, which separates the faults into a target fault and several nuisance faults which are unobservable to the residual. There are also some attempts at studying fault detection methods for linear time-varying systems (LTV), such as (Edelmayer et al, 1997) based on a time-invariant representation of a LTI system corrupted by linear time-varying parametric perturbations and (Xu and Zhang, 2002) based on the design of an adaptive observer. Recently, a design which extends the unknown input observer to the time-varying case by designing a fault detection filter has been proposed (Chen et al, 2003).…”