Content uploaded by Riddhi Mohan Bora
Author content
All content in this area was uploaded by Riddhi Mohan Bora on Mar 17, 2022
Content may be subject to copyright.
Reduced Order Synchronization of Two Different
Chaotic Systems Using Nonlinear Active Control
with or without Time Delay
Riddhi Mohan Bora
Electrical Engineering Department
National Institute of Technology, Hamirpur
Himachal Pradesh, India
borariddhi55@gmail.com
978-1-6654-4577-1/21/$31.00 ©2021 IEEE
Bharat Bhushan Sharma
Electrical Engineering Department
National Institute of Technology, Hamirpur
Himachal Pradesh, India
bhushan@nith.ac.in
Abstract—In this article, a nonlinear active control technique
is proposed so as to attain the synchronization of two different
chaotic systems. Master and slave configuration is incorporated
for the analysis. The main objective is to design Reduced Order
Synchronization (ROS) scheme, where the order of the master
system is greater than that of the slave system. Initially, active
control technique based ROS is achieved and after that the
results are extended to address reduced order synchronization
in the presence of time delays in the systems. Based on Routh-
Hurwitz criterion and Lyapunov stability theorem, the convergent
behaviour of the error dynamics is proved. The theoretical results
are validated by the detailed simulation results for Lorenz-Stenflo
and L¨
u system.
Index Terms—active control, chaos system, reduced order
synchronization, time delay chaotic system
I. INTRODUCTION
Chaotic system and their behaviour have been of intensive
interest since last few decades. The dependency on the initial
conditions is the most common and significant property of a
chaotic system. A small adjustment or infinitesimal change in
the starting conditions might result in entirely different and
unfavourable outcomes. Because of the difficulty of accurate
prediction, it has been an eye catching and challenging prob-
lem for all the research fraternities.
Since its advent in 1990, the field of chaotic system syn-
chronization has grown significantly. The synchronizability of
two separate chaotic systems with two different sets of initial
conditions was initially presented by Pecora and Carroll [1].
Since then, researchers had tried different effective methods
to achieve the same. Due to its vast applications, synchro-
nization problem has got its high priority. Some of the areas
involves, secure communication [2], cryptography [3], robotic
synchronization [4], harmonic oscillator control [5]. Further,
the applications can be found in various engineering fields
including electrical [6], mechanical [7], chemical [8], bio-
medical [9] and many more.
In literature, several synchronization techniques are avail-
able, such as generalized synchronization [10], Q-S synchro-
nization [11], active control [12], feedback linearization [13],
observer design [14], sliding mode control [15], adaptive con-
trol [16] etc. Synchronization for same order chaotic systems
have been well exploited in the literature [12]-[16]. Reduced
order synchronization have also been studied in the work given
in [17]-[18] to some extent.
After a comprehensive study, it has been found that active
control technique is mainly utilized for same order chaotic
systems [19]-[22].
Motivated by the research gap found in the literature survey,
an active control technique to attain reduced order synchro-
nization goal with or without the effect of time delay is
presented in this paper.
There are mainly 2 contributions presented here; (i) ROS
is achieved using active control method, (ii) the analysis is
proposed while taking into account the presence of time delays
in the system dynamics.
The sections of this paper are as follows: The section-
I contains an introduction to the growth of synchronisation
strategies for chaotic systems as well as a brief history of
the subject. The problem formulation for achieving an active
control technique for synchronising different order systems is
discussed in section-II. The suggested control technique is
described in sections-III and IV, together with all necessary
assumptions, and is also applied to example chaotic systems.
The section-V carries the numerical simulation and results of
MATLAB. At last, in section-VI, the summary of the study
and future scopes are explored.
II. PRO BL EM FORMULATION
In our analysis, master and slave configuration is considered.
Let us start by defining a generalized master chaotic system
in the following way:
˙
X=AF1(X) + f1(X)(1)
where, the X∈Rnis system state vector, F1(X)∈Rn,
A∈Rn×nis the system’s parameter vector, f1(X)∈Rn
is the nonlinear continuous vector function without including
parameters.
2021 International Conference on Control, Automation, Power and Signal Processing (CAPS) | 978-1-6654-4577-1/21/$31.00 ©2021 IEEE | DOI: 10.1109/CAPS52117.2021.9730665
Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY HAMIRPUR. Downloaded on March 17,2022 at 07:14:36 UTC from IEEE Xplore. Restrictions apply.
Similarly, we can consider a different controlled slave
system which can be expressed in the generalized form as
follows:
˙
Y=A1G(Y) + g(Y) + U(2)
where, the Y∈Rmis system state vector, G(Y)∈Rm,
A1∈Rm×mis the vector of the system parameters , g(Y)∈
Rmis the nonlinear continuous vector function which does
not include parameters.
The main objective is to formulate a controller U∈Rm
so as to attain the synchronization of system (2) with the
projection part of the master system which is mentioned in (3).
Remark 1: The master system (1) has a higher order than the
slave system (2) (n>m). Reduced order synchronisation is
the term used when such systems are synced.
Let us define the projection part of the master system:
˙
Xm=AmFm(Xm) + fm(Xm)(3)
where, Xm∈Rmprojection state vector, fm(Xm)∈Rm,
Am∈Rm×m,Fm∈Rmvector matrix.
The rest of the system is defined as follows:
˙
Xr=ArFr(Xr) + fr(Xr)(4)
where, Xr∈Rris vector of remaining variables of system,
fr(Xr)∈Rr,Ar∈Rr×r,Fr(Xr)∈Rrvector matrix,
respectively. Where r= (n−m).
So the problem now reduces to showing the synchronization
between projection part of the master system (3) and the
controlled slave system (2).
For reduced order synchronization, the error dynamics can
be written as:
lim
t→∞ e(t) = 0 (5)
where e(t)can be written as:
e(t) = Y(t)−Xm(t)(6)
with e(t)∈Rm
By taking the time derivative, we can re-write the error
dynamics as follows:
˙e=˙
Y−˙
Xm(7)
˙e=A1G(Y) + g(Y)−AmFm(Xm)−fm(Xm) + U(8)
˙e=A3e+H(Xm, Y ) + U(9)
with initial conditions for error system as
e(0) = Y(0) −Xm(0).
Note: The residual term is H(Xm, Y ), and the (L−A3)
matrix is the (m×m)error dynamics coefficient matrix
(11). The key challenge now is to create a feedback control
rule that directs the slave system’s chaotic attractor to keep
track of the master system’s geometrical projection features
in order to fulfill the aim (5).
III. PROP OS ED CO NT ROL SCHEME
The proposed structure of the control system will be given
as follows:
U=−H(Xm, Y ) + K(t)(10)
where, the first half of the controller eliminates the residual
components H(Xm, Y )(9) to produce a system with linear
parts only, and the second part of the controller which is K(t)
modulates the robustness of the feedback control for achieving
ROS.
A. Formulation of the K(t) matrix
Let us consider K(t)=[ki(t)]T
[ki(t)]T=−L[ei(t)]T
with L=diag(L1, L2, L3......Lm)
where the (L−A3)is a gain matrix of size m×m.
˙e=A3e−Le =−(L−A3)e(11)
Note: Now our main task is to design a proper L∈Rm×m
matrix, such that the eigen values of the coefficient matrix
(11) have positive real part. The stability of the error dynamics
may then be guaranteed using the Routh-Hurwitz criteria
[20]-[22] and Lyapunov stability theory.
IV. REDUCED ORDER SYNCHRONIZATION OF AN EXAMPLE
CH AOTI C SY ST EM U SI NG P ROPOSED S CH EM E
To validate the results of section-III, we used a 4th order
Lorenz-Stenflo system (master system) and a 3th order L¨
u
system (slave system) in this section.
The description of the master is given as mentioned below:
˙x1=−a1x1+a1x2+c1x4
˙x2=−x2−x1x3+r1x1
˙x3=−b1x3+x1x2
˙x4=−x1−a1x4(12)
The description of the slave system is given as follows:
˙y1=−a2y1+a2y2
˙y2=c2y2−y1y3
˙y3=−b2y3+y1y2(13)
According to (3) the projection part of the system (12) can
be written as:
˙x1=−a1x1+a1x2+c1x4
˙x2=−x2−x1x3+r1x1
˙x3=−b1x3+x1x2(14)
Our purpose is to achieve ROS between (14) and (13).
The error dynamics’ time derivative may be expressed as:
˙e1=a2y2−a2y1−a1x2+a1x1−c1x4+u1(15)
Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY HAMIRPUR. Downloaded on March 17,2022 at 07:14:36 UTC from IEEE Xplore. Restrictions apply.
⇒˙e1=−(a2+a1)e1+ (a2+a1)e2−a2x1+a1y1
+a2x2−a1y2−c1x4+u1(16)
˙e2=−y1y3+c2y2−r1x1+x2+x1x3+u3(17)
⇒˙e2=c2e2+r1e1−y1y3+c2x2−r1y1+x1x3
+x2+u2(18)
˙e3=y1y2−b2y3−x1x2+b1x3+u3(19)
⇒˙e3=−(b2+b1)e3+y1y2−b2x3−x1x2+
b1y3+u3(20)
Now we can develop the control inputs as follows:
u1=a2x1−a1y1−a2x2+a1y2+c1x4−L1e1(21)
u2=y1y3−c2x2+r1y1−x1x3−x2−L2e2(22)
u3=−y1y2+b2x3+x1x3−b1y3−L3e3(23)
Now we can combine the equations (21), (22), (23) and
(16), (18), (20) and write the error dynamics as follows:
˙e1=−(a2+a1)e1+ (a2+a1)e2−L1e1(24)
˙e2=r1e1+c2e2−L2e2(25)
˙e3=−(b2+b1)e3−L3e3(26)
According to (11):
˙e1
˙e2
˙e3
=−
(a2+a1+L1)−(a1+a2) 0
−r1(L2−c2) 0
0 0 (b2+b1+L3)
e1
e2
e3
(27)
Now the problem boils down to choose suitable L1, L2, L3,
so that the coefficient matrix (CM) of (27) becomes Positive
Definite Matrix (PDM) and the eigen values of the CM
possess positive real part. After choosing the values of the
diagonal gain matrix satisfactorily, we may deduce that the
error trajectories will behave in a convergent manner.
For the CM to be PDM, we need to choose the values of
L1, L2, L3, such that it follows the following conditions:
(a2+a1+L1)>0, L2>(((a1+a2)r1)/(L1+(a1+a2)))+c2
(b1+b2+L3)>0(28)
At this point, we can say that, with these above mentioned
rules it is possible to achieve synchronization between master
system’s projection part and the slave system. As the order
of the projection part of the master is greater that the salve
system, hence this synchronization can be classified as ROS
(Reduced Order Synchronization).
V. NUMERICAL SIMULATION AND DISCUSSION
For the simulation, MATLAB R2013a software is used.
Parameters of the 4th order Lorenz-Stenflo system (master
system) and the 3rd order L¨
u system (slave system) are chosen
to ensure the chaotic behaviour as follows:
a1= 1, r1= 26, b1= 0.7, c1= 1.5
a2= 36, c2= 20, b2= 3
ode45 solver is used to complete the simulation. Time step
is considered to be 0.001. The initial values are considered as
follows:
X(0) = [1,5,−1,1]
Y(0) = [−1,1,2]
According to the conditions (28) we choose the values of
gain matrix as follows:
L1>−(1.0 + 36.0) ⇒L1>−37
we choose L1= 30,
L2>(((1.0+36.0)26)/(L1+1.0+36.0))+20 ⇒L2>34.35
correspondingly, L2>34.35, so we take L2= 50,
L3>−(0.7+3.0) ⇒L3>−3.7
and also let us take L3to be equal to 10.
Now we can write the gain matrix as follows:
L1= 30 0 0
0L2= 50 0
0 0 L3= 10
(29)
Note: As a designer, we have wide range of choices for gain
matrix L. The choices of gains are such that, it follows the
conditions mentioned in (28) and also make the CM matrix
(27) a PDM.
The CM is now derived from equation (27):
67 −37 0
−26 30 0
0 0 13.7
(30)
with these selection of gain matrix we can calculate the
eigen values of the CM mentioned in (27).
Those are:
λ(1) = 84.6144, λ(2) = 12.3856, λ(3) = 13.7000
Positive real parts of the eigen values confirm that CM will
be PDM and hence, the error states (27) is stable and approach
to zero.
Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY HAMIRPUR. Downloaded on March 17,2022 at 07:14:36 UTC from IEEE Xplore. Restrictions apply.
−10
−5
0
5
10
−20
0
20
40
−10
0
10
20
30
40
50
x1
x2
x3
Fig. 1. 3D phase portrait of the projected part of the 4th order Lorenz-Stenflo
system
−10
−5
0
5
10
−20
0
20
40
0
10
20
30
40
50
y1
y2
y3
Fig. 2. 3D phase portrait of the 3r d order L¨
u system
A. Discussion of figures
Fig. 1 depicts a 3D phase portrait of the projected compo-
nent of the 4th order Lorenz-Stenflo system. Fig. 2 depicts
the 3D phase portrait of the 3rd order L¨
u system. Fig. 3 and
Fig. 4 depict the time series of the projected component of
the Lorenz-Stenflo system and the L¨
u system, respectively.
Fig. 6 depicts the error dynamics (after the application of the
controller). In Fig. 5, the error dynamics prior to the use of the
controller is shown. When the active controllers are turned on,
the error paths converge to zero. As a result, we may deduce
that the trajectories of the slave system states are similar to
the states of master system and ROS has successfully been
achieved.
B. Extended case: Attaining the ROS in the presence of time-
delay in the system
The previous section’s results are extended to observe the
changes in the structures of the controller u1,u2and u3, that
0 5 10 15 20 25 30 35 40 45 50
−10
−5
0
5
10
Time
x1 state trajectory
0 5 10 15 20 25 30 35 40 45 50
−20
−10
0
10
20
30
Time
x2 state trajectory
0 5 10 15 20 25 30 35 40 45 50
−20
0
20
40
60
Time
x3 state trajectory
Fig. 3. The time series of the projected part of the Lorenz-Stenflo system
0 5 10 15 20 25 30 35 40 45 50
−10
−5
0
5
10
Time
y1 state trajectory
0 5 10 15 20 25 30 35 40 45 50
−20
−10
0
10
20
30
Time
y2 state trajectory
0 5 10 15 20 25 30 35 40 45 50
0
10
20
30
40
50
Time
y3 state trajectory
Fig. 4. The time series of L ¨
u system
is being exposed to time delays, that are present in both the
master and slave systems. As time delay is an inherent nature
of any systems in real practice, so study the ROS with time
delays gives a concrete analysis. Here, in this analysis time
delays has been incorporated in some of the states in master
and slave system dynamics.
Master and slave systems can be written with time delays
as follows:
˙x1=a1(x2−x1) + c1x4(t−τ1)
0 10 20 30 40 50
−40
−30
−20
−10
0
10
20
30
40
Time
Error Dynamics
e1
e2
e3
Fig. 5. The error dynamics before the application of controller
Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY HAMIRPUR. Downloaded on March 17,2022 at 07:14:36 UTC from IEEE Xplore. Restrictions apply.
0 5 10 15 20 25 30 35 40 45 50
−4
−3
−2
−1
0
1
2
3
Time
Error Dynamics
e1
e1
e3
0 0.5 1 1.5 2
−4
−3
−2
−1
0
1
2
3
ZOOMING THE MARKED PORTION
From time 0 to 2 seconds
Fig. 6. The error dynamics (after the controller is applied)
˙x2=r1x1−x2(t−τ2)−x1x3
˙x3=x1x2−b1x3(31)
and
˙y1=−a2y1+a2y2
˙y2=c2y2−y1y3
˙y3=−b2y3+y1y2(t−τ2)(32)
Note: Slight changes will occur in controller u1,u2and
u3, to suppress the time delays present in the systems. The
proposed new controller are as follows:
u1=a2x1−a1y1−a2x2+a1y2+c1x4(t−τ)−L1e1(33)
u2=y1y3−c2x2+r1y1−x1x3−x2(t−τ)−L2e2(34)
u3=−y1y2(t−τ) + b2x3+x1x3−b1y3−L3e3(35)
For our analysis we take the values of time delays as:
τ1=τ2=τ3=τ= 0.3second. With this proposed
controller we get the error dynamics as presented in the Fig. 7.
We can see that almost after 0.5 second the error trajectories
are converging to 0, hence it is a clear indication that the
controller proposed to tackle time delays are well derived.
Nonlinear Active Control technique provides a very effective
and handy mathematical approach. We observed that, with
some simple modifications in the existing controllers (21)-
(23), we derived the new controllers (33)-(35). Now at this
point a comment can be made that, with the help of Nonlinear
Active Controllers we can easily tackle time delayed systems
to achieve synchronization between two different chaotic and
hyperchaotic systems (with same or different system orders)
in the master and slave configuration.
0 0.5 1 1.5 2
−4
−3
−2
−1
0
1
2
3
Time
Error Dynamics
e1
e2
e3
Fig. 7. The error dynamics with time delays
VI. CONCLUSION
This research paper is an attempt to investigate ROS be-
tween two different order chaotic systems in master and slave
configuration. A nonlinear control method is proposed, and
some adequate criterion are also developed to calculate an
appropriate linear gain matrix that ensured a stable reduced
order synchronisation for a group of chaotic systems with or
without time delays, considering the Routh-Hurwitz criterion
as well as the Lyapunov stability analysis.
The suggested controller is used to synchronize a 4th order
Lorenz-Stenflo system with a 3rd order L¨
u chaotic system. The
theoretical analysis is fully supported based on the simulation
findings. The proposed analysis can also be extended to the
systems who fall under the generalized structure of system
mentioned in (1).
Here external disturbance and model uncertainties free
master and slave systems are considered. However, the results
could be extended to accommodate the effect of parameter
uncertainties as well as external disturbances. The approach
can also be explored to address Increased Order and Added
Order Synchronization problems.
ACKNOWLEDGMENT
This research work is supported by the EE Dept. (NIT
Hamirpur, Himachal Pradesh, 177005, India).
REFERENCES
[1] L. M. Pecora, T. L. Carroll, G. A. Johnson, D. J. Mar, and J. F.
Heagy, “Fundamentals of synchronization in chaotic systems, concepts,
and applications,” Chaos, vol. 7, no. 4, pp. 520–543, 1997, doi:
10.1063/1.166278.
[2] W. Kinzel, A. Englert, and I. Kanter, “On chaos synchronization and
secure communication,” Philos. Trans. R. Soc. A Math. Phys. Eng. Sci.,
vol. 368, no. 1911, pp. 379–389, 2010, doi: 10.1098/rsta.2009.0230
[3] L. Kocarev, “Chaos-based cryptography: A brief overview,”
IEEE Circuits Syst. Mag., vol. 1, no. 3, pp. 6–21, 2001, doi:
10.1109/7384.963463.
Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY HAMIRPUR. Downloaded on March 17,2022 at 07:14:36 UTC from IEEE Xplore. Restrictions apply.
[4] L. Moysis, E. Petavratzis, M. Marwan, C. Volos, H. Nistazakis, and
S. Ahmad, “Analysis, Synchronization, and Robotic Application of a
Modified Hyperjerk Chaotic System,” Complexity, vol. 2020, 2020, doi:
10.1155/2020/2826850.
[5] R. S. S. Vieira and T. A. Michtchenko, “Relativistic chaos in the
anisotropic harmonic oscillator,” Chaos, Solitons and Fractals, vol. 117,
pp. 276–282, Dec. 2018, doi: 10.1016/j.chaos.2018.10.027.
[6] H. H. C. Iu and C. K. Tse, “A Study of Synchronization
in Chaotic Autonomous C¨
uk DC/DC Converters,” 2000. doi:
https://doi.org/10.1109/81.852945.
[7] Y. N. Li, L. Chen, Z. S. Cai, and X. Z. Zhao, “Study on chaos synchro-
nization in the Belousov-Zhabotinsky chemical system,” Chaos, Solitons
and Fractals, vol. 17, no. 4, pp. 699–707, 2003, doi: 10.1016/S0960-
0779(02)00486-1.
[8] B. Xin and W. Peng, “Prediction for Chaotic Time Series-Based AE-
CNN and Transfer Learning,” Complexity, vol. 2020, no. 1, pp. 1–9,
2020, doi: 10.1155/2020/2680480.
[9] L. Guo, X. Nian, and H. Pan, “Generalized synchronization of different
chaotic systems based on nonnegative off-diagonal structure,” Math.
Probl. Eng., vol. 2013, 2013, doi: 10.1155/2013/596251.
[10] L. Huang, L. Wang, and Y. Fu, “Generalized synchronization in
different chaotic systems based on output feedback,” in Proceed-
ings - 2008 2nd International Symposium on Intelligent Information
Technology Application, IITA 2008, 2008, vol. 3, pp. 191–195, doi:
10.1109/IITA.2008.390.
[11] A. Ouannas and R. Abu-Saris, “A Robust control method for Q - S syn-
chronization between different dimensional integer-order and fractional-
order chaotic systems,” J. Control Sci. Eng., vol. 2015, 2015, doi:
10.1155/2015/703753.
[12] F. Abu Khadra, “Tracking control of chaotic systems via optimized
active disturbance rejection control,” Math. Probl. Eng., vol. 2018, 2018,
doi: 10.1155/2018/4698953.
[13] B. B. Sharma and I. N. Kar, “Parametric convergence and con-
trol of chaotic system using adaptive feedback linearization,” Chaos,
Solitons and Fractals, vol. 40, no. 3, pp. 1475–1483, 2009, doi:
10.1016/j.chaos.2007.09.060.
[14] M. K. Vaishnav and B. B. Sharma, “Observer design synchro-
nization of fourth order Lorenz Stenflo chaotic system,” 2013 Stu-
dents Conf. Eng. Syst. SCES 2013, no. 4, pp. 1–6, 2013, doi:
10.1109/SCES.2013.6547550.
[15] V. Sharma, B. B. Sharma, and R. Nath, “Reduced order unknown
input observer for discrete time system,” IEEE Reg. 10 Annu. Int.
Conf. Proceedings/TENCON, pp. 3443–3446, 2017, doi: 10.1109/TEN-
CON.2016.7848694.
[16] H. Tirandaz, “On Complete Control and Synchronization of Zhang
Chaotic System with Uncertain Parameters using Adaptive Control
Method,” Nonlinear Eng., vol. 7, no. 1, pp. 45–50, Mar. 2018, doi:
10.1515/nleng-2017-0050.
[17] M. C. Ho, Y. C. Hung, Z. Y. Liu, and I. M. Jiang, “Reduced-order
synchronization of chaotic systems with parameters unknown,” Phys.
Lett. Sect. A Gen. At. Solid State Phys., vol. 348, no. 3–6, pp. 251–259,
2006, doi: 10.1016/j.physleta.2005.08.076.
[18] I. Ahmad, A. Bin Saaban, A. B. Ibrahim, M. Shahzad, and M. Mossa Al-
Sawalha, “Reduced-order synchronization of time-delay chaotic systems
with known and unknown parameters,” Optik (Stuttg)., vol. 127, no. 13,
pp. 5506–5514, 2016, doi: 10.1016/j.ijleo.2016.02.078.
[19] F. A. Khadra, “Synchronization of Chaotic Systems via Active Distur-
bance Rejection Control,” Intell. Control Autom., vol. 08, no. 02, pp.
86–95, 2017, doi: 10.4236/ica.2017.82007.
[20] M. Shukla and B. B. Sharma, “Hybrid projective synchronization of
fractional order Volta’s system via active control,” 2015 2nd Int. Conf.
Recent Adv. Eng. Comput. Sci. RAECS 2015, vol. 0, no. December, pp.
1–6, 2016, doi: 10.1109/RAECS.2015.7453415.
[21] I. Ahmad, A. Saaban, A. Ibrahin, and M. Shahzad, “A Research on the
Synchronization of Two Novel Chaotic Systems Based on a Nonlinear
Active Control Algorithm,” Eng. Technol. Appl. Sci. Res., vol. 5, no. 1,
pp. 739–747, 2015, doi: 10.48084/etasr.434.
[22] H. N. Agiza and M. T. Yassen, “Synchronization of Rossler and Chen
chaotic dynamical systems using active control,” Phys. Lett. Sect. A
Gen. At. Solid State Phys., vol. 278, no. 4, pp. 191–197, 2001, doi:
10.1016/S0375-9601(00)00777-5.
Authorized licensed use limited to: NATIONAL INSTITUTE OF TECHNOLOGY HAMIRPUR. Downloaded on March 17,2022 at 07:14:36 UTC from IEEE Xplore. Restrictions apply.
