Fractional PI pinning synchronization of fractional complex dynamical networks

A novel method for synchronization of fractional order complex dynamical networks using a new fractional Proportional-Integral (PI) pinning control scheme is presented in this paper. Stability of this network is proved via the Lyapunov stability theorem, and the synchronizability criterion is obtained. Although one can also design a proportional pinning control scheme to synchronize the whole network, our proposed fractional PI control is more efficient. Numerical simulations on Lorenz oscillator's interaction over a sample network have shown that the proposed fractional PI controller can provide a faster synchronization with less overshoot to the reference state compared to conventional proportional controller with the same power consumption