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Neurocomputing
journa l homepa ge: www.elsevier.com/locate/neucom
H
∞
state estimation for artificial neural networks over redundant channels
☆
Sunjie Zhang
a,
⁎
, Derui Ding
a
, Guoliang Wei
a
, Yurong Liu
b,c
, Fuad E. Alsaadi
c
a
Engineering Research Center of Optical Instrument and System, Ministry of Education, Shanghai Key Lab of Modern Optical System, University of
Shanghai for Science and Technology, Shanghai 200093, PR China
b
Department of Mathematics, Yangzhou University, Yangzhou 225002, PR China"
c
Communication Systems and Networks (CSN) Research Group, Faculty of Engineering, King Abdulaziz University, Jeddah 21589, Saudi Arabia
ARTICLE INFO
Communicated by Hongli Dong
Keywords:
H∞ state estimator
Artificial neural networks
Infinite distributed delays
Redundant channels
ABSTRACT
In this paper, a new design problem of the
H
∞
state estimator is developed for a kind of artificial neural
networks (ANNs), where both infinite distributed delays and redundant channels are happening. These adopted
redundant channels can effectively improve the reliability of networked systems from the viewpoint of
engineering. Two series of stochastic variables satisfying Bernoulli distribution, are introduced to govern the
infinite distributed delays and schedule the redundant channels. By utilizing both stochastic analysis and
Lyapunov functional approach, we obtain a lot of sufficient conditions to ensure the desired
H
∞
performance,
while the mean-square stability is also satisfied for this investigated state estimation issues of ANNs. The needed
estimator gains are designed making use of the matrix inequalities’ solution. In final, a simulation is showed to
demonstrate the effectiveness and usefulness of the developed state estimator in this paper.
1. Introduction
In the past two decades, inspired by neural networks in biology, the
artificial neural networks (ANNs) have become a research topic of general
interest. Due to their advantages in learning rule, neurons activity rule,
clustering and nonlinear function approximation, they are widely emplo yed
in various research problems, such as state estimation, signal processing,
intelligent control, system identification and so forth. It should be noted
that the above mentioned research problems are closely dependent on the
ANNs' dynamic behavior, see e.g. [2,4,8,18,23]. Therefore, the stability
analysis and the state estimation of ANNs should be deeply discussed due
to their theoretical significanceaswellaspracticalimportance.
However, it is impractical to measure the neuron states in relatively
large-scale ANNs due to the limitation in circuits. A maneuverable scheme
is to adopt the limited and crucial neuron information to estimate the
dynamics of whole networks, that is, the issue of state estimation. Recently,
in terms of the pressing need of the application, the state estimator' s design
problem for ANNs has drawn a large number of research interests, see
[7,12,15,16,21,22] and the references therein. For example, [21] has
studiedtheproblemofstateestimationfortheMarkovianjumping
recurrent neural networks (RNNs) with mixed discrete-time delays. The
similar issue has been dealt with in [12] for RNNs with a mode-dependent
Markovian functional. Very recently, [16] has studied a problem about the
state estimation for a set of ANNs with a protocol named Round-Robin,
which is proposed to improve the communication effic iency between the
ANNs and the estimator. Obviously, for above mentioned results, the
network-induced phenomena have received adequately attention. We need
to show that network-induced phenomena, like transmission time-delay,
signal quantization, channel fadings, packet dropouts and so on
[10,11,9,5,6], derive from the limited channel bandwidth during the
communication and could cause a tremendous influence on the perfor-
mance of the underlying systems if not be correctly and properly handled.
In state estimation, the statistical information of such phenomena can be
embedded into estimator design to increase the estimation performance.
Note that, rather than taking this statistical information, it would be better
to improve the reliability of communication channels or transmitted data.
From the viewpoint of engineering, two or more channels can be
availableatsametime.Theaimofsuchaschemeistoovercomethe
influ ence of packet dropouts and ensure the communication reliability. This
kind of communication scheme is called redundant channel method [1,24].
In this method, if some channel suffers from packet dropouts, another
channel will be scheduled to transmit the data. Such a transmission scheme
has been greatly employed in some actual systems such as electronic
control systems and aerospace engine syste ms. In [17],anovelhybrid
method with both div ersity scheme and adaptive modulation has been
proposed to conventional multi-channel systems with a function of channel
http://dx.doi.org/10.1016/j.neucom.2016.11.039
Received 2 September 2016; Received in revised form 20 October 2016; Accepted 21 November 2016
☆
This work was supported in part by the National Natural Science Foundation of China under Grants 61603255, 61573246, 61374039 and 61374010, the Shanghai Rising-Star
Program of China under Grant 16QA1403000, the Program for Capability Construction of Shanghai Provincial Universities under Grant 15550502500, and the China Postdoctoral
Science Foundation Grant 2016M590369.
⁎
Corresponding author.
E-mail address: zhang_sunjie@usst.edu.cn (S. Zhang).
Neurocomputing 226 (2017) 117–125
Available online 22 November 2016
0925-2312/ © 2016 Elsevier B.V. All rights reserved.
MARK