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

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 P D 1 n 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.

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