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Fuzzy Control for Networked Nonlinear Systems
Subject to Randomly Occurred Sensor Saturations
and Multiple Packet Dropouts
Xiuying Li, Member, IEEE
Department of Automation
School of Electronic Engineering, Heilongjiang University
Harbin, China
xiuxiu4480@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 focuses on the
H
∞
controller design
problem for networked Takagi-Sugeno (T-S) fuzzy systems. The
outputs measured by the sensor will be subject to saturation
phenomenon and suffer packet dropouts during the transmission
through unreliable communication links to the remote controller.
Both the sensor saturation and the packet dropouts occur
randomly which are governed by the Bernoulli distributed
variables. The observer is designed with data prediction
compensation strategy when the packet is lost and then, the
controller is designed by using the estimated states. The sufficient
conditions are derived via linear matrix inequality (LMI)
techniques, such that the resulting closed-loop system is
asymptotically mean-square stable with the predefined
disturbance attenuation performance. An example is utilized to
illustrate the effectiveness of the algorithm.
Keywords—Takagi-Sugeno fuzzy model, networked control
system, sensor saturation, packet dropout,;
H
∞
control
I. I
NTRODUCTION
Networked control systems (NCSs) have attracted a great
deal of attention in recent years owing to their successful
applications in many areas such as car suspension system,
spacecraft, manufacturing plants, self-motion robots, remote
medical service and so on [1]. Although there are many
advantages by introducing the network into the traditional
control systems, some challenging problems also exist. Due to
the packet collisions and network congestions, packet dropouts
(PDs) have become one of the most important issues during the
data transmission which would degrade the system
performance or even lead to the system unstable [2]. Fruitful
results focused on PDs are available [3-5].
In control engineering, most of the actual objects are often
nonlinear whose precise model cannot be established. In this
case, Takagi-Sugeno (T-S) fuzzy model which has been proved
to be a powerful tool to handle the nonlinearity is often used to
describe the practical plants [6]. In several decades, great effort
has been devoted to analysis and synthesis for nonlinear
control systems by applying T-S fuzzy models [7-9]. However,
the majority of the existing results are based on the assumption
of the linearity of sensors which is not always satisfied in
practical engineering especially under harsh network
environments. As an essential part of NCSs, the sensors
inevitably show nonlinear characteristics with random
occurrence due to the physical or technological constraints.
This type of nonlinearity is referred to the randomly occurred
sensor saturations (ROSSs) which can be characterized by the
sector-nonlinearity function and has gained great attention by
many researchers in studying the filtering [10,11] and control
[12,13] problems. In [12], the
∞
control problem is studied
for a class of networked systems with sensor saturations where
the considered system is not the T-S fuzzy system and the
occurrence of sensor saturation is not random. In [13], a fuzzy
controller with new compensation approach is presented for
nonlinear networked systems but the sensor saturation is not
considered. Up to now, the
∞
control problem for discrete-
time T-S fuzzy stochastic systems with ROSSs is not fully
investigated. This motivates our current study.
In this paper, the
∞
control problem is investigated for a
class of discrete-time T-S fuzzy systems where the measured
outputs will be subject to ROSSs and multiple PDs during the
transmission through the network. By applying Lyapunov
stability theory and linear matrix inequality (LMI) technique, a
sufficient condition is obtained such that the closed-loop
control system is asymptotically stable in the mean square and
the disturbance rejection attenuation is constrained to a
prescribed level. Finally, an illustrative example is given to
show the effectiveness of the proposed method.
The notations used throughout the paper are fairly standard.
n
and
0
n
denote the identity matrix and zero matrix with
dimensions
n
.
2
[0, )l ∞
is the space of square summable
vectors.
diag{ }
"
stands for a block-diagonal matrix. The
symbol
⊗
denotes the Kronecker product.
E{ }⋅
is the
mathematical expectation operator.
Prob{}⋅
means the
occurrence probability of the event “
⋅
”. The superscript “
T
”
denotes matrix transpose. For any matrix
nn
×
∈ \
, the
notation
0 ( 0)XX><
means
X
is a real symmetric positive
(negative) definite matrix. The symbol “
*
” in a matrix
represents the symmetric terms.
This work was supported by National Natural Science Foundation of
China under grant NSFC-61503126, 61573132 and Province Key Laboratory.