Aerospace and Electronic Systems Magazine May 2017 - 40
Security of SCADA Systems against Cyber-Physical Attacks
Figure 6.
FDI approach for attack detection and isolation.
on cyber-physical systems. However, this work has not considered
the negative impact of random noises.
The authors in [29] and [39] have formulated the detection and
isolation of cyber-physical attacks as the problem of detecting and
isolating transient signals in stochastic-dynamical systems under
the presence of both unknown system states and random noises.
The SCADA systems have been modeled as the following discretetime state-space model:
xk +1 = Axk + Buk + Fd k + Ba ak + wk
,
yk = Cxk + Duk + Gd k + Da ak + vk
(10)
where xk ∈ n is the vector of system states with unknown initial
values x0 ∈ n, yk ∈ m is the vector of control signals, dk ∈ q is
the vector of disturbances, yk ∈ p is the vector of sensor measurements, ak ∈ s is the vector of attack signals, wk ∈ n is the vector
of process noises, and vk ∈ p is the vector of sensor noises; the
matrices A ∈ n× n, B ∈ n× m, F ∈ n× q, C ∈ p× n, D ∈ p× m, G ∈
p× q, Ba ∈ n× s, and Da ∈ p× s are assumed to be known.
Remark 1. The attack vector ak represents both physical attacks
on physical processes and cyber attacks on control signals and
sensor measurements (see Figure 6 or more details in [29] and
[39]). In addition, the attack vector ak is designed by attackers,
while the attack matrices Ba and Da are designed by system operators.
40
Let us assume that the malicious attacks are performed within
a short period τa = [k0, k0 + L − 1], where k0 is an unknown attack
instant and L is a maximum acceptable detection delay, specified
by the designer of the attack detection and isolation algorithm.
For the detection problem, the attack vector ak can be described as
0
if k < k0
ak = θ k − k0 +1 if k0 ≤ k < k0 + L ,
if k ≥ k0 + L
0
(11)
where θ1,θ2,...,θL ∈ s are the attack profiles defined in τa. For the
isolation problem, the attack vector ak can be presented as
0
if k < k0
ak = θ k − k0 +1 ( l ) if k0 ≤ k < k0 + L ,
if k ≥ k0 + L
0
(12)
where θ1(l),θ2(l),...,θL(l) are attack profiles of type l, for 1 ≤ l ≤ K,
and K is the number of hypotheses.
For the detection of transient changes (11) and (12) in the statespace model given by (10), it is advisable to minimize the worstcase probability of missed detection md subject to an acceptable
level on the worst-case probability of false alarm fa [110], [112].
Therefore, the criterion is given by
IEEE A&E SYSTEMS MAGAZINE
MAY 2017
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