期刊
NONLINEAR DYNAMICS
卷 90, 期 3, 页码 2185-2198出版社
SPRINGER
DOI: 10.1007/s11071-017-3794-5
关键词
Fractional-order system; Congestion control algorithm; Hopf bifurcation; Bifurcation control; Fractional-order PD controller
资金
- National Natural Science Foundation of China [61573194, 61374180, 61473158, 61573096]
- Six Talent Peaks High Level Project of Jiangsu Province of China [2014-ZNDW-004]
- 1311 Talents Project through the Nanjing University of Posts and Telecommunications
In this paper, we address the problem of the bifurcation control of a delayed fractional-order dual model of congestion control algorithms. A fractional-order proportional-derivative (PD) feedback controller is designed to control the bifurcation generated by the delayed fractional-order congestion control model. By choosing the communication delay as the bifurcation parameter, the issues of the stability and bifurcations for the controlled fractional-order model are studied. Applying the stability theorem of fractional-order systems, we obtain some conditions for the stability of the equilibrium and the Hopf bifurcation. Additionally, the critical value of time delay is figured out, where a Hopf bifurcation occurs and a family of oscillations bifurcate from the equilibrium. It is also shown that the onset of the bifurcation can be postponed or advanced by selecting proper control parameters in the fractional-order PD controller. Finally, numerical simulations are given to validate the main results and the effectiveness of the control strategy.
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