Generalized fractional-order time-delayed feedback control and synchronization designs for a class of fractional-order chaotic systems

In this paper, we develop a fractional-order time-delayed feedback control (Fo-TDFC) approach combined with an optimal knowledge base to stabilize and synchronize a large class of fractional-order chaotic systems (FoCS). The proposed control laws are formulated based on the Lyapunov stability theory and the multiobjective optimization process of the closed-loop controlled system. The design and optimization of the Fo-TDFC laws are theoretically rigorous and represent a powerful tool to control and synchronize FoCS. Finally, numerical simulation results are provided to illustrate the effectiveness of the proposed method by considering the fractional-order energy resources demand-supply chaotic system as an illustrative example.