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Journal of Control Science and Engineering
Volume 2016, Article ID 8342652, 10 pages
Research Article

Hopf Bifurcation Control in a FAST TCP and RED Model via Multiple Control Schemes

1School of Electronics and Information Engineering, Anhui University, Hefei, Anhui 230601, China
2Ira A. Fulton Schools of Engineering, Arizona State University, Tempe, AZ 85287, USA
3School of Electronic Information and Electrical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

Received 10 November 2015; Accepted 5 May 2016

Academic Editor: Petko Petkov

Copyright © 2016 Dawei Ding et al. 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.


We focus on the Hopf bifurcation control problem of a FAST TCP model with RED gateway. The system gain parameter is chosen as the bifurcation parameter, and the stable region and stability condition of the congestion control model are given by use of the linear stability analysis. When the system gain passes through a critical value, the system loses the stability and Hopf bifurcation occurs. Considering the negative influence caused by Hopf bifurcation, we apply state feedback controller, hybrid controller, and time-delay feedback controller to postpone the onset of undesirable Hopf bifurcation. Numerical simulations show that the hybrid controller is the most sensitive method to delay the Hopf bifurcation with identical parameter conditions. However, nonlinear state feedback control and time-delay feedback control schemes have larger control parameter range in the Internet congestion control system with FAST TCP and RED gateway. Therefore, we can choose proper control method based on practical situation including unknown conditions or parameter requirements. This paper plays an important role in setting guiding system parameters for controlling the FAST TCP and RED model.