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State feedback control at Hopf bifurcation in an exponential RED algorithm model

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Abstract

In this paper, we show that a state feedback method, which has successfully been used to control unstable steady states or periodic orbits, provides a tool to control the Hopf bifurcation for a novel congestion control model, i.e., the exponential RED algorithm with a single link and single source. We choose the gain parameter as the bifurcation parameter. Without control, the bifurcation will occur early; meanwhile, the model can maintain a stationary sending rate only in a certain domain of the gain parameter. However, outside of this domain the model still possesses a stable sending rate that can be guaranteed by the state feedback control, and the onset of the undesirable Hopf bifurcation is postponed. Numerical simulations are given to justify the validity of the state feedback controller in the bifurcation control.

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Acknowledgments

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 61203232, 61374180, and 71171050), the Natural Science Foundation of Jiangsu Province of China (Grant No. BK2012072), and the China Postdoctoral Science Foundation funded project (Grant No. 2013M530229).

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Correspondence to Min Xiao.

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Xiao, M., Jiang, G. & Zhao, L. State feedback control at Hopf bifurcation in an exponential RED algorithm model. Nonlinear Dyn 76, 1469–1484 (2014). https://doi.org/10.1007/s11071-013-1221-0

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