Observer-Based Adaptive Fault-Tolerant Control of
A Class of Nonlinear Systems With Actuator
Failures
Yang Yang
College of Automation
Nanjing University of Posts and
Telecommunications, Nanjing, China
Email: yyang@njupt.edu.cn
Dong Yue
College of Automation
Institute of Advanced Technology
Nanjing University of Posts and
Telecommunications, Nanjing, China
Email: medongy@vip.163.com
Zhou Gu
College of Mechanical & Electronic Engineering
Nanjing Forestry University
Nanjing, China
Email: gzh1808@163.com
Abstract—The output feedback tracking control problem is
studied for a class of uncertain nonlinear systems with actu-
ator failures. An adaptive observer is designed to reconstruct
immeasureable state information of the system, and an observer-
based adaptive fault-tolerant control (FTC) strategy is developed
recursively by backstepping methods, neural networks (NNs),
FTC theory and the dynamic surface control (DSC) technique.
The proposed strategy is only dependent on output information,
and there is no requirement for accurate parameters of the
system. In theory, the stability of the closed-loop system is
proven that all signals are uniformly ultimately bounded and
the control scheme can force the tracking error converge to a
small neighborhood of the origin.
I. INTRODUCTION
Over the past two decades, adaptive control approaches have
been widely used to deal with system faults in various systems,
and one of the typical schemes is the adaptive backstopping
technique [1]–[6]. The main limitation of the papers [1]–[6]
is that it is assumed that actuators of the systems are well
working and the faults are not taken into account. It is well
known that the phenomenon of component faults frequently
occur in practical industrials [7]–[9], and it may be one
of major sources of instability of systems and has received
considerable attention from control communications. In [10]
and [11], adaptive fault-tolerant control (FTC) methods were
designed for linear systems with faults of lock-in-place and
loss of effectiveness. In [12] [13] and [14], Tao et al. and Jiang
et al. developed adaptive fault-tolerant controllers for a class
of nonlinear single-input and single-output (SISO) systems
and multi-input and multi-output (MIMO) systems. However,
the mentioned references [10]–[14] are effective under the
condition that it is assumed that discussed systems are with
matching conditions or with known nonlinear functions. To
relax these assumptions, Li et al. reported adaptive fuzzy
control ways with the help of fuzzy logical tools in [15][16].
Moreover, adaptive fuzzy output feedback FTC schemes were
emerged in for several classes of uncertain nonlinear systems
suffered from actuator failures [7][17][18]. Recently, a novel
adaptive fault tolerant controller design was proposed for a
class of nonlinear time-delay systems in [8], unknown systems
with multiple actuators in [19], multi-agent systems in [20],
and Markovian jump systems in [21]. However, the control
methods in [7][8][15][19] are based on traditional backstep-
ping ways, and computational burdens increase drastically
along with the growth of the order of the system because
of the repeat differentiation calculation of virtual functions.
Fortunately, a dynamic surface control (DSC) technique was
proposed by Swaroop et al. in [22]. The main idea of this
approach was introduced via a first-order filter at each step
and it was extended to control of a class of strict-feedback
nonlinear systems combing with NNs in [23]. On the basis
of this idea, some efforts have been made to apply this
technique for more general systems, such as strict-feedback
systems [25], non-affine pure-feedback systems [26][27], low-
triangular MIMO systems with time delays [6][28].
Inspired by the aforementioned literature, we focus our
attention to the FTC problem via a state observer. With the
help of appropriate transformation, virtual control variables
of the large-scale pure-feedback system are converted into
dominant forms. A state observer is constructed by universal
approximation theory of neural networks (NNs), and the
DSC technique is also introduced to overcome the so-called
‘explosion of complexity’ utilizing a first-order low-pass filter.
Then, an adaptive NNs fault-tolerant output control strategy
will be designed.
II. PROBLEM FORMULATION
Consider a class of nonlinear systems suffered from actuator
failures
˙x
1
(t) = f
1
(x
1
(t), x
2
(t)) ,
˙x
2
(t) = f
2
(x
2
(t), x
3
(t)) ,
.
.
.
˙x
n−1
(t) = f
n−1
(
x
n−1
(t), x
n
(t)
)
,
˙x
n
(t) = f
n
(x
n
(t)) + ϖ
T
u(t),
y(t) = x
1
(t),
(1)
2016 UKACC 11th International Conference on Control (CONTROL)
Belfast, UK, 31st August - 2nd September, 2016
978-1-4673-9891-6/16/$31.00 ©2016 IEEE
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