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Complex dynamic behaviors of a congestion control system under a novel PD1n control law: Stability, bifurcation and periodic oscillations

Author

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  • Lu, Qiu
  • Xiao, Min
  • Tao, Binbin
  • Huang, Chengdai
  • Shi, Shuo
  • Wang, Zhengxin
  • Jiang, Guoping

Abstract

In this paper, we consider the control of nonlinear dynamic in a congestion control system. A novel fractional-order proportional-derivative (PD) feedback law is firstly designed to control the Hopf bifurcation caused by the system. The proposed PD1n controller has the different order with the original congestion system. Meanwhile, the communication delay is elected as the bifurcation parameter to study the stability, bifurcations and periodic oscillations of the controlled congestion system. By the stability mechanism of fractional-order systems, we can obtain the criteria for satisfying the stability and Hopf bifurcation. It has been discovered that the Hopf bifurcation point can be delayed or advanced under the adjustment of appropriate control gain parameters and the order. Therefore, the congestion system becomes controllable and the desirable behaviors can be realized. Finally, numerical simulations are presented to demonstrate the validity of the main results and the efficiency of the control strategy in the designed fractional-order PD controller.

Suggested Citation

  • Lu, Qiu & Xiao, Min & Tao, Binbin & Huang, Chengdai & Shi, Shuo & Wang, Zhengxin & Jiang, Guoping, 2019. "Complex dynamic behaviors of a congestion control system under a novel PD1n control law: Stability, bifurcation and periodic oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 242-252.
    • Handle: RePEc:eee:chsofr:v:126:y:2019:i:c:p:242-252
    DOI: 10.1016/j.chaos.2018.09.048
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    References listed on IDEAS

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    1. Liu, Cheng-Lin & Tian, Yu-Ping, 2008. "Eliminating oscillations in the Internet by time-delayed feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 878-887.
    2. Li, Mengmeng & Wang, JinRong, 2018. "Exploring delayed Mittag-Leffler type matrix functions to study finite time stability of fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 324(C), pages 254-265.
    3. Wang, Zhanfeng & Chu, Tianguang, 2006. "Delay induced Hopf bifurcation in a simplified network congestion control model," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 161-172.
    4. Wen-bo Zhao & Xiao-ke Sun & Huicheng Wang, 2014. "Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-12, April.
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