Adaptive synchronization of two different chaotic systems containing mutually Lipschitz nonlinearities subject to state time-delays

Muhammad Riaz; Muhammad Ashraf; Keum Shik Hong; Gyoung Hahn Kim; Muhammad Rehan

doi:10.1109/ICCAS.2015.7364879

Adaptive synchronization of two different chaotic systems containing mutually Lipschitz nonlinearities subject to state time-delays

Muhammad Riaz^*
, Muhammad Ashraf
, Keum Shik Hong
, Gyoung Hahn Kim
, Muhammad Rehan

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

This article addresses the synchronization problem for two different chaotic systems with state time-delays, disturbances, and mutually Lipschitz nonlinearities. For analysis of the two different kind of chaotic oscillators, adaptive control theory, mutually Lipschitz condition and linear matrix inequalities (LMIs) based methodology are utilized to suppress the synchronization error and mismatch between the master-slave chaotic in the presence of disturbances and state delays. A novel adaptive control scheme for the synchronization of such systems is established that guarantees the convergence of the error trajectory and ensures the stability of the synchronization error system. In the end, established adaptive control law is verified by a numerical example of two different, popular in electronics, chaotic Chua's circuit and Rossler system.

Original language	English
Title of host publication	ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	60-65
Number of pages	6
ISBN (Electronic)	9788993215090
DOIs	https://doi.org/10.1109/ICCAS.2015.7364879
State	Published - 23 Dec 2015
Externally published	Yes
Event	15th International Conference on Control, Automation and Systems, ICCAS 2015 - Busan, Korea, Republic of Duration: 13 Oct 2015 → 16 Oct 2015

Publication series

Name	ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings

Conference

Conference	15th International Conference on Control, Automation and Systems, ICCAS 2015
Country/Territory	Korea, Republic of
City	Busan
Period	13/10/15 → 16/10/15

Bibliographical note

Publisher Copyright:
© 2015 Institute of Control, Robotics and Systems - ICROS.

Keywords

Different chaotic systems
adaptive control
chaos synchronization
linear matrix inequality
mutually Lipschitz nonlinearities

ASJC Scopus subject areas

Control and Systems Engineering

Access to Document

10.1109/ICCAS.2015.7364879

Cite this

Riaz, M., Ashraf, M., Hong, K. S., Kim, G. H., & Rehan, M. (2015). Adaptive synchronization of two different chaotic systems containing mutually Lipschitz nonlinearities subject to state time-delays. In ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings (pp. 60-65). Article 7364879 (ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICCAS.2015.7364879

Riaz, Muhammad ; Ashraf, Muhammad ; Hong, Keum Shik et al. / Adaptive synchronization of two different chaotic systems containing mutually Lipschitz nonlinearities subject to state time-delays. ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings. Institute of Electrical and Electronics Engineers Inc., 2015. pp. 60-65 (ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings).

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title = "Adaptive synchronization of two different chaotic systems containing mutually Lipschitz nonlinearities subject to state time-delays",

abstract = "This article addresses the synchronization problem for two different chaotic systems with state time-delays, disturbances, and mutually Lipschitz nonlinearities. For analysis of the two different kind of chaotic oscillators, adaptive control theory, mutually Lipschitz condition and linear matrix inequalities (LMIs) based methodology are utilized to suppress the synchronization error and mismatch between the master-slave chaotic in the presence of disturbances and state delays. A novel adaptive control scheme for the synchronization of such systems is established that guarantees the convergence of the error trajectory and ensures the stability of the synchronization error system. In the end, established adaptive control law is verified by a numerical example of two different, popular in electronics, chaotic Chua's circuit and Rossler system.",

keywords = "Different chaotic systems, adaptive control, chaos synchronization, linear matrix inequality, mutually Lipschitz nonlinearities",

author = "Muhammad Riaz and Muhammad Ashraf and Hong, \{Keum Shik\} and Kim, \{Gyoung Hahn\} and Muhammad Rehan",

note = "Publisher Copyright: {\textcopyright} 2015 Institute of Control, Robotics and Systems - ICROS.; 15th International Conference on Control, Automation and Systems, ICCAS 2015 ; Conference date: 13-10-2015 Through 16-10-2015",

year = "2015",

month = dec,

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doi = "10.1109/ICCAS.2015.7364879",

language = "English",

series = "ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings",

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Riaz, M, Ashraf, M, Hong, KS, Kim, GH & Rehan, M 2015, Adaptive synchronization of two different chaotic systems containing mutually Lipschitz nonlinearities subject to state time-delays. in ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings., 7364879, ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings, Institute of Electrical and Electronics Engineers Inc., pp. 60-65, 15th International Conference on Control, Automation and Systems, ICCAS 2015, Busan, Korea, Republic of, 13/10/15. https://doi.org/10.1109/ICCAS.2015.7364879

Adaptive synchronization of two different chaotic systems containing mutually Lipschitz nonlinearities subject to state time-delays. / Riaz, Muhammad; Ashraf, Muhammad; Hong, Keum Shik et al.
ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings. Institute of Electrical and Electronics Engineers Inc., 2015. p. 60-65 7364879 (ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - Adaptive synchronization of two different chaotic systems containing mutually Lipschitz nonlinearities subject to state time-delays

AU - Riaz, Muhammad

AU - Ashraf, Muhammad

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AU - Rehan, Muhammad

PY - 2015/12/23

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N2 - This article addresses the synchronization problem for two different chaotic systems with state time-delays, disturbances, and mutually Lipschitz nonlinearities. For analysis of the two different kind of chaotic oscillators, adaptive control theory, mutually Lipschitz condition and linear matrix inequalities (LMIs) based methodology are utilized to suppress the synchronization error and mismatch between the master-slave chaotic in the presence of disturbances and state delays. A novel adaptive control scheme for the synchronization of such systems is established that guarantees the convergence of the error trajectory and ensures the stability of the synchronization error system. In the end, established adaptive control law is verified by a numerical example of two different, popular in electronics, chaotic Chua's circuit and Rossler system.

AB - This article addresses the synchronization problem for two different chaotic systems with state time-delays, disturbances, and mutually Lipschitz nonlinearities. For analysis of the two different kind of chaotic oscillators, adaptive control theory, mutually Lipschitz condition and linear matrix inequalities (LMIs) based methodology are utilized to suppress the synchronization error and mismatch between the master-slave chaotic in the presence of disturbances and state delays. A novel adaptive control scheme for the synchronization of such systems is established that guarantees the convergence of the error trajectory and ensures the stability of the synchronization error system. In the end, established adaptive control law is verified by a numerical example of two different, popular in electronics, chaotic Chua's circuit and Rossler system.

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KW - adaptive control

KW - chaos synchronization

KW - linear matrix inequality

KW - mutually Lipschitz nonlinearities

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BT - ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings

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ER -

Riaz M, Ashraf M, Hong KS, Kim GH, Rehan M. Adaptive synchronization of two different chaotic systems containing mutually Lipschitz nonlinearities subject to state time-delays. In ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings. Institute of Electrical and Electronics Engineers Inc. 2015. p. 60-65. 7364879. (ICCAS 2015 - 2015 15th International Conference on Control, Automation and Systems, Proceedings). doi: 10.1109/ICCAS.2015.7364879

Adaptive synchronization of two different chaotic systems containing mutually Lipschitz nonlinearities subject to state time-delays

Abstract

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Bibliographical note

Keywords

ASJC Scopus subject areas

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