Modify adaptive combined synchronization of fractional order chaotic systems with fully unknown parameters
Volume 21, Issue 2, pp 99--112
http://dx.doi.org/10.22436/jmcs.021.02.01
Publication Date: March 26, 2020
Submission Date: November 09, 2019
Revision Date: January 15, 2020
Accteptance Date: February 12, 2020
-
1215
Downloads
-
2630
Views
Authors
A. Othman Almatroud
- Mathematics Department, Faculty of Science, University of Ha'il, Kingdom of Saudi Arabia.
O. Ababneh
- School of Mathematics, Zarqa University, Zarqa, Jordan.
M. Mossa Al-sawalha
- Mathematics Department, Faculty of Science, University of Ha'il, Kingdom of Saudi Arabia.
Abstract
This article presents a modify adaptive combined synchronization
for a class of different unknown fractional order chaotic systems.
A combination of different states of the drive systems
asymptotically synchronizes with the desired states of the
response system. Hence, increases the complexity of the
communication channel in secrete communications. The Lyapunov
stability theory proves the asymptotic stability of the error
system at the origin. The design of a suitable adaptive controller
assures the target synchronization. This work provides parameters
update laws that estimate the true values of unknown parameters.
This paper also presents two numerical examples of unknown
different fractional order chaotic systems and simulation results
that validate the efficiency and performance of the proposed
adaptive combined synchronization strategy. The presented adaptive
combined synchronization strategy can be applied to multiple
synchronization strategies. The paper suggests some future
problems related to this work.
Share and Cite
ISRP Style
A. Othman Almatroud, O. Ababneh, M. Mossa Al-sawalha, Modify adaptive combined synchronization of fractional order chaotic systems with fully unknown parameters, Journal of Mathematics and Computer Science, 21 (2020), no. 2, 99--112
AMA Style
Almatroud A. Othman, Ababneh O., Al-sawalha M. Mossa, Modify adaptive combined synchronization of fractional order chaotic systems with fully unknown parameters. J Math Comput SCI-JM. (2020); 21(2):99--112
Chicago/Turabian Style
Almatroud, A. Othman, Ababneh, O., Al-sawalha, M. Mossa. "Modify adaptive combined synchronization of fractional order chaotic systems with fully unknown parameters." Journal of Mathematics and Computer Science, 21, no. 2 (2020): 99--112
Keywords
- Chaos
- combined synchronization
- adaptive control
- unknown parameters
- fractional order
MSC
References
-
[1]
S. K. Agrawal, S. Das, A modified adaptive control method for synchronization of some fractional chaotic systems with unknown parameters, Nonlinear Dynam., 73 (2013), 907--919
-
[2]
S. K. Agrawal, S. Das, Function projective synchronization between four dimensional chaotic systems with uncertain parameters using modified adaptive control method, J. Process Control, 24 (2014), 517--530
-
[3]
S. K. Agrawal, M. Srivastava, S. Das, Synchronization of fractional order chaotic systems using active control method, Chaos Solitons Fractals, 45 (2012), 737--752
-
[4]
I. Ahmad, A. B. Saaban, A. B. Ibrahim, M. Shahzad, Global chaos synchronization of new chaotic system using linear active control, Complexity, 21 (2015), 379--386
-
[5]
I. Ahmad, A. B. Saaban, A. B. Ibrahim, M. Shahzad, N. Naveed, The synchronization of chaotic systems with different dimensions by a robust generalized active control, Optik, 127 (2016), 4859--4871
-
[6]
I. Ahmad, M. Shafiq, M. M. Al-Sawalha, Globally exponential multi switching-combination synchronization control of chaotic systems for secure communications, Chinese J. Phys., 56 (2018), 974--987
-
[7]
I. Ahmad, M. Shafiq, M. Shahzad, Global Finite-Time Multi-Switching Synchronization of Externally Perturbed Chaotic Oscillators, Circuits Systems Signal Process., 37 (2018), 5253--5278
-
[8]
M. M. Al-Sawalha, A. Al-Sawalha, Anti-synchronization of fractional order chaotic and hyperchaotic systems with fully unknown parameters using modified adaptive control, Open Phys., 14 (2016), 304--313
-
[9]
M. M. Al-Sawalha, M. Shoaib, Reduced-order synchronization of fractional order chaotic systems with fully unknown parameters using modified adaptive control, J. Nonlinear Sci. Appl., 9 (2016), 1815--1825
-
[10]
L. Y. T. Andrew, L. X. Feng, C. Y. Dong, Z. Hui, A novel adaptive-impulsive synchronization of fractional-order chaotic systems, Chinese Phys. B, 24 (2015), 7 pages
-
[11]
S. Bhalekar, V. D. Gejji, Synchronization of different fractional order chaotic systems using active control, Commun. Nonlinear. Sci. Numer. Simulat., 15 (2010), 3536--3546
-
[12]
D. Chen, R. F. Zhang, J. C. Sprott, H. T. Chen, X. Y. Ma, Synchronization between integer-order chaotic systems and a class of fractional-order chaotic systems via sliding mode control, Chaos, 22 (2012), 9 pages
-
[13]
M. R. Faieghi, H. Delavari, Chaos in fractional-order Genesio--Tesi system and its synchronization, Commun. Nonlinear Sci. Numer. Simul., 17 (2011), 7317--7341
-
[14]
Z. Gao, X. Z. Liao, Integral sliding mode control for fractional-order systems with mismatched uncertainties, Nonlinear Dynam., 72 (2013), 27--35
-
[15]
F. Gao, H. M. Srivastava, Y. N. Gao, X.-J. Yang, A coupling method involving the Sumudu transform and the variational iteration method for a class of local fractional diffusion equations, J. Nonlinear Sci. Appl., 9 (2016), 5830--5835
-
[16]
A. K. Golmankhaneh, R. Arefi, D. Baleanu, Synchronization in a nonidentical fractional order of a proposed modified system, J. Vib. Control, 21 (2015), 1154--1161
-
[17]
A. Hajipour, S. S. Aminabadi, Synchronization of chaotic Arneodo system of incommensurate fractional order with unknown parameters using adaptive method, Optik, 127 (2016), 7704--7709
-
[18]
A. S. Hegazi, E. Ahmed, A. E. Matouk, On chaos control and synchronization of the commensurate fractional order Liu system, Commun. Nonlinear. Sci. Numer. Simul., 18 (2013), 1193--1202
-
[19]
R. Hilfer, Application of fractional Calculus in Physics, World Scientific Publishing Co., River Edge (2000)
-
[20]
A. M. Liapunov, Stability of Motion, Academic Press, New York--London (1966)
-
[21]
W. Y. Ma, C. P. Li, Y. J. Wu, Impulsive synchronization of fractional Takagi-Sugeno fuzzy complex networks, Chaos, 26 (2016), 8 pages
-
[22]
A. A. Othman, M. S. M. Noorani, M. M. Al-Sawalha, daptive dual anti-synchronization of chaotic systems with fully uncertain parameters, Optik, 127 (2016), 10478--10489
-
[23]
A. A. Othman, M. S. M. Noorani, M. M. Al-Sawalha, Adaptive dual synchronization of chaotic and hyperchaotic systems with fully uncertain parameters, Optik, 127 (2016), 7852--7864
-
[24]
A. A. Othman, M. S. M. Noorani, M. M. Al-Sawalha, Dual synchronization of chaotic and hyperchaotic systems, J. Nonlinear Sci. Appl., 9 (2016), 4666--4677
-
[25]
A. A. Othman, M. S. M. Noorani, M. M. Al-Sawalha, Function projective dual synchronization of chaotic systems with uncertain parameters, Nonlinear Dyn. Syst. Theory, 17 (2017), 193--204
-
[26]
L. M. Pecora, T. L. Carroll, Synchronization in chaotic systems, Phys. Rev. Lett., 64 (1990), 821--824
-
[27]
I. Podlubny, Fractional Differential Equations, Acedemic Press, San Diego (1999)
-
[28]
M. Pourmahmood Aghababa, Control of non-linear non-integer-order systems using variable structure control theory, Trans. Inst. Measurement Control, 36 (2014), 425--432
-
[29]
M. Pourmahmood Aghababa, H. Feizi, Design of a sliding mode controller for synchronizing chaotic systems with parameter and model uncertainties and external disturbances, Trans. Inst. Measurement Control, 34 (2012), 990--997
-
[30]
A. G. Radwan, K. Moaddy, K. N. Salama, S. Momani, I. Hashim, Control and switching synchronization of fractional order chaotic systems using active control technique, J. Adv. Res., 5 (2014), 125--132
-
[31]
K. Sayevand, K. Pichaghchi, Analysis of nonlinear fractional KdV equation based on He's fractional derivative, Nonlinear Sci. Lett. A, 7 (2016), 77--85
-
[32]
M. Shafiq, I. Ahmad, Multi-Switching Combination Anti-synchronization of Unknown Hyperchaotic Systems, Arab. J. Sci. Eng., 44 (2019), 7335--7350
-
[33]
A. K. Singh, V. K. Yadav, S. Das, Dual combination synchronization of the fractional order complex chaotic systems, J. Comput. Nonlinear Dynam., 12 (2016), 8 pages
-
[34]
X. Song, S. Song, B. Li, Adaptive synchronization of two time-delayed fractional-order chaotic systems with different structure and different order, Optik, 127 (2016), 11860--11870
-
[35]
X. Song, S. Song, B. Li, I. T. Balsera, Adaptive projective synchronization for time-delayed fractional-order neural networks with uncertain parameters and its application in secure communications, Trans. Inst. Measurement Control, 40 (2017), 3078--3087
-
[36]
M. Srivastava, S. P. Ansari, S. K. Agrawal, S. Das, A. Y. T. Leung, Anti-synchronization between identical and non-identical fractional-order chaotic systems using active control method, Nonlinear Dynam., 76 (2014), 905--914
-
[37]
J. W. Sun, Q. Yin, Y. Shen, Compound synchronization for four chaotic systems of integer order and fractional order, EPL (Europhys. Lett.), 106 (2012), 9 pages
-
[38]
Z. Wang, X. Huang, H. Shen, Control of an uncertain fractional order economic system via adaptive sliding mode, Neurocomputing, 83 (2012), 83--88
-
[39]
S. Wang, Y. Yu, M. Diao, Hybrid projective synchronization of chaotic fractional order systems with different dimensions, Phys. A, 389 (2010), 4981--4988
-
[40]
G.-C. Wu, D. Baleanu, Chaos synchronization of the discrete fractional logistic map, Signal Process., 102 (2014), 96--99
-
[41]
X. J. Wu, H. T. Lu, S. L. Shen, Synchronization of a new fractional-order hyperchaotic system, Phys. Lett. A, 373 (2009), 2329--2337
-
[42]
Y. Xu, H. Wang, D. Liu, H. Huang, Sliding mode control of a class of fractional chaotic systems in the presence of parameter perturbations, J. Vib. Control, 21 (2015), 435--448
-
[43]
P. Zhou, R. J. Bai, he adaptive synchronization of fractional-order chaotic system with fractional-order $1 < q < 2$ via linear parameter update law, Nonlinear Dynam., 80 (2015), 753--765
-
[44]
H. Zhu, S. B. Zhou, Z. S. He, Chaos synchronization of the fractional-order Chen's system, Chaos Solitons Fractals, 41 (2009), 2733--2740
-
[45]
M. Zribi, N. Smaoui, H. Salim, Synchronization of the unified chaotic systems using a sliding mode controller, Chaos Solitons Fractals, 42 (2009), 3197--3209