# IEEE Systems, Man and Cybernetics Magazine - April 2021 - 44

```that can detect attacks. Data-driven and machine learningbased intrusion detection strategies employ several
approaches, such as intelligent methods [e. g., neural networks (NNs)] [119], [120], support vector machines (SVMs)
[121], [122], and naive Bayesian classifiers [123]. These
strategies rely on past system data. Therefore, their effectiveness and accuracy depend on the quality of historical
information and factors such as data noise and accuracy,
data from various operating regimes, healthy versus faulty
data, and data during various attack conditions. In the following, we survey representative data-based works.
Intelligent Strategies
Intelligent approaches [e. g., NNs and adaptive neuro-fuzzy
inference systems (ANFISs)] often build networks, including several nodes in multiple layers, to construct nonlinear
estimators to classify attacks. A data-driven method based
on an ensemble of nonlinear NNs is presented in [124] to
detect attacks against CPSs. The strategy consists of preprocessing, feature selection, and classification methods.

Algorithm 3. A resilient sliding mode
controller [118].
1)	Consider a state-space discrete linear mathematical
model of a CPS:

x (k + 1) = Ax (k ) + Bu (k )

y (k ) = Cx (k ),

(13)

where x (k ) ! R n , u (k ) ! R n , and y (k ) ! R n indicate
the state vector, control input, and measurement output,
respectively. Matrices A, B, and C denote system, input,
and output matrices, respectively, which are known. Matrix B is full rank.
2)	The state vector is observed by
x

u

y

Initialize Data Set

Attribute Arrangement

xt (k + 1) = Axt (k ) + Bu (k ) + L a(k) e DoS (k ), (14)

where xt (k ) denotes the estimated state. Vector L a(k )
indicates a switching gain that must be designed; a(k )
is a sequence with values of zero or one, representing a CPS attack or a normal condition, respectively;
e DoS (k ) = yr (k ) - yt (k ); and yt (k ) = Cxt (k ) ! R n implies
the estimated output. If there is an attack, yr (k ) = 0, while
for a normal condition, yr (k ) = y (k ).
3)	The exponentially stability of a closed-loop CPS is guaranteed if a sliding mode surface and a control input are
designed as follows:
y

s (k ) = G i xt (k ) - G i (A + BK i ) xt (k - 1)
u (k ) = K i xr (k ) - (G i B ) -1||G i L a(k) e DoS(k)||sign(s (k ))

-||K i (xr (k ) - xt (k )||sign(s (k )) - (G i B ) -1 / s (k ), (15)
where G i (i ! {0,1}) present known matrices that make
G i B hold a nonsingular property, and L a(k ) and K i are
designed to provide exponential stability. Moreover, /
denotes a regulating matrix to be designed; xr (k ) = xt (k )
for a CPS during a DoS attack, and xr (k ) = x (k ) for a CPS
under normal conditions. Generally, for stability, a positive
Lyapunov function Vs (k ) = (1/2) s T (k ) s(k ) is defined.
Then, TVs (k ) must be negative by regulating / to be
large enough, and unknown variables and parameters
are determined to satisfy this condition.

44

The preprocessing applies a third-order Butterworth lowpass filter to remove high-frequency signals resulting from
sensor measurement errors. A column-wise exaggeration
algorithm based on an average technique is utilized to
reduce the data size for the training phase. A correlation
analysis using a standard Pearson product-moment correlation coefficient is applied to identify suitable features.
Afterward, an artificial NN is implemented for the classification task to isolate attacks in the system. Simulation
results on power system data recorded in Denmark showed
a 97.6% attack detection accuracy. In [125], the authors integrate a hierarchical neuron architecture (HNA)-based NN,
and they introduce an intrusion-weighted particle (IWP)based cuckoo search optimization (CSO) technique to
diagnose SCADA intrusions. The proposed method consists
of two steps. First, optimal features are selected using the
IWP-CSO method. Then, a classifier based on an HNA-NN
is developed to identify attacks. Figure 8 presents the intrusion classification optimization algorithm. The approach is
tested and compared with other methods, such as SVMs,
and the results show better classification accuracy. Table 1
illustrates the performance of various strategies.
A data-driven cybersecure estimation approach using
an NN is developed in [126]. The physical model is combined with a generative adversarial network to detect deviations from normal measurements. A smooth training

IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE Apri l 2021

Cluster Initialization

Label Clustering

Feature Optimization
(IWP-CSO)

Training Data

Best Attribute Selection

Classification
(HNA-NN)

Best Selected
Training Data

Attack Label

Figure 8. The optimization algorithm for intrusion

classification [125].

```

# IEEE Systems, Man and Cybernetics Magazine - April 2021

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