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Fuzzy
H
f
Control for Networked T-S Model-based
Nonlinear Systems with Redundant Channels
Xiuying Li, Member, IEEE
Department of Automation
School of Electronic Engineering,
Heilongjiang University
Harbin, China
xiuxiu4480@sina.com
Baojun Wang
Department of Automation
School of Electronic Engineering,
Heilongjiang University
Harbin, China
wbjcscs@sina.com
Shuli Sun, Senior Member, IEEE
Department of Automation
School of Electronic Engineering,
Heilongjiang University
Harbin, China
sunsl@hlju.edu.cn
Abstract—This paper is concerned with the
H
f
controller
design problem for a class of networked nonlinear systems
represented by the Takagi-Sugeno (T-S) fuzzy model. The
measured outputs subjected to sensor saturations will be lost
during the transmission through unreliable communication
links. To improve the reliability of the network communication,
the sensors are equipped with redundant channels to reduce
the negative effect of packet dropouts. Sufficient conditions on
the existence of the desired controller are established by
employing Lyapunov stability theory to ensure that the
resulting closed-loop system is stochastically stable and
achieves a prescribed
H
f
performance index. An example is
utilized to illustrate the effectiveness of the proposed algorithm.
Keywords—Takagi-Sugeno fuzzy model, networked control
system, redundant channels;
H
f
control
I. INTRODUCTION
Nowadays, much attention has been received for
networked control systems (NCSs) where the information
among spatial distributed sensors, controllers, and actuators
is transmitted via the network links [1]. Although there are
some advantages by introducing the network into traditional
control systems, the data packets will suffer from some
ineluctable QoS during the transmission, such as packets
dropouts[2], network-induced delays[3], out-of-order
sequence [4] etc.. These phenomena often occur randomly
and the existence of them can deteriorate the system
performance or even destabilize the control system. Among
which, Packet dropouts have become one of the most
important issues for networked control systems owing to the
packet collisions and congestions via limited bandwidth
networks. Some ways are adopted to conduct the effect of
lost information involved by the imperfect transmission,
namely, zero-input strategy [5], hold-input strategy [6], and
prediction-input strategy [7]. In addition, the method of
multiple packets used to design the filter [8] and controller [9]
has been presented which can meet with in multi-radio
scenario. Recently, the redundant channel scheme is
proposed for the packet dropouts, which is an active way of
improving the communication quality and can reduce the
overall rates of packet dropouts [10]. Such a topology has
been widely exploited. For example, in [11], the event-
triggered distributed state estimation problem has been dealt
with over sensor networks with redundant channels.
However, the existing results in literature, see e.g. [10-12]
are all concerned with the filtering problems. In [13], the
H
f
control problem is investigated for a class of discrete-
time switched linear systems where the redundant channels
are considered to benefit the capability of overcoming the
side-effect of packet losses. However, the systems studied
are linear and the sensor saturation/ nonlinearity is not taken
into account. It is well known that by using time-stamped
technique, we can obtain the information whether a packet is
received or not. If the receiving information can be known
exactly, the actual value of random variable satisfied the
Bernoulli distribution can be known exactly. In [14], an
optimal filter is given by Kalman filter when the packets are
time- stamped where the statistic characteristics of noises
need to be known which cannot always be satisfied in reality.
However,
H
f
method can overcome this constraint. So far,
the
H
f
control for networked T-S fuzzy systems with
redundant channels is rarely involved in the literature.
Motivated by the above discussion, we focus on the
H
f
output-feedback control problem in this paper for a class of
discrete-time T-S fuzzy systems where the measurement
outputs are time stamped and redundant channels are used to
deal with the packet dropouts. By utilizing Lyapunov
stability theory, an LMI-based
H
f
fuzzy controller is
designed such that the closed-loop control system is
stochastically stable and satisfies a prescribed disturbance
rejection level.
II. P
ROBLEM FORMULATION
A. T-S Model-based Physical Plant
The considered nonlinear plant is described by a T-S
fuzzy model as follows:
Plant Rule
i
R
: IF
1
k
T
is
1i
N
, …
l
k
T
is
il
N
, THEN
1
()
kikikik
kik
kik
xAxBuDw
yCx
zLx
I
°
®
°
¯
(1)
where
,,,,
iii i
ABCD
i
L
(1,2,)il
are constant matrices
with appropriate dimensions and
l
is the number of IF-
THEN rules,
x
n
k
x
is the state of the systems,
y
n
k
y
is the measurement signal subjected to sensor saturations,
u
n
k
u
is the controller ,
z
n
k
z
is the controlled output,
w
n
k
w
, belonging to
2
[0, )l f
, is the external noise.
12
[, ,,]
l
kkk k
TTT T
represents the premise variable vector
and
ij
N
(, 1,2 , )ij l
,
denotes the fuzzy set.
This work was supported by National Natural Science Foundation of
China under grant NSFC
-
61503126, 61573132 , Heilongjiang Province
Fund under grant F2018024, Basic Research Fund of Heilongjiang
University in Heilongjiang Province under grant RCYJTD201806 and
Province Key Laboratory..