Multiple Faults Detection and Isolation via Decentralized

J Electr Eng Technol.2015; 10(6): 2393-2405 http://dx.doi.org/10.5370/JEET.2015.10.6.2393

2393Copyright ⓒ The Korean Institute of Electrical Engineers

This is an Open-Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/ licenses/by-nc/3.0/) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Multiple Faults Detection and Isolation via Decentralized Sliding Mode Observer for Reconfigurable Manipulator

Bo Zhao*, Chenghao Li**, Tianhao Ma*** and Yuanchun Li†

Abstract – This paper considers a decentralized multiple faults detection and isolation (FDI) scheme for reconfigurable manipulators. Inspired by their modularization property, a global sliding mode (GSM) based stable adaptive fuzzy decentralized controller is investigated for the system in fault free, while for the system suffering from multiple faults (actuator fault and sensor fault), the decentralized sliding mode observer (DSMO) is employed to detect their occurrence. Hereafter, the time and location of faults can be determined by a fault isolation scheme via a bank of DSMOs. Finally, the effectiveness of the proposed schemes in controlling, detecting and isolating faults is illustrated by the simulations of two 3-DOF reconfigurable manipulators with different configurations successfully.

Keywords: Reconfigurable manipulator, Multiple faults detection and isolation, Decentralized sliding mode observer, Decentralized control

1. Introduction Reconfigurable manipulators [1], which are composed of

a set of modules in standard size and interface, can be assembled into different configurations and geometries to undertake a variety of unknown or changeable tasks, such as the space exploration, smart manufacturing, high risk operations, and battle fields. However, working for a long time in the environments human can not be involved directly, faults will inevitably occur in actuator, sensor or other components, which may lead the control system to unstable or even destroyed. Therefore, the safety and reliability of reconfigurable manipulators becomes an urgent demand, and the efforts on its FDI are essential.

As a nonlinear and strong interconnected system, the controller design for reconfigurable manipulator is a quite active research field, and different approaches have been proposed during the past decades. The main challenging work lies in the dynamic parameter uncertainties caused by reconfiguration, friction, varying payloads and inter-connection among joints. To against them, several schemes were developed for reconfigurable manipulators [2-4], but they need to be redesigned when adds, removes or changes modules [5]. In contrast, the modular distributed control technology in [6] was more feasible. However, the communication time delay among the modules will lead to

the inaccurate performance [7]. Take the modularization property and interconnection into account, decentralized control strategy was established [8-12] to overcome these shortcomings. It can not only effectively reduce the computational burden in centralized control, but also avoid communication time delay in distributed control, thus it is more feasible to implement to reconfigurable manipulators.

On the other hand, the investigated FDI approaches [13] can be essentially grouped into three main categories. Model-based FDI is a powerful solution [14]. Based on the estimation error obtained from the strain gauge sensor signal and the reaction force observer [15], the sensor fault can be detected, and then the faulty sensor signal was exchanged by the estimated one to maintain the stable control performance. In the presence of parametric uncertainties and actuator faults, a robust reliable control [16] for a near space vehicle was studied based on the fuzzy state-space observer. Based on signal processing technologies, a three latent space transformation based principal component analysis [17] has been effectively applied to detect the fault in the industrial processes with a large number of high correlated variables. In [18], an artificial immunization algorithm was used to optimize the parameters in support vectors machine, it can avoid the premature convergence and guarantee the variety of solutions. Knowledge-based FDI is another effective method. A back propagation neural network (NN) was presented [19] to synthesize fault detection components based on the data collected in the training of autonomous robots. By virtue of soft computing techniques, an integrator of NN and fuzzy logic was proposed [20] for FDI of robot manipulators.

For reconfigurable manipulator systems, only several FDI schemes have been carried out. Inspired by the relationship between power efficiency and operation health

† Corresponding Author: Department of Control Science and Engineering, Changchun University of Technology, China. ([email protected])

* The State Key Laboratory of Management and Control for Complex Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China.

** Product Development, FAW Car Co., Ltd, Changchun 130012, China.

*** Department of Control Science and Engineering, Changchun University of Technology, Changchun 130012, China.

Received: November 13, 2014; Accepted: July 8, 2015

ISSN(Print) 1975-0102ISSN(Online) 2093-7423


2394 │ J Electr Eng Technol.2015; 10(6): 2393-2405

conditions, a power efficiency estimation based health monitoring and fault detection technique was developed for modular and reconfigurable robots (MRR) with a joint torque sensor [21]. By the filtered torque estimation, [22] proposed a distributed fault detection scheme with torque sensing for MRR. In [23], a hybrid controller has been constructed by a fault estimator and an impulse controller. Zhao et al. [24] compared the user defined threshold to the residual between the actual velocity and the observed one, to detect the fault occurrence or not, and the unknown input state observer was exploited for fault identification.

Sliding mode observer (SMO) [25-28] is a good idea for FDI. In [29], SMO was employed to overcome the limitation that linear observer schemes cannot be utilized for sensor fault reconstruction. The authors in [30] performed a modular fault detection scheme, which did not require motion states of any other modules. In [31], the sensor fault was converted into pseudo-actuator fault scenario by a filter, and a decentralized sliding mode observer was recruited for the position sensor or velocity sensor fault identification.

This presented idea develops an adaptive fuzzy decentralized controller based on GSM for reconfigurable manipulators. For the purpose of FDI, the DSMO is employed to detect and isolate multiple faults, which can be judged when the observation errors beyond the predefined threshold. Hereafter, the time and location of fault occurrence can be decided by the fault isolation scheme. The main contributions of this work are as follows. (i) According to their modularization property, the decentralized controller is more feasible to reconfigurable manipulators, it implies that it is no need to redesign the controller when adds or removes the modules. (ii) The interconnection term is compensated to improve the joint tracking accuracy. (iii) The actuator and sensor fault can be detected precisely even they occur simultaneously. (iv) The fault time and location can be decided by isolating the multiple faults successfully.

The remainder of this paper is organized as follows. In Section 2, the dynamic models of reconfigurable manipulators with/without faults and the control objective are described. And then the decentralized controller is designed in Section 3. Subsequently, the FDI scheme is given in detail in Section 4. Hereafter, the effectiveness of the proposed methods is confirmed by the simulations in Section 5. Finally, the conclusions are drawn in Section 6.

2. Problem Statement The dynamic model of n-DOF reconfigurable manipulator

with joint dynamic friction obtained by Newton-Euler formulation should be described as

( ) ( , ) ( ) ( , )M q q C q q q G q F q q u+ + + = (1)

where nq R∈ is the vector of joint displacements, ( ) n nM q R ×∈ is the positive definite inertia matrix,

( , ) nC q q q R∈ is the Coriolis and centripetal force, ( ) nG q R∈ is the gravity term, ( , ) nF q q R∈ is the vector

of joint dynamic friction torques, and nu R∈ is the applied joint torque.

For the development of decentralized control, each joint is considered as a subsystem of the entire manipulator system interconnected by coupling torques. By separating terms only depending on local variables ( , , )i i iq q q from those terms of other joint variables, each subsystem dynamical model can be formulated in joint space as

( ) ( , ) ( )

( , ) ( , , )i i i i i i i i i

i i i i i

M q q C q q q G qF q q Z q q q u

+ + ++ = (2)

[ ]

[ ]

1,

1,

( , , ) ( ) ( ) ( )

( , ) ( , ) ( , )

n

i ij j ii i i ij j i

n

ij j ii i i i ij j i

Z q q q M q q M q M q q

C q q q C q q C q q q

= ≠

= ≠

⎧ ⎫⎪ ⎪= + −⎨ ⎬⎪ ⎪⎩ ⎭⎧ ⎫⎪ ⎪+ + −⎨ ⎬⎪ ⎪⎩ ⎭

∑

∑

( ) ( )i i iG q G q⎡ ⎤+ −⎣ ⎦ (3)

where , , , ( ), ( , )i i i i i i iq q q G q F q q and iu are the i-th element of the vectors ),(),(,,, qqFqGqqq and u , respectively.

)(qMij and ),( qqCij are the ij-th element of the matrices )(qM and ),( qqC , respectively.

Property 1: For scalar functions ( )i iM q and ( , )i i iC q q , the following condition holds [9]

( 2 ) 0T

i i i is M C s− = (4) Let 1 2[ ] [ ] ( 1, 2, , )T T

i i i i ix x x q q i n= = = , (2) can be expressed as the following state space equation

[ ]( , ) ( ) ( , , ): i i i i i i i i i i ii

i i i

x A x B f q q g q u h q q qSy C x

⎧ = + + +⎨ =⎩

(5)

where ix and iy are the state vector and output vector of subsystem iS , respectively. And

[ ]0 1 0 1 00 0 1i i iA B C⎡ ⎤ ⎡ ⎤= = =⎢ ⎥ ⎢ ⎥⎣ ⎦ ⎣ ⎦

[ ]1

1

1

( , ) ( ) ( , ) ( ) ( , )( ) ( )( , , ) ( ) ( , , )

i i i i i i i i i i i i i i

i i i i

i i i i

f q q M q C q q q G q F q qg q M qh q q q M q Z q q q

−

−

−

= − − −

== −

(6)

The dynamic model of the i-th subsystem exhibits both

actuator and sensor faults should be described by

[ ( , ) ( )

: ( , , ) ( , , )]( , )

i i i i i i i i i i

if i ia i i i

i i i is i i

x A x B f q q g q uS h q q q f q q u

y C x f q q

= + + +⎧⎪ +⎨⎪ = +⎩

(7)

Bo Zhao, Chenghao Li, Tianhao Ma and Yuanchun Li

http://www.jeet.or.kr │ 2395

1( , , ) ( ) ( ) ( , , )ia i i i ia i i i i i if q q u t T M q q q uα ψ−= − (8) ( , ) ( ) ( , )is i i is i i if q q t T q qα φ= − (9)

where ( )iat Tα − and ( )ist Tα − are step functions, iaT and isT are the occurrence times of actuator and sensor fault of the i-th subsystem, respectively. ( , , )i i i iq q uψ and

( , )i i iq qφ are the actuator and sensor fault functions, respectively, ( , , )ia i i if q q u and ( , )is i if q q are the actuator and sensor fault terms, respectively.

Assumption 1: The actuator and sensor fault terms ),,( iiiia uqqf and ),( iiis qqf are unknown but norm

bounded with iiiiia uqqf δ≤),,( and iiiis qqf ρ≤),( , where iδ and iρ are positive constants.

The objective of this work is to detect and isolate the multiple faults occur in the i-th subsystem in real-time based on the local joint information. In other words, fault detection is to determine the fault occurrence time, and fault isolation decides the fault location.

3. Decentralized Controller Design The traditional sliding mode surface exists approaching

mode and sliding mode during the whole sliding process, while the robustness of parameter uncertainties and external disturbances only present during the sliding mode. Yet the global sliding surface [32-33] can drive the system state to the sliding surface at the very beginning, the reaching interval can be eliminated.

In this section, an adaptive fuzzy controller only depends on the local joint information is designed to handle the joint tracking control of reconfigurable manipulators in fault free.

Define the tracking error ie as

i id ie q q= − (10) Then define the global dynamic sliding mode surface as

( )i i i i is e e f tλ= + − (11)

where 0iλ > , ( )if t is the designed function for reaching the global sliding mode, which satisfies the following three conditions:

(i) the initial 0 0(0)i i i if e c e= + , where 0ie and 0ie are the initial values of ie and ie , respectively.

(ii) lim ( ) 0itf t

→∞= .

(iii) ( )if t is existence. According to the above conditions, ( )if t should be

( ) (0) ( 0)ik ti i if t f e k−= > (12)

Yields,

( )i i id i i iq s q e f tλ= − + + − (13) Assumption 2: The desired trajectories idq are twice

differentiable and bounded as

id

id iA

id

qq qq

≤ (14)

where iAq is a known positive scalar.

Assumption 3: The interconnection term ( , , )iZ q q q is explicitly bounded by [24]

1

( , , )n

i ij jj

Z q q q d S=

≤∑ (15)

where 0ijd ≥ , 21j j jS s s= + + .

Define ( , , , , )Ti i i id id idx q q q q q= , then substituting the

time derivative of (13) into (2), one can obtain that

( ) ( )( ( ))

( , ) ( , , ) ( )

( , ) ( ) ( ) ( )

i i i i i id i i i i

i i i i i i i i

i i i i i i i

M q s M q q q e f tC q q s u Z q q q x

C q q f t M q f t

λφ

= − + −

= − − + +

− −

(16)

where ( )i ixφ is the defined nonlinear function defined as

( ) ( )( ) ( , )( ) ( )i i i i id i i i i i id i i i ix M q q e C q q q e G qφ λ λ= + + + + . Now, the fuzzy logic systems are adopted to

approximate the bounded nonlinear functions ( )i ixφ , ( )i iM q and ( , )i i iC q q , yields

1( ) ( )T

i i i i i ix xφ φφ θ σ ε= + (17)

2( ) ( )Ti i iM iM i iM q qθ σ ε= + (18)

3( , ) ( , )Ti i i iC iC i i iC q q q qθ σ ε= + (19)

where 1iε , 2iε and 3iε are the fuzzy logic system approximate errors, and iφθ , iMθ , iCθ is the optimal parameter vectors satisfy the following conditions, respectively.

ˆ

ˆ ârg min ( , ) ( )i i i i

i i i i i ix U

Sup x xφ φ φ

φ φθ

θ φ θ φ∈Ω ∈

⎧ ⎫⎪ ⎪= −⎨ ⎬⎪ ⎪⎩ ⎭

(20)

ˆ

ˆârg min ( , ) ( )iM iM i iM

iM i i iM i iq U

Sup M q M qθ

θ θ∈Ω ∈

⎧ ⎫⎪ ⎪= −⎨ ⎬⎪ ⎪⎩ ⎭

(21)

ˆ

( , )

ˆ ârg min ( , , ) ( , )TiC iC

i i iC

iC i i i iC i i iq q U

Sup C q q C q qθ

θ θ∈Ω ∈

⎧ ⎫⎪ ⎪= −⎨ ⎬⎪ ⎪⎩ ⎭

(22)

where , , , ,i iM iC i iMU Uφ φΩ Ω Ω and iCU are the constraint



set of ˆ ˆ ˆ, , , ,i iM iC i ix qφθ θ θ and ( , )Ti iq q , respectively.

ˆ ˆ ˆˆ( , ), ( , )i i i i i iMx M qφφ θ θ and ˆ ˆ( , , )i i i iCC q q θ are the estimations of ( ), ( )i i i ix M qφ and ( , )i i iC q q that could be expressed as

ˆ ˆ( ) ( )T

i i i i ix xφ φφ θ σ= (23)

ˆˆ ( ) ( )Ti i iM iM iM q qθ σ= (24)

ˆ ˆ( , ) ( , )Ti i i iC iC i iC q q q qθ σ= (25)

where ˆ ˆ,i iMφθ θ and iCθ are adjustable parameters to estimate ,i iMφθ θ and iCθ , respectively.

Define the minimum approximate error as

1 2 3( ) ( ) ( ) ( , ) ( )i i i i i i i i i ix q f t q q f tε ε ε ε= − − (26) Assumption 4: The approximate error of fuzzy logic

system satisfies 0iε ε≤ , where 0 0ε > . The GSM based adaptive fuzzy decentralized control

law is designed as

0i i icu u u= + (27)

0

ˆ ˆ( ) ( , ) ( )ˆ ( ) ( )

T Ti i i i iC iC i i i

TiM iM i i i i

u x q q f t

q f t k sφ φθ σ θ σ

θ σ

= −

− + (28)

( )0ˆsgn( ) sgnic i i i iu s s Sε δ= + (29)

where ik is positive constant, iδ is the estimated value

of { }maxi ijijn dδ = , then the estimation errors are defined

as

î i iφ φ φθ θ θ= − (30)

îM iM iMθ θ θ= − (31)

îC iC iCθ θ θ= − (32)

î i iδ δ δ= − (33)

where iφθ , iMθ , iCθ and iδ are updated by

ˆ ( )i i i i is xφ φ φθ η σ= (34)

ˆ ( ) ( )iM iM i i iM is f t qθ η σ= (35)

ˆ ( ) ( , )iC iC i i iC i is f t q qθ η σ= (36)

i i i is Sδδ η= (37)

Theorem 1: Consider the subsystem dynamic model (2)

with assumptions 2-4, utilize the control law (27)-(29) and adaptive laws (34)-(37), all the variables of the closed-loop system are guaranteed to be bounded, and the H∞ tracking performance is satisfied.

Proof: Choose the Lyapunov function candidate, i.e.,

2

1

2

1 1 1( )2 2 2

1 12 2

nT T

i i i i i iM iMi iMi

TiC iC i

iC i

V M q s φ φφ

δ

θ θ θ θη η

θ θ δη η

=

⎡= + +⎢

⎢⎣⎤

+ + ⎥⎦

∑ (38)

Take property 1 into account, the time derivative of (38)

is

[

[

1

2

1

( ( , ) ( , , ) ( )

( , ) ( ) ( ) ( ))1 1 1ˆ ˆ( )2

1 1ˆ ˆ

( ( , , ) ( ) ( , ) ( )

(

n

i i i i i i i i ii

i i i i i i i

T Ti i i i i iM iM

i iM

TiC iC i i

iC in

i i i i i i i ii

i i

V s C q q s u Z q q q x

C q q f t M q f t

M q s

s Z q q q x C q q f t

M q

φ φφ

δ

φ

θ θ θ θη η

θ θ δ δη η

φ

=

=

= − − + +

− −

+ − −

⎤− − ⎥

⎦

= + −

−

∑

∑1 1ˆ ˆ) ( ) )

1 1ˆ ˆ

T Ti i i i iM iM

i iM

TiC iC i i

iC i

f t u φ φφ

δ

θ θ θ θη η

θ θ δ δη η

− − −

⎤− − ⎥

⎦

(39)

Substituting (17)-(19) and (28) into (39), we have

()

(

11

2 3

( ) ( )

( ) ( ) ( , , )

1 1 1 1ˆ ˆ ˆ ˆ

ˆ ˆ( ) ( ) ( )

nT T T

i i i iC iC i iM iM i ii

i i i i i i i i

T T Ti i iM iM iC iC i i

i iM iC i

T T T Ti i i i i iC iC iC iC i

i

V s f t f t

f t f t k s Z q q q u

s f t

φ φ

φ φφ δ

φ φ φ φ

θ σ θ σ θ σ ε

ε ε

θ θ θ θ θ θ δ δη η η η

θ σ θ σ θ σ θ σ

=

=

⎡= − − +⎣

− − − + −

⎤− − − − ⎥

⎥⎦

⎡= − − −⎣

∑

)1

ˆ( ) ( ) ( , , )1 1 1 1ˆ ˆ ˆ ˆ

n

T TiM iM iM iM i i i i i ic

T T Ti i iM iM iC iC i i

i iM iC i

f t k s Z q q q u

φ φφ δ

θ σ θ σ ε

θ θ θ θ θ θ δ δη η η η

− − + − + −⎤

− − − − ⎥⎦

∑

1

1 ˆ( ) ( ( )n

T T Ti i i i i iM iM i

ii

s f tφ φ φ φφ

θ σ θ θ θ ση=

⎡ ⎛≤ − −⎢ ⎜⎜⎢ ⎝⎣∑ (40)

{ }1 1

1 ˆ ) ( ( )

1 1ˆ ˆ) max

T TiM iM i i ic iC iC i

iMn n

TiC iC i i ij i jijiC i i j

s u f t

d s Sδ

θ θ ε θ ση

θ θ δ δη η = =

− + − −

⎤⎞− − +⎥⎟

⎥⎠ ⎦∑ ∑

It’s worth noting that i j i js s S S≤ ⇔ ≤ , and by

virtue of Chebyshev inequality,



1 1 1

n n n

i j i ii j i

s S n s S= = =

≤∑ ∑ ∑ (41)

Substituting (29), (34)-(36) and (41) into (40), we have

( )

{ }

20

1

1

20

1

20

1

ˆ( sgn( ) sgn )

1 ˆ max

1ˆ ˆ

1 ˆ( )

n

i i i i i i i i ii

n

i i ij i iiji in

i i i i i i i ii

i i i i ii

n

i i i i i i i i iii

V s s s S k s s

n d s S

k s s s s S

s S

k s s s S

δ

δ

δ

ε δ ε

δ δη

ε ε δ

δ δ δη

ε ε δ δ δη

=

=

=

=

⎡≤ − − − +⎣

⎤− +⎥

⎦

⎡≤ − + − +⎣

⎤− − ⎥

⎦⎡ ⎤

≤ − − − + −⎢ ⎥⎣ ⎦

∑

∑

∑

∑

(42)

Then substituting (37) into (42),

20

1

2

1

( )

( ) ( )

n

i i i ii

n

i ii

V k s s

k s t

ε ε=

=

⎡ ⎤≤ − − −⎣ ⎦

≤ − = Φ

∑

∑ (43)

Integrating ( )tΦ from 0 to t yields

0 0

(0) ( ) ( ) ( )t t

V V t d dτ τ τ τ≥ + Φ ≥ Φ∫ ∫ (44)

Therefore 0

0 ( ) (0)t

d Vτ τ≤ Φ ≤∫ . Since (0)V is positive

and finite, 0

lim ( )t

tdτ τ

→∞Φ∫ exists and finite. According to

Barbalat Lemma, lim ( ) 0t

t→∞

Φ = , it implies that lim 0its

→∞= ,

namely, the tracking error i id ie q q= − is convergent to zero asymptotically.

4. Fault Detection and Isolation The aim to fault detection is not only to detect whether a

fault occurs or not, but also to determine the time and location of fault occurrence, on which the decision can be made via a significant residual.

4.1. Fault detection scheme

Define the output of the first order filter iz as a new

state variable

i i i i iz a z b y= − + (45)

where iy is the sensor output, and 0, 0i ia b> ≠ . Substituting the output of (7) into (45), we have

1i i i isz az bx bf= − + + (46) Now, let [ ] [ ]1 2 3, , , ,T T

i i i i i i ix x x x q q z= = , the new state space expression of the subsystem is

[ ]( , ) ( ) ( , , )i i i i i i i i i i i i if

i i i

x A x B f q q g q u h q q q E f

y C x

⎧ = + + + +⎪⎨

=⎪⎩ (47)

where

0 1 00 0 0

0i

i i

Ab a

⎡ ⎤⎢ ⎥= ⎢ ⎥⎢ ⎥−⎣ ⎦

, 010

iB⎡ ⎤⎢ ⎥= ⎢ ⎥⎢ ⎥⎣ ⎦

, 0 01 00 0

T

iC⎡ ⎤⎢ ⎥= ⎢ ⎥⎢ ⎥⎣ ⎦

,

iaif

is

ff

f⎡ ⎤

= ⎢ ⎥⎣ ⎦

, 1 2

0 0( ) 00

i i i i iE E E g qb

⎡ ⎤⎢ ⎥⎡ ⎤= =⎣ ⎦ ⎢ ⎥⎢ ⎥⎣ ⎦

It is obvious that ( , )i iA B is controllable, ( , )i iA C is

observable. Assumption 5: There exists a proper matrix iL satisfies

0i i i iA A L C= − with the following Riccati function holds since ( , )i iA C is observable

0 0i

Ti i i iA P P A I+ = − (48)

where iP , iI are symmetric positive matrices.

Assumption 6: There exists arbitrary matrices iP and iF such that

T Ti i i iP B C F= (49)

where 1 2

1 2[ ]i i iF F F R ×= ∈ . Define ˆ

ix and îy are the estimated values of ix and

iy , respectively, the state error î i ie x x= − , output error

îy i ie y y= − . The decentralized sliding mode observer

(DSMO) based on a radial basis function neural network (RBFNN) can be established as

( )ˆˆ ˆ ˆ ˆ ˆ ˆ( , ) ( )

ˆsgn ( )

ˆ ˆ

i i i i i i i i i i i

Ti i i i i i i

i i i

x A x B f q q g q u v

e P B L y y

y C x

β

⎧ ⎡= + + +⎣⎪⎪ ⎤− + −⎨ ⎦⎪

=⎪⎩

(50)



where sgn( )Ti i i ie P Bβ is the robust term to compensate

the approximate error. The observation error dynamic model derived from (47)

and (50) is

( ) sgn( )

ˆ ˆ( ) ( ) ( - )

Ti i i i i i if i i i i i

i i i i i i i i

e A L C e E f B e P B

B f f g g u v h

β= − − −

⎡ ⎤+ − + − +⎣ ⎦ (51)

where

( ) ( )ˆˆ( ) sgn ,T Ti i i i i i i i ipv t e P B R e P B θ= − (52)

is employed to compensate the interconnection term among

the subsystems, where ( ) ( )ˆ ˆˆ ˆ,T T Ti i i i ip ip ip i i iR e P B e P Bθ θ σ= ,

ipθ and îpσ are the estimation of ipθ and ipσ , ˆ

ip ip ipθ θ θ= − and îp ip ipσ σ σ= − are their estimation

errors, respectively. ifθ and igθ are the weights of ideal

NNs, respectively. ( ) ( )iσ ⋅ ⋅ is the NN basic function, and

the approximate errors ifε and igε are norm bounded. Using the RBFNNs to approximate the uncertainty term ( , )i i if q q and ( )i ig q , where the ideal NNs as

( , ) ( , )Ti i i if if i i iff q q q qθ σ ε= − (53)

( ) ( )Ti i ig ig i igg q qθ σ ε= − (54)

ifθ and igθ denote the estimation of ifθ and igθ , the

estimated errors are îf if ifθ θ θ= − and ˆ

ig ig igθ θ θ= − , respectively. Then

ˆ ˆˆ ˆ ˆ ˆ ˆ( , ) ( , )T

i i i if if i if q q q qθ σ= (55)

ˆˆ ˆ ˆ ˆ( ) ( )Ti i ig ig ig q qθ σ= (56)

ˆ ˆ ˆ ˆ ˆ ˆ( , ) ( , ) ( , )

ˆ ˆ ˆ( ( , ) ( , ))

Ti i i i i i i if if i i

Tif if i i if i i if

f f q q f q q q q

q q q q

θ σ

θ σ σ ε

= − =

+ − + (57)

ˆ ˆ ˆ ˆ( ) ( ) ( )

ˆ ˆ( ( ) ( ))

Ti i i i i ig ig i

Tig ig i ig i ig

g g q g q q

q q

θ σ

θ σ σ ε

= − =

+ − + (58)

Define the approximate error of the NNs as

( )( )

1 ˆ ˆ ˆ( , ) ( , )

ˆ ˆ( ) ( )

Ti if if i i if i i if

Tig ig i ig i i ig i

q q q q

q q u u

ω θ σ σ ε

θ σ σ ε

= − +

+ − + (59)

( ) ( )2 ˆT T Ti i i i i ip ip i i iR e P B e P Bω θ σ= − (60)

1 2i i iω ω ω= + (61)

where ( ) { }maxTi i i i ij iij

R e P B n d E= .

Assumption 7: The interconnection term ( , , )ih q q q is bounded as

1

( , , )n

i ij jj

h q q q d E=

≤∑ (62)

where dij > 0 is unknown constant, and define

21 T T

i i i i i i iE e P B e P B= + + .

Assumption 8: The approximate error of the NN iω is bounded as i iω β≤ with iβ is a positive scalar.

The NN weights ifθ , igθ and ipθ are updated by

ˆ ˆ2 Tif if i i i ife P Bθ η σ= − (63)

ˆ ˆ2 Tig ig i i i ig ie P B uθ η σ= − (64)

ˆ ˆ2 Tip ip i i i ipe P Bθ η σ= (65)

Theorem 2: Consider the subsystem dynamic model (2)

with the assumptions 5-8, the observation error (51) obtained by the designed DSMO (50) and the subsystem state space equation (47), as well as the adaptive update laws (63)-(65), the DSMO is asymptotically stable, it implies that ie could converge to zero asymptotically.

The proof is similar to section 3, so it is omitted here. From (51), we can know that if a fault occurs, 0i ifE f ≠ ,

and definite change will occur in ie . Thus, ie reflects the occurrence of faults. Summarily, the fault detection scheme can be devised as follows.

Fault detection scheme: Faults can be detected if the residual ie exceeds a predefined threshold iϕ . Otherwise, the system is fault-free within the considered time. The detection time idt is defined as the first moment such that

ie is greater than iϕ .

4.2. Fault isolation scheme After a fault being detected, to determine its location is

next objective, which is referred to fault isolation. In this subsection, based on the DSMO, we present a fault isolation scheme, which could avoid the affection caused by the faulty system to the fault-free subsystems.

Let ( , )ike k s a= describes the observation error. k s= denotes the sensor fault. Define state observe error and the output error as ˆ

is is ie x x= − and îys is ie y y= − , the

designed sensor fault observer is expressed as

( ) ( )ˆˆ ˆ ˆ ˆ ˆ ˆ( , ) ( )

ˆsgn

ˆ ˆ

is i is i i i i i i i i

Ti is i i is is i i is

is i is

x A x B f q q g q u v

e P B E L y y

y C x

β υ

⎧ ⎡= + + +⎣⎪⎪ ⎤− + + −⎨ ⎦⎪

=⎪⎩

(66)



where

,

0 ,

is iysis iys

is iysis

iys

F eif e

F e

if e

ρ ςυ

ς

⎧− >⎪⎪= ⎨⎪ ≤⎪⎩

(67)

where isρ is an adjustable constant, ς is a sufficiently small positive scalar, thereby the output error is limited within a neighborhood.

Assumption 9: There exists arbitrary matrices iP and isF such that

T Ti is i isP E C F= (68)

where 1 2

1 2[ ]is is isF F F R ×= ∈ . Comparing (47) to (66), the observation error dynamic

could be expressed as

( )1 2

ˆ ˆ( ) ( ) ( ) ( )

sgn

is i i i is i i i i i i i i

Tis is i ia i is i i is i i

e A L C e B f f g g u v h

E E f E f B e PBυ β

⎡ ⎤= − + − + − + −⎣ ⎦

+ − − − (69)

where ( )ˆ,Ti is i i iPe P Bν θ is utilized to compensate the

interconnection, the RBFNNs ˆ ˆˆ ˆ( , , )i i i iff q q θ and ˆˆ ˆ( , )i i igg q θ

approximate the unknown terms ( , )i i if q q and ( )i ig q ,

( )sgn Ti is i ie P Bβ is a robust term, which could offset the

approximation error. k=a denotes the actuator fault. Define the state

observation error as iaiia xxe ˆ−= , output error as

iaiias yye ˆ−= , the designed actuator fault observer is described as

1 2 1 1

2

2 2 2

3 1 3 3 3

ˆ ˆ

ˆ ˆ ˆˆ ˆ ˆ ˆ ˆ( , , ) ( , )ˆ( , )

ˆ ˆ ˆ

ia ia i ia

ia i i i if i i ig i

i ia iP i ia

ia i ia i ia i ia i ia

x x K e

x f q q g q u

e K e

x b x a x b K e

θ θ

ν θ

υ

⎧ = +⎪⎪ = +⎪⎨⎪ + +⎪⎪ = − + +⎩

(70)

where

3

33

3

,

0 ,

iai ia

iaia

ia

eif e

e

if e

γ ςυ

ς

⎧− >⎪= ⎨⎪ ≤⎩

(71)

where iγ is an adjustable scalar, ς is still a sufficiently small positive constant.

Comparing (47) to (70), the dynamic observation error is

1 2 1 1

2 2 2

3 1 3 3 3

ˆ ˆ( ) ( )ia ia i ia

ia i i i i i i i i ia i ia

ia i ia i ia i is i ia i ia

e e K e

e f f g g u h v g f K ee b e a e b f b K eυ

= −⎧⎪

= − + − + − + −⎨⎪ = − + − −⎩

(72)

Theorem 3: Consider a bank of observers (66) and (70),

the observation error dynamic model as (69) and (72), and the assumptions 5-9 with the adaptive laws (63)-(65), the observation errors can converge to zero. In other words, the estimated state can follow to the actual state ix . Once the subsystem is faulty, ike could definitely change.

Proof: When k s= , choose Lyapunov candidate as

1

1

1 1 12 2 2

n

s isin

T T T Tis i is if if ig ig ip ip

if ig ipi

V V

e Pe θ θ θ θ θ θη η η

=

=

=

⎡ ⎤= + + +⎢ ⎥

⎢ ⎥⎣ ⎦

∑

∑

(73) Its time derivative

1

1 ˆ

1 1ˆ ˆ

nT T T

s is i is ia i is if ififi

T Tig ig ip ip

ig ip

V e Pe e Pe θ θη

θ θ θ θη η

=

⎡= + +⎢

⎢⎣⎤

+ + ⎥⎥⎦

∑ (74)

Substituting (47) and (66) into (74), one can obtain that

0 01

1

( ) 2 ( )

1 1 1ˆ ˆ ˆ22 2

2 ( ) 2 ( )

i

nT T T

s is i i i is is i i i i ii

T T T Ti is i i if if ig ig ip ip

if ig ip

nT Tis i i i i is i i is ia

i

V e A P P A e e PB f g u

e PB

e PB v h e PE f

β θ θ θ θ θ θη η η

υ

=

=

⎡= + + +⎣

− + + +

⎤ ⎡ ⎤+ − + −⎦ ⎣ ⎦

∑

∑

(75)

According to similar proof in section 2, we have

( )

( )

( )

2min

1

2min 1

1

2min

1

2 ( )

2 ( )

nT

s i is is i is is iain

i is is iys i iin

i isi

V Q e e P E f

Q e F e

Q e

λ υ

λ ρ α

λ

=

=

=

⎡ ⎤≤ − + −⎣ ⎦

⎡ ⎤≤ − − −⎣ ⎦

⎡ ⎤≤ −⎣ ⎦

∑

∑

∑

(76)

It is clear that ( ) (0)V t V≤ , according to Barbalat

Lemma, tlim 0ise→∞

= , which means ise converge to zero. When k= a, choose the Lyapunov candidate function as



1 2 3a a a aV V V V= + + (77)

where

21 1

1

12

n

a iai

V e=

⎛ ⎞= ⎜ ⎟⎝ ⎠∑ (78)

2 2 2 22 2

1

1 1 1 12 2 2 2

n

a ia if ig ipif ig ipi

V e θ θ θη η η=

⎛ ⎞= + + +⎜ ⎟⎜ ⎟

⎝ ⎠∑ (79)

23 3

1

12

n

a iai

V e=

⎛ ⎞= ⎜ ⎟⎝ ⎠∑ (80)

① The time derivative of 3aV is

()

(

)

3 3 31

23 3 1 3 2 3

1

3 3

3 3 3 11

3 2

( )

( )

sgn( )

(( ) )

( )

n

a ia iain

i i ia i ia ia i i iai

i i ia ian

ia i i ia i iai

i ia i i

V e e

a K e b e e b e

b e e

e a K e b e

b e

α

γ

γ α

=

=

=

=

≤ − + + +

−

≤ − + −

− −

∑

∑

∑

(81)

3 0aV ≤ if 3iK and iγ satisfy 3 3 1( ) 0i i ia i iaa K e b e+ − > and 2 0i iγ α− > at the same time. According to the sliding mode equivalent principle,

( )2 3 1( )sgn( )i i ia iaeqe eγ α− = (82)

where 2 3( )sgn( )i i iaeγ α− is the discontinuous equivalent output injection value.

② The time derivative of 1aV is

( )

( )

1 1 11

1 2 1 11

1 1 1 21

( )

( )

( )

n

a ia iai

n

ia ia i iain

ia i ia iai

V e e

e e K e

e K e e

=

=

=

=

= −

≤ − −

∑

∑

∑

(83)

1 0aV ≤ if the selected 1iK satisfies 1 1 2 0i ia iaK e e− > .

③ The time derivative of 2aV is

2 2 2 21

ˆ ˆ(( ) ( ) )n

a ia i i i i i i i i iai

V e f f g g u h K eν=

⎡= − + − + − −⎣∑

2 21

2 1 2 2

22 2

22 2 2 2

1 1 1ˆ ˆ ˆ

1 ˆˆ ˆ( ) (

1 ˆ ˆ ˆ)

1 ˆ

ˆ ˆ

if if ig ig ip iPif ig ip

n

ia if if if if ia ig ig iifi

ig ig ia i ia i ia ip ipig

i ia ip ipip

ia ip ip i ia ia i

e e u

e e h e

K e

e K e e

θ θ θ θ θ θη η η

θ σ θ θ θ ση

θ θ ω θ ση

θ θη

θ σ ω

=

⎤− − − ⎥

⎥⎦⎡

≤ − +⎢⎢⎣

− + + −

⎤− − ⎥

⎥⎦

≤ − − +

∑

{ }

11

21 1

1 ˆ max

n

in n

ip ip ij ia jijip i j

d e Eθ θη

=

= =

⎡⎣

⎤− +⎥

⎥⎦

∑

∑ ∑

(84)

Noticing that 2 2ia ja i je e E E≤ ⇔ ≤ , by virtue of

Chebyshev inequality,

2 21 1 1

n n n

ia j ia ii j i

e E n e E= = =

≤∑ ∑ ∑ (85)

Substituting (85) into (84), we have

{ }2 2 2 11

22 2

2 2 11

22 2 2 2

2 2 21

ˆ ˆ( max )

1 ˆ

1 ˆˆ( )

( )

n

a ia ij i ip ip ia ii ij

i ia ip ipip

n

ia ip ip ip ip ia iipi

ia i i ia

n

ia i i iai

V e n d E e

K e

e e

e K e

e K e

θ σ ω

θ θη

θ σ θ θ ωη

ω

ω

=

=

=

⎡⎢≤ − +⎢⎣

⎤− − ⎥

⎥⎦⎡

≤ − +⎢⎢⎣

⎤+ − ⎦

⎡ ⎤≤ −⎣ ⎦

∑

∑

∑

(86)

2 0aV ≤ if the selected 2iK satisfies 2 2 0i ia iK e ω− > .

From the analysis above, it is clear ( ) (0)V t V≤ , thus eia

is bounded. According to Barbalat Lemma, tlim 0iae→∞

=

which means iae can converge to zero.

5. Numerical simulation In order to verify the effectiveness of the proposed

methods, two 3-DOF reconfigurable manipulators with different configurations shown as Fig. 1 are adopted for numerical simulation.



Fig.1. Reconfigurable manipulators for simulation

The friction terms of configuration a and configuration b

are respectively expressed as follows: Configuration a:

1 1 1

2 2 2

3 3 3

10sin(3 ) 2sgn( )( , ) 1.2 5sin(2 ) sgn( )

0.6 7sin(4 ) sgn( )

q q qF q q q q q

q q q

+ +⎡ ⎤⎢ ⎥= + +⎢ ⎥⎢ ⎥+ +⎣ ⎦

(87)

Configuration b:

1 1 1

2 2 2

3 3 3

2 5sin(2 ) sgn( )( , ) 1.5 5sin( ) 1.2sgn( )

1.8 5sin(3 ) sgn( )

q q qF q q q q q

q q q

+ +⎡ ⎤⎢ ⎥= + +⎢ ⎥⎢ ⎥+ +⎣ ⎦

(88)

The joint desired trajectories of configuration a are

1

2

3

0.5cos( ) 0.2sin(3 )0.2sin( ) 0.4cos(2 )

0.3cos(3 ) 0.5sin(2 )

d

d

d

q t tq t tq t t

= +

= − +

= − (89)

The joint desired trajectories of configuration b are

1

2

3

0.3cos(2 ) 0.1sin( )0.2sin(3 ) 0.3cos(2 )0.5sin(2 ) 0.3cos( )

d

d

d

q t tq t tq t t

= +

= +

= + (90)

The initial positions and velocities of each joint are

1 2 3(0) (0) (0) 1q q q= = = and 1 2 3(0) (0) (0) 0q q q= = = .

5.1. Simulation for decentralized control scheme In this subsection, the proposed decentralized controller

(27) is applied to the reconfigurable manipulator in fault-free. The initial values of iφθ , iMθ , iCθ and iδ are zeros. The control parameters are 0.02i iφ δη η= = , 01.00 =ε ,

0.01iM iCη η= = , 5=ik , 25=iλ , tii eftf 20)0()( −= with

))0()0(()0()0()0( iidiiidi qqqqf −+−= λ . From Fig. 2, one can see that the actual trajectories take

about only 0.2s to follow their desired trajectories, which means each joint in configuration a obtained good tracking performance.

To further test the effectiveness of the proposed decentralized controller, configuration b is employed for

simulation with the same control law, and the Fig. 3 shows excellent tracking performance as well. It demonstrates that the proposed control scheme is feasible to different configurations without any control parameters modification.

5.2. Simulation for FDI

5.2.1 Simulation results of fault detection

In this subsection, the predefined threshold of observation

error is 0.03iϕ = , the observer gains are 1 2000iL = ,

0 1 2 3 4 5 6 7 8 9 10-1

-0.5

0

0.5

1

Time(sec)

Join

t 1

Pos

ition

(rad

)

desired trajectory

actual trajectory

0 1 2 3 4 5 6 7 8 9 10-1

-0.5

0

0.5

1

Time(sec)

Join

t 2

Pos

ition

(rad

)

desired trajectory

actual trajectory

0 1 2 3 4 5 6 7 8 9 10-1

-0.5

0

0.5

1

Time(sec)Jo

int

3 P

ositi

on(r

ad)

desired trajectoryactual trajectory

Fig. 2. Joint tracking curves of configuration a

0 1 2 3 4 5 6 7 8 9 10-0.5

0

0.5

1

Time(sec)

Join

t 1

Pos

ition

(rad

)

desired trajectory

actual trajectory

0 1 2 3 4 5 6 7 8 9 10-0.5

0

0.5

1

Time(sec)

Join

t 2

Pos

ition

(rad

)

desired trajectory

actual trajectory

0 1 2 3 4 5 6 7 8 9 10-1

-0.5

0

0.5

1

Time(sec)

Join

t 3

Pos

ition

(rad

)

desired trajectory

actual trajectory

Fig. 3. Joint tracking curves of configuration b



2 1000iL = and 3 30iL = , adaptive gains are 0.02ifη = , 0.01igη = and 0.01ipη = , the robust coefficient is

0.01iβ = , the filter coefficients are set as 1ia = , 1ib = , respectively.

For the i-th subsystem of reconfiguration manipulators, the RBFNNs are utilized to approximate the terms

( , ), ( )i i i i if q q g q and ( )Ti i i iR e PB . Where T

nxxX ],,[ 1=

is the input vector of NN, Tm ],,[ 1 σσσ = is the radial

basis function, and the NN is expressed as

2 2exp( / 2 )j j jX c bσ = − − (91)

where 1, 2, ,j m= … denotes the number of nodes in the hidden layer, jc and jb are the central and the width of RBFNN’s j-th node,

1[ , , ]T T T

j nc ξ ξ= , 10jb =

where 1, 2, ,i n= denotes the number of hidden layers in

NN, and [ ]1.5 1 0.5 0 0.5 1 1.5 TTiξ = − − − .

The injected faults are defined as

1 1 1

2 2

10sin(2 ) , 30.5 , 5

a

s

f q q tf q t

= ≥⎧⎨ = − ≥⎩

(91)

The observation error curves of configuration a and b

shown as Fig. 4 and Fig. 5, respectively, the red lines present the given thresholds. In these figures, from t=3s and t=5s, the actuator fault 1af and sensor fault 2sf are embedded on joint 1 and joint 2, respectively. One can observe that the observation errors exceed the thresholds

once the fault occurs. Therefore, this proposed scheme can detect the fault in real time.

0 1 2 3 4 5 6 7 8 9 10-0.2

-0.1

0

0.1

0.2

Time(sec)

Join

t 1

obse

rvat

ion

erro

r(ra

d)

0 1 2 3 4 5 6 7 8 9 10-0.2

0

0.2

0.4

0.6

Time(sec)

Join

t 2

obse

rvat

ion

err

or(r

ad)

0 1 2 3 4 5 6 7 8 9 10-0.2

-0.1

0

0.1

0.2

Time(sec)

Join

t 3

obse

rvat

ion

err

or(r

ad)

Fig. 5. Observation performance of configuration b in

faulty

0 1 2 3 4 5 6 7 8 9 10-0.2

-0.1

0

0.1

0.2

Time(sec)

Join

t 1

obse

rvat

ion

err

or(r

ad)

0 1 2 3 4 5 6 7 8 9 10-0.2

-0.1

0

0.1

0.2

Time(sec)

Join

t 2

obse

rvat

ion

err

or(r

ad)

(a) Actuator observer output error curves of configuration a

0 1 2 3 4 5 6 7 8 9 10-0.2

-0.1

0

0.1

0.2

Time(sec)

Join

t 1

obse

rvat

ion

err

or(r

ad)

0 1 2 3 4 5 6 7 8 9 10-0.2

0

0.2

0.4

0.6

Time(sec)

Join

t 2

obse

rvat

ion

err

or(r

ad)

(b) Sensor observer output error curves of configuration a

Fig. 6. The bank of observers’ output error curves of configuration a

0 1 2 3 4 5 6 7 8 9 10-0.2

-0.1

0

0.1

0.2

Time(sec)

Join

t 1

obse

rvat

ion

erro

r(ra

d)

0 1 2 3 4 5 6 7 8 9 10-0.2

0

0.2

0.4

0.6

Time(sec)

Join

t 2

obse

rvat

ion

err

or(r

ad)

0 1 2 3 4 5 6 7 8 9 10-0.2

-0.1

0

0.1

0.2

Time(sec)

Join

t 3

obse

rvat

ion

erro

r(ra

d)

Fig. 4. Observation performance of configuration a in faulty



5.2.2 Simulation results of fault isolation

In this subsection, utilize DSMOs (66) and (70), the

actuator fault observer gains are set as ki1 =100, ki2 =300, ki3 =20. The adjustable sliding mode parameters are

130iρ = , 800iγ = , the sensor observer parameters and the fault are as in section 5.2.1.

Fig. 6(a) shows the actuator observer output curves, one can see that the observation error of joint 1 of configuration a exceeds the predefined threshold after t=3s, and that of joint 2 lies within the given threshold, it proofs that the actuator fault can be isolated from sensor fault. Meanwhile, Fig. 6(b) shows that of sensor fault, the same conclusion can be obtained. To further test the proposed isolation scheme, the configuration b is employed for simulation, whose results shown as Fig. 7. It’s worth noting that joint 3 is fault free according to the results of fault detection in the previous subsection, therefore, its simulation result can be omitted here.

6. Conclusions By virtue of DSMO, a multiple faults detection and

isolation schemes for reconfigurable manipulator are

presented in this paper. Based on the modularization property and Lyapunov stability theory, the adaptive fuzzy decentralized controller is applied to the reconfigurable manipulator in fault-free. Then the multiple faults including actuator fault and sensor fault can be detected by means of the observation errors whether exceed the predefined thresholds or not. After being detected, multiple faults are isolated to decide which joint and which component is faulty. Its effectiveness has been demonstrated by the simulation of two 3-DOF reconfigurable manipulators with different configurations in the presence of multiple faults.

Acknowledgements This work was supported by the National Natural

Science Foundation of China (61374051) and the Scientific and Technological Development Plan Project in Jilin Province of China (20150520112JH).

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[3] Biglarbegian, M., Melek, W.W. and Mendel J.M., “Design of Novel Interval Type-2 Fuzzy Controllers for Modular and Reconfigurable Robots: Theory and Experiments,” IEEE Transactions on Industrial Elec-tronics, vol. 58, no. 4, pp. 1371-1384, 2011.

[4] Melek, W.W. and Najjaran, H., “Study of the effect of external disturbances on the position control of IRIS modular and reconfigurable manipulator,” in the Proceeding of 2005 IEEE International Conference on Mechatronics Automation, pp. 144-147, 2005.

[5] Biglarbegian, M., Melek, W. W., Mendel, J. M., “On the stability of interval Type-2 TSK fuzzy logic control systems,” IEEE Transactions on systems man and Cybernetics part B:Cybernetics, vol. 40, no. 3, pp. 798-818, 2010.

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[8] Li, Z., Melek, W.W. and Clark, C., “Decentralized robust control of robot manipulators with harmonic drive transmission and application to modular and

0 1 2 3 4 5 6 7 8 9 100

0.1

0.2

Time(sec)

Join

t 1

obse

rvat

ion

erro

r(ra

d)

0 1 2 3 4 5 6 7 8 9 10-0.2

-0.1

0

0.1

0.2

Time(sec)

Join

t 2

obse

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Fig. 7. The bank of observers’ output error curves of configuration b



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Bo Zhao He received Ph.D. degree in the Department of Control Science and Engineering from Jilin University, China in 2014. Now, he is a post-doctoral at Institute of Automation, Chinese Aca-demy of Science, China. His interest covers fault diagnosis and fault tolerant control, and intelligent control.

Chenghao Li He received M.E. degree in the Department of Control Science and Engineering from Jilin University, China in 2013. Now, he is a production engineer of FAW Car Co., Ltd. China. His interest covers fault diagnosis and fault tolerant control.

Tianhao Ma He received his M.E. degree in the Department of Control Science and Engineering from Chang-chun University of Technology, China in 2015. His interest covers intelligent control and robust control.

Yuanchun Li He received Ph.D. degree in the Department of General Mechanics from Harbin Institute of Technology, China in 1990. Now, he is a professor in the Department of Control Science and Engineering, Changchun University of Technology. His research interest covers complex

system modeling and robot control.

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Multiple Faults Detection and Isolation via Decentralized