IEEE Systems, Man and Cybernetics Magazine - April 2021 - 43

isolating an abnormality, the communication channel will
be alerted to provide a resilient, secure framework.
Sliding Mode Observers
Sliding mode controllers and observers are categorized as
model-based, nonlinear approaches for control and estimation tasks. They also utilize a state-space mathematical
model to control uncertain systems and estimate states
based on output measurements. A sliding mode strategy
forces a system state toward a manifold, from which state
trajectories and estimation errors slide toward the origin
of the state space, hence regulating the state when controlling the system and forcing the estimate of the state
toward its actual value, all in a finite time and in the face
of uncertainties and disturbances. Therefore, sliding mode
control and estimation strategies have desirable properties, such as robustness, simple implementation, and disturbance rejection [106], [112], [113]. However, since
switching is inherent to sliding mode strategies, such
approaches may cause chattering, excite unmodeled
dynamics, and lead to energy losses and damage to instruments, such as actuators, due to possible high-frequency
switching around the sliding surface [112]. Therefore, a
soft sliding mode is used instead of a hard mode to reduce
adverse effects and improve efficiency [114].
Corradini and Cristofaro [115] develop an attack isolation method based on a sliding-mode technique for CPSs.
The system under attack is considered to be linear and to
have unknown inputs perturbing the state and measurements. A robust state observer is designed to detect and
reconstruct the attack, with guaranteed performance.
Bounded external perturbations and modeling errors are
exposed, and the attack detector is robust to undesirable
effects that are typically present. Note that the suggested
sliding mode method requires knowledge of an upper bound
on the severity of an attack. A sliding mode observer is
introduced in [116] for CPSs with unknown inputs. Cyberattacks target CPSs through sensors. Attacks, states, and
unknown inputs are augmented into a state-space model in
the form of a descriptor system, which is basically a differential algebraic representation. A sliding mode observer is
developed to reconstruct attacks, states, and unknown
inputs. Convergence conditions are also proved. Simulations indicate the effectiveness of the proposed strategy.
A finite-time sliding mode controller is developed in
[117] for CPSs represented as a Markovian jump system.
Randomly occurring injection attacks in a probabilistic
manner are launched in control signals. A sliding mode
controller is developed so that state trajectories are forced
to a specified sliding surface within a given time. Modedependent scalars are inserted into the coupled Lyapunov
inequalities to obtain feasible solutions for closed-loop
CPS finite-time boundedness. Tests on a robot arm confirm the controller's performance. A resilient control method is proposed in [118] for CPSs experiencing DoS attacks.
A physical system is formulated with a switched model,
	

which can be analyzed using attack duration and frequency. A switching sliding mode controller is designed to
maintain stability during attacks. The resilient sliding
mode controller is illustrated in Algorithm 3.
An observer is also developed to reconstruct data that
are unavailable during a DoS attack. A defense policy is
defined using an integration of zero-sum-game theory and
attack duration and frequency to determine a switching
logic for the resilient controller. Simulation results indicate
that the proposed controller performs well.
Data-Driven Methods
Data-driven methods are effective whenever a mathematical model of a system is not readily available or difficult to
construct and when a system contains parameter uncertainties. To be effective, data-driven approaches require
the availability of rich historical system data under various
operating conditions. The main objective of data-driven
cybersecure control strategies is to use past historical
data from a system to design an estimator or a classifier
Algorithm 2. A detector for multiagent
CPSs [111].
1)	Consider that n agents are connected in a CPS. The
state-space discrete linear model for agent i is formulated as follows:
	

x i (k + 1) = Ax i (k ) + Bu i (k ) + B d d (k ) + B f f (k )

y i (k ) = Cx i (k ) + D d d (k ) + D f f (k ),

(10)

	where x i (k ) ! R n , u i (k ) ! R n , y i (k ) ! R n , d (k ) ! R n ,
and f (k ) ! R n represent state, control, output, disturbance, and fault vectors for agent i, respectively. Matrices
A, B, C, B d ,   B f ,   D d ,  and D f are known, with appropriate
dimensions for agent i.
2)	The multiagent observer-based detector is designed as
follows:
x

u

y

d

f

xt ij (k + 1) = Axt ij (k ) + Bu i (k ) + L (y ij (k ) - yt ij (k ))
	

yt ij (k ) = Cxt ij (k )
r ij (k ) = V (y ij (k ) - yt ij (k )),

(11)

	where xt ij(k ) and yt ij (k ) indicate the estimated state and
estimated output of i, provided by node j. Here, u i (k ) are
produced by the communication network, L and V are
designed by optimization, and r ij denotes the residual of
i estimated by j. If J thj #||r ij (k )||2, an anomaly is detected.
Otherwise, there is no anomaly. Attacks and disturbances
can be distinguished from faults by a cooperative detector using multiple agents, such that
influenceattacksanddisturbances
" Min. (12)
	
faultinfluence

Vehicle 4

Vehicle 2
Vehicle 1

Vehicle 5

Vehicle 3

Figure 7. A multiagent vehicle system [111].

Ap ri l 2021

IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE	

43



IEEE Systems, Man and Cybernetics Magazine - April 2021

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