Abstract—The problem of
fault detection for networked
control systems with random delay and packet loss is studied in
this paper. The conducted system is discretized by delta operator,
then a fault detection filter and a residual generator are
developed which the fault is detected. Sufficient conditions of
asymptotic stability for the residual system with
performance can be obtained in terms of linear matrix
inequalities and Lyapunov functional techniques. A numerical
example is given to illustrate the effectiveness of the mentioned
method.
I. INTRODUCTION
Networked control systems (NCSs) [1] are feedback
control systems which data are transmitted via network. These
features bring many advantages such as low cost, easing
maintainability, high reliability, flexibility, and information
sharing [2-3]. With such good performances, NCSs have a
wide range of applications in various areas (e.g. the industry,
medicine, robots,transportation). However, compared with
traditional control systems, NCSs possesses some new
problems, for example time delay, packet loss and so on [4-8].
The mentioned issues caused by the network reduce the
stability and reliability of the systems.
With the wide application of NCSs, studies of fault
detection are becoming increasingly important, and produce
numerous results. The fault detection problem for a class of
linear discrete-time systems in a networked environment was
concerned with [9]. The random time delay and missing
phenomenon were characterized by a set of Kronecker delta
functions. The design of robust fault detection for NCSs with
large transfer delays was studied in [10], which system with
long random delay was modeled as a Markov jump system.
The problem of fault detection for a class of NCSs with
random delays and data losses was considered in [11]. Then a
discrete-time Markov jump linear system model was
established with partially known transition probabilities.
At present, researches on fault detection for networked
control system are based primarily on the traditional shift
*This work was supported by the National Natural Science Foundation of
China under Grant 61471323.
J. Gao and D. Zhang are with the School of Information Engineering,
Zhengzhou University, Zhengzhou, 450001, China (corresponding author
D. Zhang, phone: +86-371-67781545; fax: +86-371-67781270; e-mail:
djzhang@zzu.edu.cn).
operator [12]. However, when the sampling period is close to
zero, the discrete time model obtained by the shift operator
does not approach to the continuous time model. In order to
solve the problem, delta operator is firstly used by Goodwin to
discretize continuous time system instead of shift operator [13].
Compared to shift operator, delta operator can unify the
continuous time system and the discrete time system under fast
sampling [14-17]. The sliding mode control of uncertain
nonlinear systems against actuator faults and external
disturbances using delta operator approach was considered in
[18]. The robust stabilization of uncertain time-delayed
systems via delta operator approach was studied in [19]. The
linear quadratic Gaussian control problem for networked
control systems was conducted in reference [20]. But there are
few results about NCSs with random delay and packet loss
using delta operator, which is the motivation of the present
paper.
In this paper, the short random time delay is considered as
a Markov process and the packet loss is described as a
stochastic variable meeting Bernoulli distribution. The system
is modeled as a Markov jump system via delta operator. Then a
filter is established to generate residual signal and detect faults.
The sufficient conditions of asymptotically stability for the
residual system with
performance can be obtained by
using Lyapunov stability theory and linear matrix inequalities
(LMI) techniques. At last, a simulation is given to illustrate the
feasibility of the proposed method.
Natation: Superscript
expresses the matrix transpose
and
represents the n-dimensional Euclidean space. For a
matrix
and two symmetric matrix
and
.
where * is the entries implied by symmetry. Symbol
denotes an identity matrix, and
indicates mathematical
expectation.
II. PROBLEM FORMULATION
Consider a continuous-time linear time-invariant (LTI)
system described by:
Fault Detection for Networked Control Systems
with Random Delay via Delta Operator*
Jie Gao and Duanjin Zhang
2017 11th Asian Control Conference (ASCC)
Gold Coast Convention Centre, Australia
December 17-20, 2017
978-1-5090-1572-6/17/$31.00 ©2017 IEEE 1807