Fractional-order PID control of tipping in network congestion

Tracing the rapid progress of communication network, the control of dynamic evolution of network has become a central issue. There are a lot of tipping phenomena in network congestion systems. Therefore, tipping control principally centres on traditional control policies, and some advanced control approaches need to be supplemented. In this paper, a fractional-order proportional-integral-derivative (PID) controller is introduced to a network congestion model to ponder corresponding bifurcation-induced tipping regulation. First, a fractional-order congestion model with fractional-order PID controller is constructed. Then the onset of the tipping induced by Hopf bifurcation of the uncontrolled model is studied. By contrast, the tipping point can be delayed under the controller for the controlled model. Some conditions under which Hopf bifurcation occurs are given. The stable and unstable ranges of control parameters for the controlled model are also deduced. At last, some simulated examples are given to verify the theoretical results and demonstrate the superiority of the controller in tipping regulation. Moreover, the bidirectional effects of the controller are displayed by manipulating the control parameters.