Delft University of Technology
A sliding mode observer approach for attack detection and estimation in Autonomous
Vehicle Platoons using event triggered communication
Keijzer, Twan; Ferrari, Riccardo M.G.
DOI
10.1109/CDC40024.2019.9029315
Publication date
2019
Document Version
Final published version
Published in
Proceedings 2019 IEEE 58th Conference on Decision and Control (CDC 2019)
Citation (APA)
Keijzer, T., & Ferrari, R. M. G. (2019). A sliding mode observer approach for attack detection and estimation
in Autonomous Vehicle Platoons using event triggered communication. In
Proceedings 2019 IEEE 58th
Conference on Decision and Control (CDC 2019)
(pp. 5742-5747). IEEE .
https://doi.org/10.1109/CDC40024.2019.9029315
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A Sliding Mode Observer Approach for Attack Detection and Estimation in
Autonomous Vehicle Platoons using Event Triggered Communication
Twan Keijzer
Delft Centre for Systems and Control
Delft University of Technology
t.keijzer@tudelft.nl
Riccardo M.G. Ferrari
Delft Centre for Systems and Control
Delft University of Technology
r.ferrari@tudelft.nl
Abstract— Platoons of autonomous vehicles are being inves-
tigated as a way to increase road capacity and fuel efficiency.
Cooperative Adaptive Cruise Control (CACC) is one approach
to controlling platoons longitudinal dynamics, which requires
wireless communication between vehicles. In the present paper
we use a sliding mode observer to detect and estimate cyber-
attacks threatening such wireless communication. In particular
we prove stability of the observer and robustness of the de-
tection threshold in the case of event-triggered communication,
following a realistic Vehicle-to-Vehicle network protocol.
I. INTRODUCTION
Autonomous vehicle platoons and Cooperative Adaptive
Cruise Control (CACC) are topics that received significant
attention by researchers in recent years [1]–[6]. CACC
is a longitudinal cooperative control technique that allows
platoons, or strings, of autonomous vehicles to coordinate
themselves. The goal is to have vehicles in the platoon trav-
elling closer together than human drivers, or non-cooperative
control approaches like Adaptive Cruise Control, can. Ben-
efits of this lower inter-vehicle spacing include better fuel
efficiency and road utilization. Vehicles in a CACC platoon
measure relative position and velocity of the preceding
vehicle, and also communicate (see figure 1) in order to attain
string stability, which is an important property resulting in
dampening of velocity changes down the platoon [6].
Wireless communication!
ii+1 i-1
v v v
i
d
i-1 i+1
i+1 i-1
i
d
d
radar!
Fig. 1. CACC equipped string of vehicles. The V2V communication is
implemented wirelessly, and is subjected to a class of cyber attacks.
The reliance of CACC platoons on inter-vehicle wireless
communications, be it periodic or event-triggered [7]–[9],
may expose them to the same kind of threats as other
networked control systems or Cyber-Physical Systems (CPS),
such as Denial of Service (DoS), routing, replay and stealthy
data injection attacks (see [10], [11]). Indeed, vulnerabilities
of Vehicle-to-Vehicle (V2V) networks to cyber attacks have
been investigated in [12]–[15]. While CACC can provide
limited robustness to network induced effects such as random
packet losses (see [16], [17]), the case of a malicious
attacker targeting the (V2V) network should be addressed
by dedicated detection and fault-tolerant control methods.
While the case of faults in autonomous vehicles forma-
tions was addressed in [18] and [19] with an observer-
based approach, few works dealt with cyber-attacks. [20]
considered the problem of designing a model based observer
for detecting DoS attacks, which were characterised as an
equivalent time delay in the communication network.
In this paper we are going to extend some preliminary
results presented by the authors in [21], where a Sliding-
Mode Observer (SMO) was introduced for estimating false
data injection attacks. The contribution of the paper is
twofold: we prove the stability of the SMO under event-
triggered communication and less restrictive assumptions on
measurement uncertainties, and we introduce robust adaptive
attack detection thresholds for such a scenario. In particular,
we will assume the vehicle platoon is using a realistic event-
triggered communication protocol based on the current ETSI-
ITS G5 V2V communication standard [22], [23].
The use of sliding mode observers for fault detection
was pioneered by [24] and developed further by [25], [26],
amongst others. By monitoring the so-called equivalent out-
put injection (EOI), this method allows to estimate actuator
and sensor faults or, as in [21] and the present case, a false
data injection attack. Previous results considered continuous
communication, and did not derive an adaptive detection
threshold guaranteed to be robust against uncertainties or
communication-induced effects. The literature on fault detec-
tion for event-triggered systems, instead, includes works such
as [27]–[29], which are concerned with the simultaneous de-
sign of the triggering condition and the fault detector, while
[30] addressed the case of asynchronous communication and
packet loss for fault detection of networked control systems.
While several works considered the case of event-triggered
sliding mode control, such as [31]–[34], the present approach
would be, to the best of the authors knowledge, the first
contribution considering sliding mode observers for fault,
or cyber-attack detection and estimation in systems where
event–triggered communication is present.
The remainder of the paper is organized as follows.
Section II introduces event-triggered CACC for a vehicle
platoon and describes the attack and its effect on the platoon.
Section III presents the sliding mode observer and character-
izes its stability, and section IV presents the attack detection
threshold and provides theoretical results on its robustness.
Section V provides preliminary results on attack estimation.
In sections VI and VII, respectively, the simulation results,
and conclusion and future work are presented.
A. Notation
Throughout the paper, a notation such as x
i
will denote a
variable x pertaining to the i–th vehicle, while x
i,(j)
will
denote the j–th component of the vector x
i
.
2019 IEEE 58th Conference on Decision and Control (CDC)
Palais des Congrès et des Expositions Nice Acropolis
Nice, France, December 11-13, 2019
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II. PROBLEM FORMULATION
A. Error Dynamics of a Platoon using CACC
In the present paper we will use the CACC formulation
in [6] and its extension to event triggered communication
introduced in [8], while the event-triggering condition will
follow [22], [23]. We will consider a string of m ∈ N
homogeneous vehicles (see Figure 1), each modeled as
"
˙p
i
(t)
˙v
i
(t)
˙a
i
(t)
#
=
"
v
i
(t)
a
i
(t)
1
τ
(u
i
(t) − a
i
(t))
#
, (1)
where p
i
(t), v
i
(t), a
i
(t) and u
i
(t) ∈ R are the position,
velocity, acceleration and the input of the i-th vehicle, re-
spectively; furthermore, τ represents the engine’s dynamics.
Each vehicle is assumed to measure its own local output y
i
,
[p
i
v
i
a
i
]
>
+ ξ
i
and, with its front radar, the relative output
y
i,i−1
, [d
i
∆v
i
]
>
+ η
i
, where d
i
(t) , (p
i−1
(t)−p
i
(t)−L)
is the inter-vehicle distance, L is the length of each vehicle,
∆v
i
, v
i−1
− v
i
is the relative velocity and ξ
i
and η
i
are
the measurement uncertainties affecting the vehicle sensors.
Assumption 1: For each i–th vehicle, the measurement
uncertainties ξ
i
and η
i
are unknown but they are upper
bounded by known quantities
¯
ξ
i
and ¯η
i
, i.e. |ξ
i,(j)
(t)| ≤
¯
ξ
i,(j)
(t) and |η
i,(j)
(t)| ≤ ¯η
i,(j)
(t) for all j, and all t.
The objective of the i–th vehicle is to keep a desired inter-
vehicle distance d
r,i
using a constant time headway policy
d
r,i
(t) = r
i
+ hv
i
(t) , (2)
while making the relative velocity ∆v
i
tend to zero in steady
state. in eq. (2) r
i
and h are the desired distance at stand still,
and the time headway between the vehicles respectively. [6]
Let us introduce the position error e
i
(t) , d
i
(t) − d
r,i
(t)
and its time derivative ˙e
i
(t) = ∆v
i
−ha
i
(t). In [6], a CACC
control law is initially proposed in ideal conditions, as the
solution to the following equation
˙u
i
(t) =
1
h
[−u
i
(t) + (k
p
e
i
(t) + k
d
˙e
i
(t)) + u
i−1
(t)] . (3)
As can be seen from Eq. (3), the local control law depends
on measured quantities, such as the relative position and
velocity, which will be corrupted by noise. Furthermore,
the control law depends on the intended acceleration of the
preceding vehicle, u
i−1
(t), which shall be received through
a wireless V2V communication network.
In this paper the presence of measurement uncertainties
and non-ideal communication are explicitly incorporated in
the control law giving
˙u
i
(t) =
1
h
h
−u
i
(t) +
k
p
ˆe
i
(t) + k
d
ˆ
˙e
i
(t)
+ ˜u
i−1
(t)
i
, (4)
where ˆe
i
, e
i
+η
i,(1)
−hξ
i,(2)
,
ˆ
˙e
i
, ˙e
i
+η
i,(2)
−hξ
i,(3)
, and
˜u
i−1
(t) = u
i−1
(t) + ∆u
i−1
(t) is the last received value of
u
i−1
(t). ∆u
i−1
will be further defined in subsection II-B.
By following similar steps as in [6] and [21], we can write
the i–th vehicle error dynamics, under control law (4), as
E
i
:
˙x
e
i
(t) = A
e
x
e
i
(t) + B
e
ζ
i
(t)
y
e
i
(t) = C
e
x
e
i
(t) + D
e
ζ
i
(t)
, (5)
where C
e
= D
e
and the following quantities were introduced
A
e
,
"
0 1 0
0 0 1
−
k
p
τ
−
k
d
τ
−
1
τ
#
, B
e
,
"
0 0 0
0 0 0
−
k
p
τ
−
k
d
τ
−
1
τ
#
C
e
,
1 0
0 1
0 0
>
, x
e
i
,
"
e
i
(t)
˙e
i
(t)
¨e
i
(t)
#
, ζ
i
,
"
η
i,(1)
− hξ
i,(2)
η
i,(2)
− hξ
i,(3)
∆u
i−1
(t)
#
(6)
The stability and performance of the error dynamics E
i
and
the string-stability of the platoon have been analysed in [6]
and [8]. As the present paper is concerned with the design
of a cyber-attack detection and estimation scheme, and not
the event-triggered CACC control scheme itself, for well-
posedness we will require the following
Assumption 2: Control law u
i
(Eq. (4)) and triggering
condition σ (Eq. (8)) are chosen such that, without cyber-
attacks and when Assumption 1 holds, E
i
is stable for each
vehicle i and string stability of the platoon is guaranteed.
B. Attack and communication-induced effects
In this paper, following [8], [22], [23], the transmission of
u
i−1
is assumed to be event triggered. Furthermore a man-in-
the-middle attack on the transmitted u
i−1
is considered. We
are not interested here in the actual implementation of the
attack, for this, one can refer to [12]–[15]. For the observer,
the effects of communication, ∆u
i−1,C
(t), and the attack,
φ
i
(t), will be combined in ∆u
i−1
(t) = ∆u
i−1,C
(t) + φ
i
(t).
The event-triggered communication causes a variable de-
lay in the signal received by car i, defined as
τ
0
= 0, τ
l+1
, inf {t ≥ τ
l
: σ = 1} , (7)
where τ
l
is the last transmission time, and σ is a triggering
condition based on the local measurements, y
i−1
, in car i−1:
σ , (t − τ
l
≥ T
H
∨ (t − τ
l
> T
L
∧
∃j = {1, 2} : |y
i−1,(j)
(τ
l
) − y
i−1,(j)
(t)| ≥ ∆y
L,(j)
)).
(8)
Here T
L
, T
H
and ∆y
L
∈ R
2
are user-designed parameters
that define, respectively, the minimum and maximum inter-
triggering times, and the threshold for communication.
In summary, communication is triggered on changes in
local measurements of car i−1 since the last communication.
This is combined with a minimum and maximum inter-
triggering time. The error introduced by the event-triggered
communication is denoted by ∆u
i−1,C
(t).
III. SLIDING MODE OBSERVER
In this section a Sliding Mode Observer (SMO) for the
dynamics E
i
in eq. (5) is presented. To this end, first the
change of variables z
1,i
=
h
x
e
i
,(1)
x
e
i
,(2)
i
, ζ
1,i
=
ζ
i,(1)
ζ
i,(2)
, z
2,i
=
x
e
i
,(3)
, b = −
1
τ
is performed in order to separate the
measured and unknown states, giving:
h
˙z
1,i
˙z
2,i
i
=
h
A
11
A
12
A
21
A
22
ih
z
1,i
z
2,i
i
+
h
0
A
21
ζ
1,i
+ b∆u
i−1
i
, (9)
y
e
i
= z
1,i
+ ζ
1,i
. (10)
An observer design is presented, in eqs. (11) and (12), to
make the states slide along
y,i
(t) = 0 even in the presence
of noise-, communication- and attack-induced effects.
ˆ
˙z
1,i
ˆ
˙z
2,i
=
h
A
11
A
12
A
21
A
22
ih
ˆz
1,i
ˆz
2,i
i
−
h
ν
i
0
i
(11)
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ν
i
(t) = (A
11
+ P )
y,i
(t) + M
i
sgn(
y,i
(t)) (12)
Here M
i
is a positive constant, and P ∈ R
2×2
is a positive
definite matrix. Both are chosen to they verify the hypothesis
of Theorem 1, to guarantee the SMO stability. The observer
error dynamics can be written as in eqs. (13), (14).
1,i
(t) = ˆz
1,i
(t) − z
1,i
(t)
2,i
(t) = ˆz
2,i
(t) − z
2,i
(t)
y,i
(t) = ˆz
1,i
(t) − (z
1,i
(t) + ζ
1,i
) =
1,i
(t) − ζ
1,i
(13)
˙
i
(t) =
h
A
11
A
12
A
21
A
22
i
i
(t)−
ν
i
(t)
A
21
ζ
1,i
(t) + b∆u
i−1
(t)
(14)
Theorem 1:
1,i
(t), under the observer dynamics in (14),
can be bounded by ¯
1
=
¯
ζ if M
i
> |A
12
¯
2,i
| +
A
11
¯
ζ
.
Proof: This proof will only consider the upper bound of
1,i
(t), the lower bound can be proved in a similar manner. It
will be proven that if
1,i
>
¯
ζ, then ˙
1,i
< 0. This is sufficient
to prove
¯
ζ ≥
1,i
∀ t. First note that
1,i
>
¯
ζ implies
y,i
> 0,
so the first row of eq. (14) can be rewritten to
˙
1,i
= P (ζ
1,i
−
1,i
) + A
11
ζ
1,i
+ A
12
2,i
− M
i
(15)
Substituting the condition on M
i
gives
˙
1,i
<P (ζ
1,i
−
1,i
) + (A
11
ζ
1,i
− |A
11
¯
ζ|)
+ (A
12
2,i
− |A
12
¯
2,i
|) ≤ 0
(16)
¯
ζ, ¯
2,i
and other bounds are proven in the appendix.
In this paper, as in [24] and subsequent works on SMO-
based fault estimation, the EOI, derived from ν
i
, will be
used for estimating attacks [24]. The EOI used here will be
obtained from the filter in eq. (17) [35].
ν
i,fil
=
K
s + K
ν
i
, (17)
where K > 0 is a design constant and s is the Laplace
domain complex variable.
IV. ATTACK DETECTION THRESHOLDS
As a novel contribution, we are introducing two pairs of
robust attack detection thresholds on ν
i,fil
, which are guar-
anteed against false alarms, even in the presence of mea-
surement uncertainties and event-triggered communication.
Each pair will comprise an upper and a lower bound on the
values of ν
i,fil
in non-attacked conditions. The two pairs
are termed One-Switch-Ahead (OSA) and Multiple-Switches-
Ahead (MSA) thresholds, for reasons that will be apparent
in next sections. For the sake of clarity, in Subsections IV-A
and IV-B we will assume there is no event-triggered com-
munication, i.e. ∆u
i−1,C
(t) = 0. The effects of its presence
on the thresholds will be illustrated in Subsection IV-C.
For the sake of notation, we will assume that the SMO is
initialized at time t
0
, and that sgn(
y,i
(t
0
)) = 1. This means
that between t
0
and the next switch at t
1
, and all following
odd intervals [t
2k
t
2k+1
], with k ∈ N, the discontinuous
term ν
i
and
y,i
(t) are positive, ν
i,fil
will be increasing, and
1,i
(t) will be decreasing. This is also shown in Figure 2.
Furthermore ν
i,fil
will be initialised at ν
i,fil
(t
0
) = 0 and we
will denote a threshold value calculated at t
k
by ¯ν
i,fil
(t
k
).
For brevity, we will derive only the upper bound of each
threshold, which is of interest in the odd time intervals, as the
lower bounds and the behaviour during even time intervals
can be obtained via similar reasoning.
A. One-Switch-Ahead (OSA) Threshold
Let us consider the behaviour of ν
i,fil
during the odd
interval, [t
2k
t
2k+1
] (see Figure 2a). By introducing, in eq.
(18), the upper bound ¯ν on ν
i
, the time domain solution to
(17) can be upper bounded during the interval as in eq. (19).
¯ν =
(A
11
+ P )(¯
1
+
¯
ζ)
+ M
i
(18)
ν
i,fil
(t) ≤ e
−K(t−t
2k
)
ν
i,fil
(t
2k
) + (1 − e
−K(t−t
2k
)
)¯ν (19)
Remark 1: The right-hand side of eq. (19) is an upper
bound for ν
i,fil
(t). However, it can be easily proved that
the inequality in eq. (19) will also hold in case of an attack.
Therefore, it is not a valid threshold for attack detection.
Next, in eq. (19), the hypothetical maximum time between
switches
¯
t = max(t
2k+1
− t
2k
) can be defined as an upper
bound for t. It will be shown in the following that this bound
can be exceeded in case of an attack, and therefore eq. 20
is a valid threshold for attack detection.
¯ν
i,fil,OSA
(t
2k
) = e
−K
¯
t
ν
i,fil
(t
2k
) + (1 − e
−K
¯
t
)¯ν , (20)
¯
t corresponds to the longest time for which
y,i
=
1,i
−
ζ
1,i
can stay positive. This is the case when
1,i
decreases
from its maximum value, ¯
1
, to its minimum value, −¯
1
,
with a minimum rate ˙
1
= min(|˙
1,i
|). Note that, for this to
happen, ζ
1,i
<
1,i
during the whole time. This is visualised
in Figure 2b and results in the following expression for
¯
t
¯
t =
2¯
1
˙
1
(21)
The bounds, ¯
1
, ˙
1
, and
¯
ζ are derived in theorem 1, Appen-
dices A and C respectively, and shown in eqs. (22)-(24).
¯
1
=
¯
ζ =
¯η
i,(1)
+ h
¯
ξ
i,(2)
¯η
i,(2)
+ h
¯
ξ
i,(3)
(22)
˙
1
= − |A
12
¯
2,i
| + M
i
(23)
¯
2,i
=
2,i,0
e
A
22
t
−
2A
21
¯
ζ − b∆u
i−1
A
22
(24)
One can see in eq. 24 that ¯
2,i
depends on the attack. The
threshold is designed assuming no attack, so ∆u
i−1
= 0.
Therefore, it is easy to check that if there is an attack,
2,i
can become bigger than ¯
2,i
(with ∆u
i−1
= 0). Therefore
eq. 20 is a valid threshold for attack detection.
At t
2(k+1)
this threshold needs to be recalculated using a
new initial value of ν
i,fil
(t
2(k+1)
), as illustrated in Figure 2.
This re-initialisation on the signal the threshold is attempting
to bound leads to inconsistent detection. Even though an
attack can cause detection between recalculations, it is also
dependent on the noise behaviour. As before, ζ
1,i
<
1,i
needs to hold during
¯
t for the threshold to be reached, and
even though this chance is non-zero in case of an attack, in
every period [t
2k
t
2k+1
] there is a large chance an attack
is not detected. Therefore in the next section a threshold is
designed that is not dependent on ν
i,fil
.
B. Multiple-Switches-Ahead (MSA) Threshold
The MSA threshold is based on the possible behaviour of ν
fil
over more than one switch ahead in time, after a hypothetical
occurrence of the worst case behaviour considered for the
OSA threshold.
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