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Mathematical Problems in Engineering
Volume 2018, Article ID 6581493, 15 pages
Research Article

Parameter Identification and Hybrid Synchronization in an Array of Coupled Chaotic Systems with Ring Connection: An Adaptive Integral Sliding Mode Approach

Department of Electrical Engineering, Capital University of Science and Technology, Islamabad, Pakistan

Correspondence should be addressed to Nazam Siddique; moc.liamg@qiddis.mizan

Received 10 August 2017; Revised 11 October 2017; Accepted 28 November 2017; Published 30 January 2018

Academic Editor: Ton D. Do

Copyright © 2018 Nazam Siddique and Fazal ur Rehman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This article presents an adaptive integral sliding mode control (SMC) design method for parameter identification and hybrid synchronization of chaotic systems connected in ring topology. To employ the adaptive integral sliding mode control, the error system is transformed into a special structure containing nominal part and some unknown terms. The unknown terms are computed adaptively. Then the error system is stabilized using integral sliding mode control. The controller of the error system is created that contains both the nominal control and the compensator control. The adapted laws and compensator controller are derived using Lyapunov stability theory. The effectiveness of the proposed technique is validated through numerical examples.