design and analysis of a fault isolation scheme for a class of uncertain nonlinear systems

Design and analysis of a fault isolation scheme for a class

of uncertain nonlinear systems

Xiaodong Zhang a, Marios M. Polycarpou b,*, Thomas Parisini c

a Department of Electrical Engineering, Wright State University, Dayton, OH 45435, USAb KIOS Research Center for Intelligent Systems and Networks, Department of Electrical and Computer Engineering,

University of Cyprus, Nicosia 1678, Cyprusc Department of Electrical, Electronic and Computer Engineering, University of Trieste, 34100 Trieste, Italy

Received 20 November 2007; accepted 4 March 2008

www.elsevier.com/locate/arcontrol

Annual Reviews in Control 32 (2008) 107–121

Available onl
ine 16 May 2008
Abstract

This paper presents a unified fault isolation scheme for handling both process faults and sensor faults in a class of uncertain nonlinear systems.

The proposed fault diagnosis architecture consists of a fault detection estimator and a bank of isolation estimators, each corresponding to a

particular fault type. The design of the fault isolation decision scheme is based on the derivation of appropriate adaptive thresholds for each fault

isolation estimator. Fault isolability conditions characterizing the class of process faults and sensor faults that are isolable by the proposed scheme

are derived. A rigorous isolability analysis is presented via the use of the so-called fault mismatch functions, which are defined between pairs of

possible faults. A simulation example is used to illustrate the proposed fault isolation scheme.

# 2008 Elsevier Ltd. All rights reserved.

1. Introduction

A consequence of modern technological advances is the

creation of large-scale critical infrastructure systems, which

need to operate reliably at all times, despite the possible

occurrence of faulty behavior in some subsystems or

components. Examples of such large-scale infrastructure

systems include power generation and distribution systems,

telecommunication networks, water distribution networks, etc.

The design of fault diagnosis and accommodation schemes is a

crucial step in achieving reliable and safe operation of such

large-scale systems.

In recent years, there has been a lot of research activity in the

design and analysis of fault diagnosis and accommodation

schemes for different classes of dynamic systems (see, for

example, Basseville & Nikiforov, 1993; Blanke, Kinnaert,

Lunze, Staroswiecki, & Schrder, 2006; Chen & Patton, 1999;

Frank, 1990; Gertler, 1998; Patton, 1997; Patton, Frank, &

Clark, 1989). Considerable effort has been devoted to the

development of fault diagnosis schemes for nonlinear systems

in the framework of various kinds of assumptions and fault

scenarios (see, for instance, De Persis & Isidori, 2001; Floquet,

* Corresponding author.

E-mail address: [email protected] (M.M. Polycarpou).

1367-5788/$ – see front matter # 2008 Elsevier Ltd. All rights reserved.

doi:10.1016/j.arcontrol.2008.03.007

Barbot, Perruquetti, & Djemai, 2004; Garcia & Frank, 1997;

Hammouri, Kinnaert, & El Yaagoubi, 1999; Krishnaswami &

Rizzoni, 1997; Seliger & Frank, 1991; Wang, Huang, & Daley,

1997, and the references cited therein).

The overall fault diagnosis procedure can be investigated in

three steps: (i) fault detection is the process of determining

whether a fault has occurred or not; (ii) fault isolation deals with

the issue of determining the location/type of fault; and (iii) fault

identification provides an estimate of the magnitude or severity

of the fault. In some cases, the issues of fault isolation and fault

identification are interwoven, since they both may deal with

determining the type of fault that has occurred. Beyond fault

diagnosis, there is the problem of fault accommodation, which

deals with the design and analysis of control reconfiguration

schemes for handling the presence of faults.

In this paper, we focus on the fault isolation problem,

which is a crucial step in the design of intelligent control

and health management systems, especially for large-scale

systems. Typically, fault isolation goes into effect after a

fault is detected with the objective of determining the

location/type of the fault. The fault isolation problem has

been studied in the context of several different formulations

including: (a) determining the particular type of the fault

among a set of known (or partially known) possible fault

types (for example, a bearing may exhibit abnormal behavior

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http://dx.doi.org/10.1016/j.arcontrol.2008.03.007

X. Zhang et al. / Annual Reviews in Control 32 (2008) 107–121108

as a result of spalling, pitting, or over-rolling of debris); (b)

determining the particular faulty components among the set

of all components under consideration (for example, sensor

validation for jet engines; Yan & Goebel, 2003); (c) for

spatially distributed systems (Ferrari, Parisini, & Polycarpou,

2007), determining the physical location of the faulty

subsystem (for example, locating faulty sensors in a distri-

buted wireless sensor network monitoring a large physical

region of interest).

In previous papers (Zhang, Parisini, & Polycarpou, 2005;

Zhang, Polycarpou, & Parisini, 2001), the authors investi-

gated the nonlinear fault isolation problem in the context of

type (a) and (b), respectively. Specifically, in Zhang et al.

(2001), a fault isolation method was developed to determine

which particular process fault, among a set of possible

partially known process fault types, has occurred (in the

context of type (a) above). In Zhang et al. (2005), a sensor

fault isolation algorithm was developed with the objective to

determine the particular faulty sensor among a set of sensor

components under consideration. However, in Zhang et al.

(2005, 2001) process faults and sensor faults were considered

separately. In other words, for the process fault isolation

problem (Zhang et al., 2001), we assumed the sensors are

healthy, and for the sensor fault isolation problem (Zhang

et al., 2005), we assumed there are no process faults. In real-

world applications, both the process (including plant and

actuators) and the sensors are prone to faults. Fault isolation

methods that only consider process faults may provide an

incorrect isolation decision in the presence of sensor faults,

and vice versa. The objective of this paper is to develop a

fault isolation methodology for a class of nonlinear systems

that deals with both process faults and sensor faults in a

unified framework.

An architecture based on adaptive and learning techniques

has been presented with the aim of detecting and isolating

process faults or sensor faults (Demetriou, 1998; Farrell,

Berger, & Appleby, 1993; Polycarpou & Helmicki, 1995;

Vemuri, 2001; Wang et al., 1997; Zhang et al., 2005, 2001).

In this paper, a design methodology for fault isolation of

the considered class of process faults and sensor faults is

presented, as well as a rigorous analytical framework aimed

at characterizing the behaviors of the proposed scheme. The

analysis of the fault isolation scheme focuses on: (i)

determining adaptive thresholds for each fault isolation

estimator; and (ii) deriving isolability conditions of the

process faults and sensor faults under consideration.

The adaptive decision thresholds are derived under a worst

case scenario, such that, if a particular fault occurs, the

output estimation error of the corresponding fault isolation

estimator always remains below its threshold, therefore

avoiding the presence of false alarms. The fault isolability

condition characterizes the class of process faults and sensor

faults which are isolable by the proposed detection and

isolation scheme. This condition is investigated on the

basis of the so-called fault mismatch function, which

provides a suitable measure of the mutual ‘‘difference’’

between faults.

The paper is organized as follows. Section 2 defines the

classes of nonlinear systems and faults to be investigated. In

Section 3, the design of the proposed fault detection and

isolation (FDI) scheme is described. In Section 4 the design of

adaptive thresholds is addressed, while in Section 5 the fault

isolability analysis is carried out. In Section 6 a simulation

example is presented and Section 7 contains some concluding

remarks.

2. Problem formulation

Consider a class of nonlinear multi-input-multi-output

(MIMO) dynamic systems described by

x ¼ Axþ gðy; uÞ þ hðx; u; tÞ þ bxðt � TxÞfðy; uÞy ¼ Cxþ dðx; u; tÞ þ byðt � TyÞFuðtÞ (1)

where x2Rn is the system state vector, u2Rm is the input

vector, y2Rl is the output vector, g : Rl �Rm 7!R

n,

h : Rn �Rm �R

þ 7!Rn, f : Rl �R

m 7!Rn, and d :

Rn �R

m �Rþ 7!R

l are smooth vector fields, and ðA;CÞ is

an observable pair. The state equations

xN ¼ AxN þ gðyN; uÞyN ¼ CxN

represents the known nominal system dynamics, while the

healthy system is described by

xH ¼ AxH þ gðyH; uÞ þ hðxH; u; tÞyH ¼ CxH þ dðxH; u; tÞ:

The difference between the nominal model and the actual

(healthy) system is due to the vector fields h and d, which

represent the modeling uncertainties in the state equation and

output equation, respectively. The changes in the system

dynamics as a result of a process fault are characterized by the

term bxðt � TxÞfðy; uÞ in (1). Specifically, bxðt � TxÞ denotes

the time profile of a process fault which occurs at some

unknown time Tx, and fðy; uÞ represents the nonlinear fault

function. The changes in the system dynamics as a result of a

sensor fault are characterized by byðt � TyÞFuðtÞ in (1).

Specifically, the vector FuðtÞ represents a time-varying bias due

to a sensor fault, and the function byðt � TyÞ characterizes the

time profile of the fault, where Ty is the unknown fault

occurrence time.

In this paper, we only consider the case of abrupt (sudden)

faults (for some results on incipient faults, see Demetriou and

Polycarpou, 1998; Zhang, Polycarpou & Parisini, 2002);

therefore, bxð�Þ and byð�Þ take the form of a step function bð�Þgiven by

bðt � T0Þ ¼0; if t< T0

1; if t� T0

�

where T0 ¼ Tx for process faults, and T0 ¼ Ty for sensor faults.

Moreover, the analysis is based on the assumption that only a

single fault occurs, which is either a process fault or a sensor

fault.

X. Zhang et al. / Annual Reviews i

The class of sensor faults under consideration is

represented by FuðtÞ, where F 2Rl is the fault distribution

vector, and uðtÞ is the magnitude of the time-varying

sensor bias. Because of the single fault assumption, the

sensor fault distribution vector F has only one non-zero

entry, which represents the corresponding corrupted output

measurement. Depending on the location of the fault, the

distribution vector F belongs to a class of l possible vectors

F1;F2; . . . ;Fl, where, for any j ¼ 1; . . . ; l, only the jth

component of vector F j is different from zero. Accordingly,

the scalar u jðtÞ 2R is the magnitude of the time-varying bias

in the jth sensor.

The process fault function f under consideration is modeled

as a nonlinear function of measurable quantities y and u. It is

assumed that there are N types of possible process faults in the

fault class; specifically, fðy; uÞ belongs to a finite set of

functions given by

FP¼4ff1ðy; uÞ; . . . ;fNðy; uÞg: (2)

Each fault function f p; p ¼ 1; . . . ;N, is described by

f pðy; uÞ¼4½ðu p1 Þ

>g p

1 ðy; uÞ; . . . ; ðu pn Þ

>g pn ðy; uÞ�

>(3)

where upi ; i ¼ 1; . . . ; n, is an unknown parameter vector

assumed to belong to a known compact and convex set Q pi

(i.e., upi 2Q

pi �R

ypi ) and g p

i : Rl �R

m 7!Ry

pi is a known

smooth vector field. As discussed in Zhang et al. (2001,

2002), the process fault model described by (2) and (3) char-

acterizes a general class of nonlinear faults where the vector

field g pi represents the functional structure of the pth fault

affecting the ith state equation, while the unknown parameter

vector upi characterizes the ‘‘magnitude’’ of the fault. The

dimension y pi of each parameter vector u p

i is determined both

by the type of fault and by the specific state equation con-

sidered.

The main objective of this paper is to develop a robust fault

isolation scheme for process faults and sensor faults in

nonlinear dynamic systems modeled by (1). It is worth noting

that in addition to nonlinear systems in the form of (1), the

presented algorithm can also be applied to more general

nonlinear systems which are transformable to (1) using a local

diffeomorphism (Isidori, 1995; Marino & Tomei, 1995; Vemuri

& Polycarpou, 1997).

Throughout the paper, the following assumptions are made:

Assumption 1. The modeling uncertainties, represented by h

and d in (1), are unstructured and unknown nonlinear func-

tions of x, u, and t, but bounded by given known functionals,

i.e., 8 ðx; y; uÞ 2X � Y � U and 8 t� 0;

jhðx; u; tÞj � hðy; u; tÞ; jdðx; u; tÞj � dðy; u; tÞ; (4)

where the bounding functions hðy; u; tÞ and dðy; u; tÞ are

known and uniformly bounded in Y � U �Rþ, X �R

n is

some compact domain of interest, and U �Rm and Y �R

l

are the compact sets of admissible inputs and outputs,

respectively.

Assumption 2. The system state vector x belongs to a possibly

unknown compact set X �Rn before and after the occurrence

of a fault, that is, xðtÞ 2X , for all t� 0.

Assumption 3. The rates of change of the process fault para-

meter vector u pðtÞð p ¼ 1; . . . ;NÞ, and the sensor bias

u jðtÞ ð j ¼ 1; . . . ; lÞ, are uniformly bounded, respectively, i.e.,

for process faults, ju pðtÞj � a p, for all t� 0, where

n Control 32 (2008) 107–121 109

u p ¼ ½ðu p1 Þ

>; . . . ; ðu p

n Þ>�

>;

and a p is a known positive constant;

f
or sensor bias, ju jðtÞj � d for all t� 0, where d is a known
positive constant.

Assumption 1 characterizes the class of modeling uncer-

tainties under consideration. The bounds on the unstructured

modeling uncertainties are needed in order to be able to

distinguish between the effects of faults and modeling

errors (Emami-Naeini, Akhter, & Rock, 1988; Zhang et al.,

2002).

Assumption 2 requires the boundedness of the state

variables before and after the occurrence of a fault. Hence,

it is assumed that the feedback control system is capable of

retaining the boundedness of the state variables even in the

presence of a fault. This is a technical assumption required for

well posedness since the fault isolation design that we consider

does not influence the closed-loop dynamics and stability. It is

important to note that the proposed fault detection and

isolation design does not depend on the structure of the

controller.

Finally, in Assumption 3 known bounds on the rates of

change of u pðtÞ and u jðtÞ are assumed. In practice, the rate

bounds a p and d can be set by exploiting some a priori

knowledge on the fault developing dynamics. In the case of a

constant fault size or bias, we simply set a p ¼ 0 or d ¼ 0.

Remark 1. It is worth noting that the above formulation

considers both process faults and sensor faults under one

unified framework. The unknown process fault magnitude is

represented by u pðtÞ, for p ¼ 1; . . . ;N, and the unknown sensor

bias magnitude is represented by u jðtÞ, for j ¼ 1; . . . ; l, respec-

tively.

3. Fault detection and isolation architecture

As shown in Fig. 1, the fault detection and isolation

architecture is based on a bank of N þ lþ 1 nonlinear adaptive

estimators, where N is the number of different nonlinear

process faults in the fault class FP, and l is the number of

sensors or output variables. One of the nonlinear adaptive

estimators is the fault detection estimator (FDE) used for

detecting the occurrence of any faults, while the remaining

N þ l nonlinear adaptive estimators are fault isolation

estimators (FIEs), which are activated for the purpose of fault

isolation only after a fault is detected.

Fig. 1. Architecture of the fault detection and isolation scheme.


3.1. Fault detection scheme

Based on the system model given by (1), the following FDE

is chosen:

˙x0 ¼ Ax0 þ Lðy� y0Þ þ gðy; uÞ; x0ð0Þ ¼ 0

y0 ¼ Cx0

where x0 and y0 denote the estimated state and output vectors,

respectively, and L2Rn�l is a design gain matrix. Moreover, let

e0x¼4

x� x0 denote the state estimation error. Then, for

t<min ðTx; TyÞ, we have

e0xðtÞ ¼ A0e

0xðtÞ � Ldðx; u; tÞ þ hðx; u; tÞ; (5)

where the gain L is chosen such that the matrix A0¼4ðA� LCÞ is

Hurwitz. Each component e0y j¼4y j � y0

j ; j ¼ 1; . . . ; l, of the

output estimation error is given by

e0y jðtÞ ¼ C je

0xðtÞ þ d jðx; u; tÞ; (6)

where C j is the jth row vector of matrix C, and d j is the jth

component of the measurement uncertainty d. From (5) and (6),

we have

je0y jðtÞj �

Z t

0

k j e�l jðt�tÞjhðx; u; tÞ � Ldðx; u; tÞj dt

þ jd jðxðtÞ; uðtÞ; tÞj þ k jx e�l j t (7)

where k j and l j are positive constants chosen such that

jC j eA0tj � k j e�l jt (since A0 is Hurwitz, constants k j and

l j satisfying the above inequality always exist; Ioannou &

Sun, 1995), and x is a (possibly conservative) bound for jxj,such that jxj � x, 8 x2X (by Assumption 2). It is worth

noting that, since the effect of this bound decreases expo-

nentially, the use of such a conservative bound will not

weaken significantly the performance of the fault detection

scheme. By using the bounding functions (4), from (7) we

obtain

je0y jðtÞj �

Z t

0

k j e�l jðt�tÞ½hðy; u; tÞ þ kLk � dðy; u; tÞ� dt

þ d jðyðtÞ; uðtÞ; tÞ þ k jx e�l jt: (8)

According to (8), a fault is detected when at least one

component of the modulus of the output estimation error

e0y jðtÞ exceeds its corresponding threshold e0

y jðtÞ, which is

defined as

e0y jðtÞ¼4

Z t

0

k j e�l jðt�tÞ½hðy; u; tÞ þ jLj � dðy; u; tÞ� dt

þ d jðyðtÞ; uðtÞ; tÞ þ k jx e�l jt: (9)

More precisely, the fault detection time Td is defined as the

first time instant such that je0y jðtÞj> e0

y jðtÞ, for some t� 0

and some j2f1; . . . ; lg, that is, Td¼4

inf [ lj¼1ft� 0 :

je0y jðtÞj> e0

y jðtÞg. It is worth noting that the adaptive thresholds

e0y jðtÞ given by (9) can be easily implemented using linear

filtering techniques (Zhang et al., 2002).

3.2. Fault isolation estimators and decision scheme

Now, assume that a fault is detected at some time Td;

accordingly, at t ¼ Td the fault isolation estimators are

activated. Each FIE corresponds to one potential fault type.

Specifically, among the N þ l FIEs employed in the fault

isolation scheme, N FIEs are designed based on the functional

structure of the process faults defined in (2) and (3), and the

remaining l FIEs are designed based on the functional structure

of the potential sensor faults. The following N FIEs correspond

X. Zhang et al. / Annual Reviews in Control 32 (2008) 107–121 111

to process faults: for p ¼ 1; . . . ;N,

˙xp ¼ Ax p þ gðy; uÞ þ Lðy� y pÞ þV p ˙u

pþ f

pðy; u; u pÞ; x pðTdÞ ¼ 0

Vp ¼ A0V

p þ Z pðy; uÞ; V pðTdÞ ¼ 0

fp ¼ ½ðu p

1 Þ>

g p1 ðy; uÞ; . . . ; ðu p

n Þ>

g pn ðy; uÞ�

>

y p ¼ Cx p;

(10)

where up

i 2Ry

pi , for i ¼ 1; . . . ; n, is the estimate of the fault

parameter vector in the ith state equation of the pth isolation

estimator. It is noted that, according to (3), the fault

approximation model fp

is linear in the adjustable weights

up. Consequently, the gradient matrix Z p¼4@f

pðy; u; u pÞ=@u p ¼diag½ðg p

1 Þ>; . . . ; ðg p

n Þ>� does not depend on u

p.

The adaptation in the isolation estimators arises due to the

unknown parameter vector u p¼4½ðu p1 Þ

>; . . . ; ðu p

n Þ>�

>. The

adaptive law for adjusting each up

is derived using the

Lyapunov synthesis approach (see for example Ioannou & Sun,

1995), with the projection operator restricting up

to the

corresponding known set Q p (in order to guarantee stability of

the learning algorithm in the presence of modeling uncertainty

Vemuri & Polycarpou, 1997). Specifically, the learning

algorithm is chosen as follows

˙up¼ PQ pfGV p>C>e p

y g; (11)

where e py ðtÞ¼

4yðtÞ � y pðtÞ denotes the output estimation error of

the pth estimator, and G > 0 is a symmetric, positive-definite

learning rate matrix.

Analogously, the following l FIEs correspond to sensor

faults: for q ¼ N þ 1; . . . ;N þ l,

˙xq ¼ Axq þ gðy; uÞ þ Lðy� yqÞ þVq ˙u

q; xqðTdÞ ¼ 0;

Vq ¼ A0V

q � LFq; VqðTdÞ ¼ 0;

yq ¼ Cxq þ Fquq;

˙uq¼ PQqfgqðCVq þ FqÞ>eq

yg;

(12)

where eqyðtÞ¼

4yqðtÞ � yqðtÞ denotes the output estimation error,

again the projection operator P restricts the parameter estima-

tion uq

to a predefined compact and convex region Qq�R

(Vemuri & Polycarpou, 1997), and gq 2R is the learning rate.

Remark 2. The parameter estimates up

and uq

also provide

useful information for fault isolation. However, it is important

to stress that it cannot be guaranteed that, for the actual fault,

the parameter estimates up

and uq

will converge to the true

values, unless we assume persistency of excitation (Farrell &

Polycarpou, 2006; Ioannou & Sun, 1995), a condition which, in

general, is too restrictive (in this paper, we do not assume

persistency of excitation.)

The stability and learning capability of the FIEs described by

(10) and (12) have been rigorously investigated in Zhang et al.

(2005, 2001). The analytical results guarantee the boundedness

of the variables in the bank of FIEs. Moreover, it has been

shown that the ability of the isolation estimators to learn the

fault function is limited by the modeling uncertainties h and d,

the fault function approximation error, and the rate of change of

the time-varying fault parameter vector.

Now let us consider the pth process fault, where

p ¼ 1; . . . ;N, and the qth sensor fault, where

q ¼ N þ 1; . . . ;N þ l, in a unified framework. Then, we have

N þ l faults in the augmented fault class. More specifically, for

s ¼ 1; . . . ;N þ l, fault s is a process fault, if 1 � s � N, and

fault s is a sensor fault, if N þ 1 � s � N þ l.The fault isolation decision scheme is based on the

following intuitive principle: for s ¼ 1; . . . ;N þ l, if fault s

occurs at time T0 and is detected at time Td, then a set of

adaptive threshold functions fmsjðtÞ; j ¼ 1; . . . ; lg can be

designed for the sth isolation estimator, such that the jth

component of its output estimation error satisfies

jesy jðtÞj � ms

jðtÞ, for all t> Td. Consequently, for each

s ¼ 1; . . . ;N, such a set of adaptive thresholds fmsjðtÞ; j ¼

1; . . . ; lg can be associated with the output estimation of the sth

isolation estimator. In the fault isolation procedure, if for a

particular isolation estimator s, there exists some

j2f1; . . . ; lg, such that the jth component of its output

estimation error satisfies jesy jðtÞj>ms

jðtÞ for some finite time

t> Td, then the possibility of the occurrence of fault s can be

excluded. Based on this intuitive idea, the following fault

isolation decision scheme is devised:

Fault Isolation Decision Scheme: If , for each

r2f1; . . . ;N þ lgnfsg, there exist some finite time tr > Td

and some j2f1; . . . ; lg, such that jery jðtrÞj>mr

jðtrÞ, then the

occurrence of fault s is concluded.

Remark 3. Compared with other adaptive multiple model

based fault diagnosis schemes (see, for example, Boskovic

& Mehra, 1999; Korbicz, Koscielny, Kowalczuk, & Cholewa,

2008; Menke & Maybeck, 1995; Witczak, 2007), the FDI

scheme presented in this paper considers a class of nonlinear

systems in the presence of unstructured modeling uncertainty.

The robustness and fault sensitivity are enhanced by appro-

priately designed adaptive thresholds. Moreover, within the

fault isolation framework, in fault diagnosis literature one can

find several types of observer schemes, including the dedicated

observer scheme (DOS) (Clark, 1978) and the generalized

observer scheme (GOS) (Frank, 1990; Patton et al., 1989).

As can be seen from the fault isolation decision scheme

described above, our method falls within the GOS architectural

framework.

In the next section, we will derive the threshold msðtÞassociated with each isolation estimator.


4. Adaptive thresholds for fault isolation

The threshold functions msjðtÞ clearly play a significant

role in the proposed fault isolation scheme. The following

lemma provides a bounding function for the output

estimation of the sth isolation estimator in the case that

fault s occurs.

Lemma 1. Suppose that fault s, occurring at time t ¼ T0,

is detected at time t ¼ Td, where s ¼ 1; . . . ;N þ l. Then,

for all t� Td , the jth component of the output estimation

error of the sth isolation estimator satisfies the following

inequality:

jesy jðtÞj � k j

Z t

Td

e�l jðt�tÞ½hðyðtÞ; uðtÞ; tÞ þ rskVsk

þ kLkdðyðtÞ; uðtÞ; tÞ� dt þ d jðy; u; tÞ

þ j�sðtÞjjusðtÞj þ k jx e�l jðt�TdÞ; (13)

where usðtÞ¼4 u

sðtÞ � usðtÞ is the parameter estimation error and

�s¼4 C jVs; if 1 � s � N

C jVs þ Fs

j; if N < s � N þ l

�(14)

and

rs¼4 as; if 1 � s � Nd; if N < s � N þ l

:

�(15)

Proof. Denote the state estimation error of the sth isolation

estimator by esxðtÞ¼

4xðtÞ � xsðtÞ, for s ¼ 1; . . . ;N þ l. The proof

consists of two parts.

Part I: In the presence of a process fault p, p ¼ 1; . . . ;N, (or

equivalently, fault s with 1 � s � N), by using (1), the system

dynamics for t> Tx is given by

x ¼ Axþ gðy; uÞ þ hðx; u; tÞ þ f pðy; uÞy ¼ Cxþ dðx; u; tÞ (16)

Using (16) and (10), after some simple algebraic manipula-

tion, we obtain

e px ðtÞ ¼ A0e

px ðtÞ þ hðx; u; tÞ � Ldðx; u; ;tÞ � Z pu

p �V p ˙up:

By using Z p ¼ Vp � A0V

p, we have

e px ðtÞ ¼ A0e

px ðtÞ þ hðx; u; tÞ � Ldðx; u; ;tÞ �V p ˙u

p

� ðV p � A0VpÞu p

¼ A0ðe px ðtÞ þV pu

pÞ þ hðx; u; tÞ � Ldðx; u; ;tÞ

� d

dtðV pu

pÞ �V pup

By letting e px ðtÞ¼

4e p

x ðtÞ þV pup, the above equation can be

rewritten as

˙epx ðtÞ ¼ A0e

px ðtÞ þ hðx; u; tÞ � Ldðx; u; tÞ �V pu

p: (17)

By defining e py jðtÞ¼4y jðtÞ � y p

j ðtÞ and using (16) and (10), we

have:

e py jðtÞ ¼ C je

px ðtÞ þ d jðx; u; tÞ

¼ C jðe px ðtÞ �V pu

pÞ þ d jðx; u; tÞ (18)

Now based on (17), (18), (14), and (15), as well as

Assumptions 1 and 3, it can be easily shown that

je py jðtÞj � k j

Z t

Td

e�l jðt�tÞ½hðyðtÞ; uðtÞ; tÞ þ a pkV pk


þ jC jVpjju pðtÞj þ k jx e�l jðt�TdÞ: (19)

Part II: In the presence of a sensor fault q, q ¼ 1; . . . ; l, (or

equivalently, fault s with N < s � N þ l), by using (1), the

system dynamics for t> Ty are given by

x ¼ Axþ gðy; uÞ þ hðx; u; tÞy ¼ Cxþ dðx; u; tÞ þ FquqðtÞ (20)

The dynamics of the output estimation error of the qth FIE

described by (12) has been investigated in Zhang et al. (2005):

jeqy jðtÞj � jC jV

q þ Fqj jju

qðtÞj þ k jx e�l jðt�TdÞ

þ k j

Z t

Td

e�l jðt�tÞ½hðyðtÞ; uðtÞ; tÞ þ djVqj

þ kLkdðyðtÞ; uðtÞ; tÞ� dt þ d jðy; u; tÞ: (21)

Now the proof of (13) easily follows from (14), (15), (19), and

(21). &

Although Lemma 21 provides an upper bound on the output

estimation error of the sth estimator, the right-hand side of (13)

cannot be directly used as a threshold function for fault isolation

because usðtÞ is not available. However, as the estimate u

s

belongs to the known compact set Qs, we have jus � usðtÞj �

ksðtÞ for a suitable ksðtÞ depending on the geometric properties of

set Qs (see Zhang et al., 2001, 2002). Hence, based on the above

discussions, the following threshold function is chosen:

jmsjðtÞj � k j

Z t

Td

e�l jðt�tÞ½hðyðtÞ; uðtÞ; tÞ þ rskVsk


þ j�sðtÞjjksðtÞj þ k jx e�l jðt�TdÞ: (22)

Remark 4. The threshold described by (22) represents an

adaptive threshold, which has obvious advantages over a fixed

threshold in terms of fault sensitivity and robustness (Chen and

Patton, 1999). Note that this adaptive threshold can be easily

implemented on-line using linear filtering techniques.

Remark 5. The adaptive threshold function described by (22)

is influenced by several sources of uncertainty entering the

fault isolability problem, such as modeling uncertainty h,

measurement errors d and parametric uncertainty ks. Intuitively,


the smaller the uncertainty (resulting in a smaller threshold

msjðtÞ, the easier the task of isolating the faults. On the other

hand, as clarified in the next section, the capability to isolate a

fault depends not only on msjðtÞ, but also on the degree that the

faults are ‘‘different’’ from each other.

5. Fault isolability analysis

For our purpose, a fault is said to be isolable if the fault

isolation scheme is able to reach a correct decision in finite

time. Intuitively, faults are isolable if they are mutually different

according to a certain measure quantifying the difference in the

effects that different faults have on measurable outputs and on

the estimated quantities in the isolation scheme. In this respect,

we introduce the fault mismatch function between the sth fault

and the rth fault:

hsrj ðtÞ¼

4�sus ��r u

r; r; s ¼ 1; . . . ;N þ l; r 6¼ s (23)

where �s and �r, defined in (14), represent respectively the

functional structure of fault s and fault r related to the jth output

variable, y j.

Remark 6. The fault mismatch function hsrj ðtÞ is related to

both the structural difference between the faults (i.e., �s and

�r) and the properties of the isolation scheme (i.e., the

estimates ur). However, as described in Section 3.2, the fault

isolation estimators are designed based on the structure of the

faults (i.e., Z p and Fq). Moreover, the adaptive thresholds are

designed in such a way that faults can not be isolated unless

their structures are sufficiently different (see Zhang et al.,

2005, 2001, 2002). Therefore, the structural difference

between the faults has a predominant effect on the isolability

properties than the actual behavior of the estimates ur

pro-

vided by the FIEs.

The following theorem characterizes (in a non-closed form)

the class of isolable faults.

Theorem 1. Consider the fault isolation scheme described by

(10)–(12) and (22). Suppose that Assumptions 1–3 hold and

x1

x2

x3

x4

2664

3775 ¼

0 1 0 0�k

Jl

�Fl

Jl

k

Jl0

0 0 0 1k

Jm0

�k

Jm

�Fm

Jm

266664

377775

x1

x2

x3

x4

2664

3775þ

0�mgl

Jlsin x1

0u

Jm

266664

377775þ

0

h

0

0

26643775þ bxðt � TxÞfxðy; uÞ

y ¼1 0 0 0

0 0 1 0

0 0 0 1

24

35

x1

x2

x3

x4

2664

3775þ

0

0

d3

24

35þ byðt � TyÞFu

that a fault s, s ¼ 1; . . . ;N þ l, occurring at time t ¼ T0 is

detected at time t ¼ Td. Then fault s is isolable if , for each

r2f1; . . . ;N þ lgnfsg, there exist some time tr > Td and some

j2f1; . . . ; lg, such that the fault mismatch function hsrj ðtrÞ

satisfies the following inequality:

jhsrj ðtrÞj> j�rjkrðtrÞ þ 2d jðyðtrÞ; uðtrÞ; trÞ

þ jZ tr

Td

C j eA0ðtr�tÞðhðx; u; tÞ � Ldðx; u; tÞ �VsusÞ dtj

þ k j

Z tr

Td

e�l jðtr�tÞ½hðy; u; tÞ þ rrkVrk þ kLkdðy; u; tÞ� dt

þ 2k jx e�l jðtr�TdÞ:

(24)

Proof. See Appendix A. &

Remark 7. It is worth noting that, by replacing the

unknown quantities hðxðtÞ; uðtÞ; tÞ and dðxðtÞ; uðtÞ; tÞ in

the right-hand side of inequality (24) with their bounds

hðyðtÞ; uðtÞ; tÞ and dðyðtÞ; uðtÞ; tÞ, respectively, a more

practical version of condition (24) can be obtained. Moreover,

such a condition can be checked by suitable numerical tech-

niques.

6. Simulation results

Consider a single-link robotic arm with a revolute elastic

joint rotating in a vertical plane whose motion equations are

Jlq1 þ Flq1 þ kðq1 � q2Þ þ mgl sin q1 ¼ 0

Jmq2 þ Fmq2 � kðq1 � q2Þ ¼ u

where q1 and q2 are the link displacement and the rotor

displacement, respectively. The link inertia Jl, motor rotor

inertia Jm, elastic constant k, link mass m, gravity constant

g, center of mass l, and viscous friction coefficients Fl and Fm

are positive constant parameters. The control u is the torque

delivered by the motor.

By choosing x1 ¼ q1, x2 ¼ q1, x3 ¼ q2, x4 ¼ q2, and

assuming that x1, x3, and x4 are available for measurement,

the above model can be rewritten in state space form as

It is worth noting that the effects of modeling uncertainty,

process faults, and sensor faults have been included in the

above model. More specifically, the modeling uncertainty h in

Fig. 3. The case of an actuator fault (i.e., process fault #1): the three residual components (solid line) and their corresponding thresholds associated with the FIE for

process fault #1.

Fig. 2. The case of an actuator fault (i.e., process fault #1): selected residual (solid line) and its threshold associated with the FDE, FIE for sensor fault #1, FIE for

sensor fault #2, and FIE for process fault #2.


Fig. 5. The case of a process fault resulting in a reduction of link mass (i.e., process fault #2): the three residual components (solid line) and their corresponding

thresholds associated with the FIE for process fault #2.

Fig. 4. The case of a process fault resulting in a reduction of link mass (i.e., process fault #2): selected residual (solid line) and its threshold associated with the FDE,

FIE for sensor fault #1, FIE for sensor fault #2, and FIE for process fault #1.



the state equation is assumed to be to up to 5% error in the mass

of the link. In other words, h ¼ 0:05ðmgl=JlÞsin y1. The

unknown modeling uncertainty in the output equation is

assumed to be d3 ¼ 0:01sin ð10tÞ, which leads to d3 ¼ 0:01.

In this example, we consider the following four types of

faults, including two process faults and two sensor faults:

Actuator fault. We consider a simple multiplicative actuator

Fi

pr

fault by letting u ¼ uþ u1u, where u is the nominal control

input in the non-fault case and u1 2 ½�1 0� is the parameter

characterizing the magnitude of the fault. Note that the case

u1 ¼ 0 represents the normal operation condition (no fault),

while u1 ¼ �1 corresponds to the complete failure of the

actuator. Therefore, the actuator fault can be described by

f ¼ f1¼4½0 0 0 u1g1ðuÞ�>, where g1ðuÞ ¼ ð1=JmÞu and

u1 2 ½�1; 0�. It is worth noting that in this paper the process

faults under consideration include faults in both the plant and

the actuators.

A
process fault which results in a reduction in the mass of link.
Then the fault function is in the form of f ¼ f2¼4½0 u2g2ðyÞ 0 0�>, where g2ðyÞ ¼ �ð1=JlÞmgl sin ðyÞand u2 2 ½�1; 0� represents the percentage of change in the

mass.

A
bias in the sensor measuring y2 represented by F ¼ F2 ¼½0 1 0�> and u2 ½0; 0:2�.
g. 6. The case of a sensor fault in y2 (i.e., sensor fault #1): selected residual (solid

ocess fault #1, and FIE for process fault #2.

A
bias in the sensor measuring y3 represented by F ¼ F3 ¼½0 0 1�> and u2 ½0; 0:2�.
Based on the fault diagnosis scheme presented in Sections

3 and 4, a fault detection estimator and four fault isolation

estimators are constructed. The simulations are performed

with the following robot parameters (in SI units): k ¼ 2,

Fm ¼ 1, Fl ¼ 0:5, Jm ¼ 1, Jl ¼ 2, m ¼ 4, g ¼ 9:8, and

l ¼ 0:5. The initial conditions of the plant are chosen to

be xð0Þ ¼ 0 and the input to the system is given by

u ¼ 2 sin ð2tÞ. The modeling uncertainty on the state equation

is h ¼ ð�0:04=JlÞmglsin x1, and the modeling uncertainty d3

in the output equation is defined above. Moreover, we set the

observer gain matrix L ¼ ½�3:35 0 0; �1:3925 � 1

0; 0 � 1:5 � 1; �2 2 � 1:1�, so that the poles

of the matrix A0 are located at �2:1, �1:5, �1:7, and �1:9,

respectively. Consequently, the constants k1 ¼ 1, l1 ¼ 1:2,

k2 ¼ 1, l2 ¼ 1:4, k3 ¼ 1, l3 ¼ 1:9. The learning rate of the

adaptive algorithm is set to 5.

Figs. 2 and 3 show the simulation results when an actuator

fault, with u1 ¼ �0:6, occurs at Tx ¼ 5 s. Specifically, selected

residuals (solid line) generated by the FDE, the FIE for sensor

fault #1, the FIE for sensor fault #2, and the FIE for process

fault #2, are shown in Fig. 2. As can be seen, the fault is

line) and its threshold associated with the FDE, FIE for sensor fault #2, FIE for

Fig. 8. The case of a sensor fault in y3 (i.e., sensor fault #2): selected residual (solid line) and its threshold associated with the FDE, FIE for sensor fault #1, FIE for

process fault #1, and FIE for process fault #2.

Fig. 7. The case of a sensor fault in y2 (i.e., sensor fault #1): the three residual components (solid line) and their corresponding thresholds associated with the FIE for

sensor fault #1.


Fig. 9. The case of a sensor fault in y3 (i.e., sensor fault #2): the three residual components (solid line) and their corresponding thresholds associated with the FIE for

sensor fault #2.


detected almost immediately at approximately Td ¼ 5:38 s. At

that time, the four isolation estimators are activated. It can be

seen that at least one of the residual components generated by

each unmatched FIE, including the FIES for sensor fault #1,

sensor fault #2, and process fault #2, exceeds its threshold

(shown in the top right figure and the two figures at the bottom

in Fig. 2, respectively), while all three residual components

generated by the FIE for the actuator fault always remain below

their thresholds (shown in Fig. 3), thus indicating the presence

of an actuator fault (or process fault 1 as defined).

Analogously, Figs. 4 and 5 show the simulation results when

a process fault resulting in a reduction of link mass, with

u2 ¼ �0:6, occurs at Tx ¼ 5 s. The case of a sensor fault in y2,

with u ¼ 0:15 and Ty ¼ 5 s is reported in Figs. 6 and 7. The

fourth case of a sensor fault in y3, with u ¼ 0:15 and Ty ¼ 5 s is

illustrated in Figs. 8 and 9. In each of these cases, the fault is

successfully detected and isolated.

7. Concluding remarks

In this paper, the design and analysis of a unified fault isolation

method for process faults and sensor faults for a class of nonlinear

uncertain systems has been presented. Analytical results regar-

ding adaptive thresholds for fault isolation and fault isolability

conditions are established. Future research work will involve the

consideration of a larger class of nonlinear systems. Another

direction of future research is to investigate the fault isolation

problem for distributed systems in the context of type (c).

Acknowledgments

This work was supported in part by the Research Challenge

Program of Wright State University, the Research Promotion

Foundation of Cyprus and the Italian Ministry for University

and Research.

Appendix A. Proof of Theorem 1

The state estimation error and output estimation error

associated with the rth fault isolation estimator is

erxðtÞ¼

4xðtÞ � xrðtÞ, and er

yðtÞ¼4

yðtÞ � yrðtÞ, respectively. Based

on the values of s and r, the proof consists of the following

four parts.

Part I: The isolability of a process fault s from another

process faults r, where 1 � s � N, and r 2f1; . . . ;Ngnfsg. In

this case, the dynamics of the system is given by (16), and the

dynamics of FIE r is described by (10). Therefore, the output

estimation error eryðtÞ is

eryðtÞ ¼ Cer

xðtÞ þ dðx; u; tÞ:

The dynamics of the state estimation error erxðtÞ is described

by

erxðtÞ ¼ Aer

xðtÞ � LeryðtÞ þ hðx; u; tÞ þ Zsus � Zr u

r �Vr ˙ur

¼ A0erxðtÞ � Ldðx; u; tÞ þ hðx; u; tÞ þ Zsus � Zr u

r �Vr ˙ur

(A.1)


Substituting Zs ¼ Vs � A0V

s and Zr ¼ Vr � A0V

r into

(A.1), we obtain:

erxðtÞ ¼ A0ðer

xðtÞ �Vsus þVr urÞ � Ldðx; u; tÞ þ hðx; u; tÞ

þ d

dtðVsus �Vr u

rÞ �Vsus

By letting erxðtÞ¼

4er

xðtÞ �Vsus þVr ur, we have:

˙erxðtÞ ¼ A0e

rxðtÞ þ hðxðtÞ; uðtÞ; tÞ � LdðxðtÞ; uðtÞ; tÞ �Vsu

s

(A.2)

By defining the jth component of the output estimation

error as

ery jðtÞ¼4y jðtÞ � yr

jðtÞ; (A.3)

and using (16) and (10), we have:

ery jðtÞ ¼ C je

rxðtÞ þ d jðx; u; tÞ ¼ C jðer

xðtÞ þVsus �Vr urÞ þ d j

(A.4)

By using (14) and (23), we can see that in this case

the fault mismatch function hsrj ðtÞ is given by hsr

j ðtÞ¼ C jðVsus �Vr u

rÞ:Therefore, (A.4) can be rewritten as

follows

ery jðtÞ ¼ C je

rxðtÞ þ hsr

j ðtÞ þ d jðx; u; tÞ: (A.5)

By applying the triangle inequality, we have

jery jðtÞj � jhsr

j ðtÞj � jC jerxðtÞj � jd jðx; u; tÞj: (A.6)

Using (A.2) and again the triangle inequality, we

obtain


j ðtÞj � k jx e�l jðt�TdÞ

��Z t

Td

C jeA0ðt�tÞð�Ldðx; u; tÞ �Vsu

s þ hðx; u; tÞÞ dt

�� jd jðx; u; tÞj

(A.7)

Now taking into account the corresponding adaptive

threshold mrjðtÞ given by (22), we can immediately conclude

that, if condition (24) is satisfied at tr, we obtain

jery jðtrÞj>mr

jðtrÞ, which implies that the possibility of the

occurrence of fault r can be excluded at time t ¼ tr. Note that

the special case of us ¼ 0 was considered in Zhang et al.

(2001).

Part II: The isolability of a process fault s from a

sensor fault r, where 1 � s � N, and r 2fN þ 1; . . . ;N þ lg.In this case, the dynamics of the system is given by

(16), and the dynamics of FIE r is described by (12).

Therefore, the output estimation error eryðtÞ is given

by

eryðtÞ ¼ Cer

xðtÞ þ dðx; u; tÞ � Fr ur:

The dynamics of the state estimation error erxðtÞ is described

by

erxðtÞ ¼ Aer

xðtÞ � LeryðtÞ þ hðx; u; tÞ þ Zsus �Vr ˙u

r

¼ A0erxðtÞ þ hðx; u; tÞ � Ldðx; u; tÞ þ LFr u

r þ Zsus

�Vr ˙ur

(A.8)

By substituting LFr ¼ �Vr þ A0V

r and Zs ¼ Vs � A0V

s

into (A.8), and by means of some simple algebra (along the

same reasoning reported in the proof of Part I), we have

˙erxðtÞ ¼ A0e

rxðtÞ þ hðxðtÞ; uðtÞ; tÞ �Vsu

s � LdðxðtÞ; uðtÞ; tÞ(A.9)

where erxðtÞ¼

4er

xðtÞ �Vsus þVr ur. By using (16) and (12), we

can see that the output estimation error ery jðtÞ, defined in (A.3),

is given by

ery jðtÞ ¼ C je

rxðtÞ þ d jðx; u; tÞ � Fr

j ur

¼ C jðerxðtÞ þVsus �Vr u

rÞ þ d jðx; u; tÞ � Frj u

r

¼ C jerxðtÞ þ ðC jV

sus � ðC jVr þ Fr

jÞurÞ þ d jðx; u; tÞ:

(A.10)

By using (14) and (23), we can see that in this case the fault

mismatch function hsrj ðtÞ is given by

hsrj ðtÞ ¼ C jV

sus � ðC jVr þ Fr

jÞur:

Therefore, (34) can be rewritten in the same form as (A.5),

where erxðtÞ is given by (A.9).

Now the proof of Theorem 1 for this case easily follows by

using the same reasoning method as reported in Part I of the

proof.

Part III: The isolability of a sensor fault s from a process

fault r, where N þ 1 � s � N þ l, and r2f1; . . . ;Ng. In this

case, the dynamics of the system is given by (20), and the

dynamics of FIE r is described by (10). Therefore, the output

estimation error eryðtÞ is given by

eryðtÞ ¼ Cer

xðtÞ þ dðx; u; tÞ þ Fsus:

Thedynamics of the state estimation errorerxðtÞ is described by

erxðtÞ ¼ Aer

xðtÞ � LeryðtÞ þ hðx; u; tÞ � Zr u

r �Vr ˙ur

¼ A0erxðtÞ þ hðx; u; tÞ � Ldðx; u; tÞ � LFsus � Zr u

r

�Vr ˙ur

(A.11)

By substituting LFs ¼ �Vs þ A0V

s and Zr ¼ Vr � A0V

r

into (35), and by means of some simple algebra (along the same

reasoning reported in the proof of Part 1), we have

˙erxðtÞ ¼ A0e

rxðtÞ þ hðxðtÞ; uðtÞ; tÞ �Vsu

s � LdðxðtÞ; uðtÞ; tÞ(A.12)


where erxðtÞ¼

4er

xðtÞ �Vsus þVr ur. By using (20) and (10), we

can see that the output estimation error ery jðtÞ, defined in (A.3),

is given by

ery jðtÞ ¼ C je

rxðtÞ þ d jðx; u; tÞ þ Fs

jus

¼ C jðerxðtÞ þVsus �Vr u

rÞ þ d jðx; u; tÞ þ Fsju

s

¼ C jerxðtÞ þ ððC jV

s þ FsjÞus � C jV

r urÞ þ d jðx; u; tÞ:

(A.13)

By using (14) and (23), we can see that in this case the fault

mismatch function hsrj ðtÞ is given by

hsrj ðtÞ ¼ ðC jV

s þ FsjÞus � C jV

r ur:

Therefore, (A.13) can be rewritten in the same form as (A.5),

where erxðtÞ is given by (A.12).

Now the proof of Theorem 1 for this case easily follows by

using the same reasoning method as reported in Part I of the

proof.

Part IV: The isolability of a sensor fault s from another

sensor fault r, where N þ 1 � s � N þ l and

r 2fN þ 1; . . . ;N þ lgnfsg. In this case, the dynamics of the

system is given by (20), and the dynamics of FIE r are described

by (12). Therefore, the output estimation error eryðtÞ is given by

eryðtÞ ¼ Cer

xðtÞ þ dðx; u; tÞ þ Fsus � Fr ur:

The dynamics of the output estimation error of this case have

been analyzed in Theorem 1 of (Zhang et al., 2005).

Specifically, the following result was proved:


j ðtÞj � d jðy; u; tÞ � jC j eA0ðt�TdÞjx

� jZ t

Td

C j eA0ðt�tÞðhðx; u; tÞ � Ldðx; u; tÞ �VsusÞ dtj:

where

hsrj ðtÞ ¼ ðC jV

s þ FsjÞus � ðC jV

r þ FrjÞu

r; (A.14)

Clearly, the fault mismatch function hsrj ðtÞ follows the defini-

tion in (23) and (14), and, again, the proof easily follows.

Based on the analysis of the above four cases, it can be

concluded that, if condition (24) is satisfied at tr, for each

r 2f1; . . . ;N þ lg=fsg, then fault s is isolable.

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Xiaodong Zhang received the B.S. degree from Huazhong University of

Science and Technology, Wuhan, China, the M.S. degree from Shanghai Jiao

Tong University, Shanghai, China, and the Ph.D. degree from University of

Cincinnati, Cincinnati, OH, USA, all in electrical engineering, in 1994, 1997

and 2002, respectively. From 2002 to 2005, he was a Sr. Research Engineer at

Intelligent Automation Inc., Rockville, MD, USA. In 2005, he joined General

Motors Research and Development Center, Warren, MI, USA, as a senior

researcher, and in 2007, he joined Wright State University, Dayton, OH, USA,

as an assistant professor. His research interests include intelligent control

systems, fault diagnosis and prognosis, fault-tolerant control, cooperative

and distributed control.

Marios M. Polycarpou received the B.A. degree in computer science and the

B.Sc. degree in electrical engineering, both from Rice University, Houston, TX,

USA in 1987, and the M.S. and Ph.D. degrees in electrical engineering from the

University of Southern California, Los Angeles, in 1989 and 1992, respectively.

In 1992, he joined the University of Cincinnati, Cincinnati, OH, where he

became a professor of electrical and computer engineering and computer

science. In 2001, he was the first faculty to join the newly established

Department of Electrical and Computer Engineering, University of Cyprus,

Nicosia, Cyprus, where he is currently professor and Director of the KIOS

Center for Intelligent Systems and Networks. His current research interests

include intelligent systems and control, adaptive and cooperative control

systems, computational intelligence, fault diagnosis, and distributed agents.

He is the author or co-author of more than 175 articles published in refereed

journals, edited books and refereed conference proceedings, and one textbook,

published by Wiley in 2006. He is also the holder of three patents. Prof.

Polycarpou is currently the Editor-in-Chief of the IEEE Transactions on Neural

Networks. He served as the Chair of the Technical Committee on Intelligent

Control, IEEE Control Systems Society (2003–2005) and as Vice President,

Conferences, of the IEEE Computational Intelligence Society (2002–2003). He

is currently a member of the Board of Governors of the IEEE Control Systems

Society, and an AdCom member of the IEEE Computational Intelligence

Society. Prof. Polycarpou is a Fellow of IEEE.

Thomas Parisini received the ‘‘Laurea’’ degree (Cum Laude and printing

honours) from the University of Genoa in 1988 and the Ph.D. degree in

Electronic Engineering and Computer Science in 1993. In 2001 he was

appointed full professor and Danieli Endowed Chair of Automation Engineer-

ing at the University of Trieste. Thomas Parisini is the Chair of the Conference

Editorial Board and an elected member of the Board of Governors of the IEEE

Control Systems Society. Moreover, he is a member of the European Control

Association council. He was a Distinguished Lecturer of the IEEE Control

Systems Society. He is the co-recipient of the 2004 Outstanding Paper Award of

the IEEE Transactions on Neural Networks. Thomas Parisini is currently

serving as an Associate Editor of the International Journal of Control, and

as Subject Editor of the International Journal of Robust and Nonlinear Control

and served as Associate Editor of Automatica, of the IEEE Transactions on

Automatic Control, and of the IEEE Transactions on Neural Networks. He is the

Program Chair of the 47th IEEE Conf. on Decision and Control to be held in

Cancun, MX, in 2008 and has been appointed as General Co-Chair of the 2013

IEEE Conf. on Decision and Control. His research interests include neural-

network approximations for optimal control and filtering problems, fault

diagnosis for nonlinear systems, hybrid control systems and control of dis-

tributed systems. Thomas Parisini is a Distinguished Member of the IEEE.

design and analysis of a fault isolation scheme for a class of uncertain nonlinear systems

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