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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI 10.1109/TAC.2019.2953210, IEEE
Transactions on Automatic Control
IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1
Observer-Based Control for Cyber-Physical Systems With
Periodic DoS Attacks Via A Cyclic Switching Strategy
Yanzheng Zhu, Member, IEEE and Wei Xing Zheng, Fellow, IEEE
Abstract—This paper studies the observer-based output feedback
control problem for a class of cyber-physical systems with periodic
Denial-of-Service (DoS) attacks, where the attacks coexist both in the
measurement and control channels in the network scenario. The periodic
DoS attacks are characterized by a cyclic dwell-time switching strategy,
such that the resulting augmented system can be converted into a class
of discrete-time cyclic dwell-time switched systems including a stable
subsystem and an unstable subsystem. By means of a cyclic piecewise
linear Lyapunov function approach, the exponential stability and l
2
-
gain analysis, and observer-based controller design are carried out for
the augmented discrete-time cyclic switched system. Then the desired
observer and controller gains in piecewise linear form are determined
simultaneously so as to ensure that the resulting closed-loop system is
exponentially stable with a prescribed H
∞
performance index. Finally,
a practical application of unmanned ground vehicles under periodic DoS
attacks is provided to verify the effectiveness of the developed control
approach.
Index Terms—Cyclic dwell-time switching, observer-based control,
periodic DoS attacks, piecewise linear Lyapunov functions, unstable
subsystems.
I. INTRODUCTION
Cyber-physical systems (CPSs) have been attracting more and more
attention in the fields of control engineering and industry applications.
According to the classic work [1], the denial of service (DoS) is the
most likely type of attack to control systems. Amongst DoS jammers,
a simple type is that of periodic or Pulse-Width Modulated (PWM)
jammers. From the viewpoint of the jammer, periodic signals are
motivated by energy constraints, detection avoidance, and ease of
implementation. So periodic signals represent a main type of jamming
signals studied in the communications literature, such as the IEEE
802.15.4 protocol [2] and the TCP protocol [3]. More recently, the
related works have been reported in the control field, e.g., [4]–
[10]. In particular, an irreducible and periodic Markov chain was
used to describe the periodic jamming attacks in [4], which largely
motivates us to introduce another cyclic dwell-time switching idea to
characterise the periodic DoS attacks herein. Note that controllers
may be inactive due to various environmental factors (e.g., DoS
attacks) [11], [12], such that the whole system is in an open loop
under the network environment. Therefore, the entire networked CPSs
can be regarded as a class of switched systems including a stable
subsystem in the absence of DoS attacks and an unstable subsystem in
the presence of DoS attacks. The corresponding study was originally
reported in [13] for continuous-time switched systems with average
dwell time (ADT) switching, and then was extended to other types of
switched systems with both stable and unstable subsystems [14]–[16].
This work was supported in part by the National Natural Science Foundation
of China under Grants 61973131, 61603221, and U1813201, in part by the
Scientific Research Funds of Huaqiao University under Grant 605-50Y19010,
in part by the Australian Research Council under Grant DP120104986, and
in part by the NSW Cyber Security Network in Australia under Grant
P00025091. (Corresponding author: Wei Xing Zheng.)
Y. Zhu is with the College of Mechanical Engineering and Automation,
Huaqiao University, Xiamen, Fujian 361021, China, and also with the School
of Computing, Engineering and Mathematics, Western Sydney University,
Sydney, NSW 2751, Australia (e-mail: yanzhengzhu@hqu.edu.cn).
W. X. Zheng is with the School of Computing, Engineering and Mathe-
matics, Western Sydney University, Sydney, NSW 2751, Australia (e-mail:
w.zheng@westernsydney.edu.au).
On the other hand, cyclic switching [17] (i.e., the switching signal
is cyclic, and the switching sequence and the duration belonging
to each subsystem are fixed), is usually considered as an effective
scheduling strategy once the switching sequences are required to
be preassigned. The system satisfying such a cyclic switching is of
great interest in various fields in practice, such as power circuits with
switching semiconductor devices [18], autonomous agents with peri-
odic communications [19], networked control systems with periodic
protocols [20], etc. In addition, the cyclic switching strategy can also
exhibit its superiority to cope with the parameter adaptive control
or underactuated control issues. The stability, stabilization control,
and performance analysis problems for cyclic switched systems have
been broadly examined during the past decades, see, e.g., [18], [19],
[21]–[25] and the references therein. To the best of the authors’
knowledge, the control synthesis issue of cyclic dwell-time switched
systems with both unstable and stable subsystems, originating from
the control issue of CPSs under periodic DoS attacks, has not been
fully addressed in the discrete time domain as yet, which is one of
main motivations for the current work.
Moreover, the state variables are usually not fully measurable in
many practical dynamic systems, and the observer-based output-
feedback controller design approach has been frequently used to
handle a large number of real-world issues [26]–[29]. By virtue of
the measurement outputs and control inputs, the state of dynamic
systems can be reconstructed by a state observer, and the observer-
based design strategy has been applied to cope with various advanced
control issues, such as output feedback control, supervision control,
fault tolerant control, etc. In particular, a piecewise linear Lyapunov
function approach was proposed to investigate the issues of robust
stability and state feedback controller synthesis for linear switched
systems with dwell time in [30], and further was used to study the
robust switching control issue of linear systems in [31], both of which
allow derivation of sufficient conditions in terms of linear matrix
inequalities (LMIs). What is noteworthy is that the typical CPSs
may encounter DoS attacks that periodically occur in both sides of
measurement outputs and control inputs. However, the corresponding
observer-based output feedback controller design for CPSs is still
an open issue in the face of the aforesaid network scenario, not to
mention using the cyclic switching strategy to model the periodic
DoS attacks behavior. This is another of main motivations for the
current work.
Motivated by the above discussions, the observer-based output
feedback control problem is investigated for a class of discrete-
time CPSs with periodic DoS attacks in this paper. The cyclic
dwell-time switching strategy is employed here, which ensures that
the corresponding observer-based control issue can be smoothly
addressed via the cyclic piecewise linear (CPWL) Lyapunov func-
tion approach. Both unstable (open-loop) and stable (closed-loop)
subsystems are considered at the same time owing to the occurrence
of DoS attacks. Moreover, it is assumed that the DoS attacks coexist
in both measurement and control communication channel as occurred
in reality. The main contributions in this paper are summarized as
follows: i) The cyclic dwell-time switching property is used for the
first attempt to represent the periodic DoS attack behavior of CPSs,
which coexist in both measurement and control channels; ii) The