PI Pinning Control with Fractional order for Complex Dynamical Network Synchronization

This research presents a new method for synchronization of fractional order complex dynamical networks using a Proportional-Integral (PI) pinning control. Lyapunov method is used to prove the stability of the network and synchronizability conditions are studied. The nodes of this network are modeled via Lorenz's chaotic dynamic system. Synchronization of the network is studied and simulated based on the coupling strength and feedback gains. The synchronizablity criteria are evaluated for the proposed controller. The proposed new method has high degree of freedom in control. The results show the fractional PI controller performs well on over shoot and convergence speed.