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- Title
Fractional-order PD control at Hopf bifurcations in a fractional-order congestion control system.
- Authors
Tang, Yuhong; Xiao, Min; Jiang, Guoping; Lin, Jinxing; Cao, Jinde; Zheng, Wei
- Abstract
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.
- Subjects
HOPF bifurcations; COMPUTER simulation; FEEDBACK control systems; FRACTIONS; ALGORITHMS
- Publication
Nonlinear Dynamics, 2017, Vol 90, Issue 3, p2185
- ISSN
0924-090X
- Publication type
Article
- DOI
10.1007/s11071-017-3794-5