无线网络控制系统中DoS攻击的最优调度策略

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"这篇2016年的文章来源于《IEEE Transactions on Control System Technology》,卷24,第3期,作者包括Heng Zhang, Peng Cheng, Ling Shi和Jiming Chen,探讨了无线网络控制系统（WNCS）中的DoS攻击调度策略。文章关注的是攻击者如何在有限的能量条件下优化其攻击计划，以最大程度地破坏系统性能。" 在无线网络控制系统中，DoS（拒绝服务）攻击是一种常见的安全威胁，它可以干扰通信，导致系统性能急剧下降。近年来，虽然已有许多文献研究了WNCS的安全问题，但针对攻击者如何有效地安排攻击时间以最大化影响的研究却相对较少。本文填补了这一研究空白，专注于控制系统的性能表现。文章首先分析了在任意攻击计划下，线性二次高斯（LQG）控制成本函数的特性。LQG控制是一种广泛应用的优化控制理论，它结合了线性控制和统计决策理论，以最小化系统的预期性能指标。在考虑到攻击者的能量限制后，作者推导出了最优的干扰攻击计划以及相应的成本函数。这样的优化攻击策略旨在最大程度地增加LQG控制成本，从而破坏系统的正常运行。此外，文章还讨论了在最优攻击计划下系统的稳定性问题。这涉及到分析系统在持续攻击下的动态行为，以确定是否存在一种攻击方式可以使系统失去稳定性。进一步，研究扩展到了具有多个子系统的WNCS。在这种复杂环境中，攻击者可能需要更精细的策略来同时或依次攻击多个子系统，以实现最大的破坏效果。通过不同的示例，文章展示了这些优化攻击计划如何影响系统性能，从而提供了对实际安全威胁的深入理解。这篇论文对于理解WNCS的安全脆弱性、设计防御策略以及优化攻击者的行为都具有重要的理论和实践价值。它不仅为系统设计者提供了关于潜在风险的知识，也为未来的安全研究指明了方向，特别是在考虑资源受限的攻击者策略时。

IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 24, NO. 3, MAY 2016 843

Optimal DoS Attack Scheduling in Wireless

Networked Control System

Heng Zhang, Peng Cheng, Member, IEEE,LingShi,Member, IEEE,

andJimingChen,Senior Member, IEEE

Abstract—Recently, many literature works have considered the

security issues of wireless networked control system (WNCS).

However, few works studied how the attacker should optimize

its attack schedule in order to maximize the effect on the

system performance due to the insufﬁciency of energy at the

attacker side. This paper ﬁlls this gap from the aspect of

control system performance. We consider the optimal jamming

attack that maximizes the Linear Quadratic Gaussian (LQG)

control cost function under energy constraint. After analyzing

the properties of the cost function under an arbitrary attack

schedule, we derive the optimal jamming attack schedule and the

corresponding cost function. System stability under this optimal

attack schedule is also considered. We further investigate the

optimal attack schedule in a WNCS with multiple subsystems.

Different examples are provided to demonstrate the effectiveness

of the proposed optimal denial-of-service attack schedule.

Index Terms—Attack scheduling, Denial-of-Service (DoS)

attack, energy constraint, Linear Quadratic Gaussian (LQG)

control, system stability.

I. INTRODUCTION

IRELESS networked control systems (WNCSs),

in which physical elements (plants, sensors,

controllers, and actuators) communicate via wireless networks,

have received increasing research interests [1]–[4]. WNCSs

have a wide spectrum of applications in mobile sensor

networks, remote surgery, intelligent transportation, unmanned

aerial vehicles, mobile robots, and so on. Security issues in

WNCSs have been investigated from different viewpoints in

Manuscript received January 26, 2015; revised May 18, 2015; accepted

July 8, 2015. Date of publication August 26, 2015; date of current version

April 18, 2016. Manuscript received in ﬁnal form July 19, 2015. This work

was supported in part by the National Natural Science Foundation of China

under Grant U1401253 and Grant 61429301, in part by the National Program

for Special Support of Top Notch Young Professionals, and in part by

the Fundamental Research Funds for the Central Universities under

Grant 2014XZZX001-03. The work of L. Shi was supported by

The Hong Kong University of Science and Technology Caltech Partnership

under Grant FP004. The work of H. Zhang was supported by the University

Science Research General Project of Jiangsu Province under

Grant 15KJB510002. Recommended by Associate Editor Y. Shi.

(Corresponding author: Jiming Chen.)

H. Zhang is with the State Key Laboratory of Industrial Control

Technology, Cyber Innovation Joint Research Center, Zhejiang University,

Hangzhou 310027, China, and also with the Huaihai Institute of Technology,

Lianyungang 222000, China (e-mail: ezhangheng@gmail.com).

P. Cheng, and J. Chen are with the State Key Laboratory of

Industrial Control Technology, Cyber Innovation Joint Research

Center, Zhejiang University, Hangzhou 310027, China (e-mail:

pcheng@iipc.zju.edu.cn; jmchen@ieee.org).

L. Shi is with the Department of Electronic and Computer Engineering,

The Hong Kong University of Science and Technology, Hong Kong (e-mail:

eesling@ust.hk).

Color versions of one or more of the ﬁgures in this paper are available

online at http://ieeexplore.ieee.org.

Digital Object Identiﬁer 10.1109/TCST.2015.2462741

recent years due to the increasing amount of cyber attacks

that make WNCSs more and more vulnerable [5]–[9].

Various efforts have been devoted to studying the inﬂuence

of speciﬁc malicious attacks, e.g., Denial-of-Service (DoS)

attacks [10], replay attacks [11], and data injection attacks [7],

on particular systems. Thereinto, the DoS attack, which aims

to prevent the communication between system components,

has been widely studied since this attack pattern is the

most accomplishable one and can result in serious conseque-

nces [10], [12], [13]. A typical DoS technique in WNCS is

jamming attack, which can interfere with the radio frequencies

on the communication channels [14].

Recently, researchers have studied the LQG problems under

DoS attack [10], [15], [16]. A semideﬁnite programming-based

solution was presented in [10] to ﬁnd an optimal feedback

controller that minimizes a cost function subject to safety and

energy constraints in the presence of an attack with identical

independent distributed actions. In [15], the optimal control

law is designed against an intelligent jammer with limited

actions. In [16], an event-trigger control strategy is derived

in the presence of an energy-constrained periodic jamming

attacker. The common characteristic of these related works

is that they aim to ﬁnd optimal defensive control law. Our

work, however, is from the viewpoint of the attacker,

i.e., we look for the optimal attack strategies to maximize

the LQG cost function. This is equally important as one can

design an effective defensive control law only when he knows

how the attacker behaves.

In almost all types of attacks, energy constraint is

inherent and will affect an attacker’s strategies [17]–[19].

Kashyap et al. [17] studied a zero-sum game on Multiple Input

Multiple Output (MIMO) Gaussian Rayleigh fading channels

between an intelligent DoS jammer and a decoder with bilat-

eral power constraints. Li et al. [18] investigated the optimal

jamming attack strategies by controlling the probability of

jamming and transmission range. Zuba et al. [19] studied

the effect of jamming attack on underwater wireless sensor

networks and investigated the minimal energy consumption

and the probability of detection in order to launch an effective

DoS jamming attack.

In this paper, we aim to design an optimal attack schedule

to maximize the attacking effect on the WNCS. Speciﬁcally,

we ﬁrst consider a system where one sensor measures the

system state and sends the data packets to a remote estimator

through a wireless channel. The attacker has a limited energy

budget in every active period and decides at each sampling

time whether or not to jam the channel. Then, we extend it

to the scenario with multiple subsystems. In this scenario, the

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