Complex Dynamic Behaviors of A Congestion Control System under A Fractional-order PD Control

Abstract

This paper proposed an original fractional-order proportional-derivative (PD) feedback controller which is designed to control the Hopf bifurcation caused by the congestion control system. The proposed P D 1 n controller has the different order with the original congestion system. The proposed fractional-order PD controller has the different order with the controlled system and the communication delay is selected as the bifurcation parameter. Then the conditions of the stability and Hopf bifurcation are obtained by analyzing its characteristic equation and the stability domain can be extended 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 carried out to testify the validity of the theoretical analysis in the designed fractional-order PD controller.