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Mathematical Problems in Engineering
Volume 2011, Article ID 521549, 11 pages
Research Article

An Adaptive Tracking Control of Fractional-Order Chaotic Systems with Uncertain System Parameter

Ping Zhou1,2 and Rui Ding1,2

1Center of System Theory and Its Applications, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2Key Laboratory of Network Control and Intelligent Instrument of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Received 19 April 2011; Revised 22 August 2011; Accepted 22 September 2011

Academic Editor: J. Rodellar

Copyright © 2011 Ping Zhou and Rui Ding. 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.


An adaptive tracking control scheme is presented for fractional-order chaotic systems with uncertain parameter. It is theoretically proved that this approach can make the uncertain parameter fractional-order chaotic system track any given reference signal and the uncertain system parameter is estimated through the adaptive tracking control process. Furthermore, the reference signal may belong to other integer-orders chaotic system or belong to different fractional-order chaotic system with different fractional orders. Two examples are presented to demonstrate the effectiveness of the proposed method.