Abstract

The paper elaborates on various synchronization aspects for nonlinear systems belonging to a specific class, under different scenarios. The method proposed in the article refers to the Lyapunov direct method and Extended Kalman Filter technique to ensure the convergence of the slave state trajectories to the corresponding master state trajectories. Initially, an output feedback-based synchronization approach is attempted, assuming that bounds of unmeasurable states are available for controller synthesis. However, this approach has limitations in handling complete parametric uncertainty for the considered class of systems. To overcome this limitation, a state feedback-based synchronization scheme is presented, and an appropriate state feedback controller and parametric adaptation laws are designed analytically. In the case where only output states are accessible for feedback, and the system is subjected to complete parametric uncertainty, an Extended Kalman Filter based estimation scheme is used. This approach facilitates achieving synchronization despite the presence of external channel noise disturbances with a Gaussian distribution. The potency of the proposed results is successfully substantiated for the chaotic Lorenz system, which belongs to the considered class of nonlinear systems. Ultimately, numerical simulations are provided to corroborate the efficacy of proposed synchronization and estimation strategy.

References

1.
Lassoued
,
A.
,
Boubaker
,
O.
, and
National Institute of Applied Sciences and Technology
,
2016
, “
On New Chaotic and Hyperchaotic Systems: A Literature Survey
,”
Nonlinear Anal.: Modell. Control
,
21
(
6
), pp.
770
789
.10.15388/NA.2016.6.3
2.
Balootaki
,
M. A.
,
Rahmani
,
H.
,
Moeinkhah
,
H.
, and
Mohammadzadeh
,
A.
,
2020
, “
On the Synchronization and Stabilization of Fractional-Order Chaotic Systems: Recent Advances and Future Perspectives
,”
Phys. A
,
551
, p.
124203
.10.1016/j.physa.2020.124203
3.
Suykens
,
J.
, and
Vandewalle
,
J.
,
1997
, “
Master-Slave Synchronization of Lur'e Systems
,”
Int. J. Bifurcation Chaos
,
07
(
03
), pp.
665
669
.10.1142/S0218127497000455
4.
Zhang
,
H.
,
Lewis
,
F. L.
, and
Das
,
A.
,
2011
, “
Optimal Design for Synchronization of Cooperative Systems: State Feedback, Observer and Output Feedback
,”
IEEE Trans. Autom. Control
,
56
(
8
), pp.
1948
1952
.10.1109/TAC.2011.2139510
5.
Suykens
,
J.
,
Curran
,
P.
, and
Chua
,
L.
,
1997
, “
Master-Slave Synchronization Using Dynamic Output Feedback
,”
Int. J. Bifurcation Chaos
,
07
(
03
), pp.
671
679
.10.1142/S0218127497000467
6.
Park
,
J. H.
,
2006
, “
Synchronization of Genesio Chaotic System Via Backstepping Approach
,”
Chaos, Solitons Fractals
,
27
(
5
), pp.
1369
1375
.10.1016/j.chaos.2005.05.001
7.
Quan
,
B.
,
Wang
,
C.
,
Sun
,
J.
, and
Zhao
,
Y.
,
2018
, “
A Novel Adaptive Active Control Projective Synchronization of Chaotic Systems
,”
ASME J. Comput. Nonlinear Dyn.
,
13
(
5
), p.
051001
.10.1115/1.4039189
8.
Follmann
,
R.
,
Macau
,
E. E.
, and
Rosa
,
E.
, Jr.
,
2009
, “
Detecting Phase Synchronization Between Coupled Non-Phase-Coherent Oscillators
,”
Phys. Lett. A
,
373
(
25
), pp.
2146
2153
.10.1016/j.physleta.2009.04.037
9.
Khamsuwan
,
P.
, and
Kuntanapreeda
,
S.
,
2016
, “
A Linear Matrix Inequality Approach to Output Feedback Control of Fractional-Order Unified Chaotic Systems With One Control Input
,”
ASME J. Comput. Nonlinear Dyn.
,
11
(
5
), p.
051021
.10.1115/1.4033384
10.
Ranjan
,
R. K.
,
Sharma
,
B. B.
, and
Chauhan
,
Y.
,
2021
, “
Stabilization of a Class of Chaotic Systems With Uncertainty Using Output Feedback Control Methodology
,” IEEE 6th International Conference on Computing, Communication and Automation (
ICCCA
)
, Arad, Romania, Dec. 17–19, pp.
533
538
.10.1109/ICCCA52192.2021.9666409
11.
Cruz-Ortiz
,
D.
,
Chairez
,
I.
, and
Poznyak
,
A.
,
2022
, “
Sliding-Mode Control of Full-State Constraint Nonlinear Systems: A Barrier Lyapunov Function Approach
,”
IEEE Trans. Syst., Man, Cybern.: Syst.
,
52
(
10
), pp.
6593
6606
.10.1109/TSMC.2022.3148695
12.
Muñoz-Vázquez
,
A. J.
, and
Martínez-Reyes
,
F.
,
2019
, “
Output Feedback Fractional Integral Sliding Mode Control of Robotic Manipulators
,”
ASME J. Comput. Nonlinear Dyn.
,
14
(
5
), p.
054502
.10.1115/1.4043000
13.
Pallav
,
S.
, and
Handa
,
H.
,
2022
, “
Stabilization of Uncertain Nonlinear Chaotic System Using PI SMC
,”
International Conference on Signal & Data Processing
,
Springer
, Singapore, June 10–11, pp.
477
485
.
14.
Wang
,
Z.
,
2010
, “
Chaos Synchronization of an Energy Resource System Based on Linear Control
,”
Nonlinear Anal.: Real World Appl.
,
11
(
5
), pp.
3336
3343
.10.1016/j.nonrwa.2009.11.026
15.
Sang
,
Y.
, and
Zhang
,
Z.
,
2023
, “
Discrete Time Partial-State Feedback Model Reference Disturbance Rejection Control
,”
Int. J. Adaptive Control Signal Process.
,
37
(
1
), pp.
298
314
.10.1002/acs.3525
16.
Kazemy
,
A.
, and
Shojaei
,
K.
,
2019
, “
Adaptive Synchronization of Complex Dynamical Networks in Presence of Coupling Connections With Dynamical Behavior
,”
ASME J. Comput. Nonlinear Dyn.
,
14
(
6
), p.
061003
.10.1115/1.4043146
17.
Zhu
,
C.
,
Li
,
X.
, and
Cao
,
J.
,
2021
, “
Finite-Time H Dynamic Output Feedback Control for Nonlinear Impulsive Switched Systems
,”
Nonlinear Anal.: Hybrid Syst.
,
39
(
1
), p.
100975
.10.1016/j.nahs.2020.100975
18.
Wang
,
X.
, and
Wang
,
Y.
,
2011
, “
Adaptive Control for Synchronization of a Four-Dimensional Chaotic System Via a Single Variable
,”
Nonlinear Dyn.
,
65
(
3
), pp.
311
316
.10.1007/s11071-010-9893-1
19.
Lu
,
J. G.
, and
Chen
,
G.
,
2009
, “
Global Asymptotical Synchronization of Chaotic Neural Networks by Output Feedback Impulsive Control: An LMI Approach
,”
Chaos, Solitons Fractals
,
41
(
5
), pp.
2293
2300
.10.1016/j.chaos.2008.09.024
20.
Yang
,
Z.-J.
,
Hara
,
S.
,
Kanae
,
S.
, and
Wada
,
K.
,
2011
, “
Robust Output Feedback Control of a Class of Nonlinear Systems Using a Disturbance Observer
,”
IEEE Trans. Control Syst. Technol.
,
19
(
2
), pp.
256
268
.10.1109/TCST.2010.2049998
21.
Hashtarkhani
,
B.
, and
Khosrowjerdi
,
M. J.
,
2019
, “
Neural Adaptive Fault Tolerant Control of Nonlinear Fractional Order Systems Via Terminal Sliding Mode Approach
,”
ASME J. Comput. Nonlinear Dyn.
,
14
(
3
), p.
031009
.10.1115/1.4042141
22.
Wu
,
W.
,
He
,
L.
,
Zhou
,
J.
,
Xuan
,
Z.
, and
Arik
,
S.
,
2022
, “
Disturbance-Term-Based Switching Event-Triggered Synchronization Control of Chaotic Lurie Systems Subject to a Joint Performance Guarantee
,”
Commun. Nonlinear Sci. Numer. Simul.
,
115
, p.
106774
.10.1016/j.cnsns.2022.106774
23.
Jiang
,
G.-P.
,
Tang
,
W. K.-S.
, and
Chen
,
G.
,
2006
, “
A State-Observer-Based Approach for Synchronization in Complex Dynamical Networks
,”
IEEE Trans. Circuits Syst. I: Regular Papers
,
53
(
12
), pp.
2739
2745
.10.1109/TCSI.2006.883876
24.
Andrieu
,
V.
, and
Tarbouriech
,
S.
,
2019
, “
LMI Conditions for Contraction and Synchronization
,”
IFAC-PapersOnLine
,
52
(
16
), pp.
616
621
.10.1016/j.ifacol.2019.12.030
25.
Sharma
,
B.
, and
Kar
,
I.
,
2009
, “
Contraction Theory Based Adaptive Synchronization of Chaotic Systems
,”
Chaos, Solitons Fractals
,
41
(
5
), pp.
2437
2447
.10.1016/j.chaos.2008.09.031
26.
Ranjan
,
R. K.
, and
Sharma
,
B. B.
,
2023
, “
Reduced-Order Observer-Based Synchronization and Output Tracking in Chain Network of a Class of Nonlinear Systems Using Contraction Framework
,”
Int. J. Dyn. Control
,
11
(
5
), pp.
2523
2537
.10.1007/s40435-023-01147-z
27.
Chauhan
,
Y.
,
Sharma
,
B.
, and
Ranjan
,
R. K.
,
2021
, “
Synchronization of Nonlinear Systems in Chain Network Configuration With Parametric Uncertainty
,” 18th India Council International Conference (
INDICON
),
IEEE
, Guwahati, India, Dec. 19–21, pp.
1
6
.10.1109/INDICON52576.2021.9691586
28.
Tie-Dong
,
M.
,
Hua-Guang
,
Z.
, and
Jie
,
F.
,
2008
, “
Exponential Synchronization of Stochastic Impulsive Perturbed Chaotic Lur'e Systems With Time-Varying Delay and Parametric Uncertainty
,”
Chin. Phys. B
,
17
(
12
), pp.
4407
4417
.10.1088/1674-1056/17/12/013
29.
Chang
,
W.
,
Park
,
J. B.
,
Joo
,
Y. H.
, and
Chen
,
G.
,
2003
, “
Static Output-Feedback Fuzzy Controller for Chen's Chaotic System With Uncertainties
,”
Inf. Sci.
,
151
, pp.
227
244
.10.1016/S0020-0255(02)00297-9
30.
Leung
,
H.
, and
Zhu
,
Z.
,
2001
, “
Performance Evaluation of EKF-Based Chaotic Synchronization
,”
IEEE Trans. Circuits Syst. I: Fundam. Theory Appl.
,
48
(
9
), pp.
1118
1125
.10.1109/81.948440
31.
Sharma
,
B. B.
, and
Kar
,
IN.
,
2009
, “
Chaotic Synchronization and Secure Communication Using Contraction Theory
,”
Pattern Recognition and Machine Intelligence: Third International Conference, PReMI 2009
,
Springer
,
New Delhi, India
, Dec. 16–20, pp.
549
554
.
32.
Yamada
,
W. A.
, and
Castro
,
R. S.
,
2021
, “
An LMI-Based Cooperative Control Design Framework for the Bounded Exponential Consensus of Nonlinear Systems
,” 60th IEEE Conference on Decision and Control (
CDC
), Austin, TX, Dec. 14–17, pp.
6678
6683
.10.1109/CDC45484.2021.9683115
33.
Bora
,
R. M.
, and
Sharma
,
B. B.
,
2022
, “
LMI Based Adaptive Robust Control Scheme for Reduced Order Synchronization (ROS) for a Class of Chaotic Systems
,”
IFAC-PapersOnLine
,
55
(
1
), pp.
253
258
.10.1016/j.ifacol.2022.04.042
34.
Khalil
,
H. K.
,
2002
,
Nonlinear Systems Third Edition
, Vol.
115
,
Patience Hall
, New York.
You do not currently have access to this content.