Stabilization of different dimensional fractional chaotic maps

The study of chaotic dynamics in fractional-order maps has received great attention in the past years. Dynamics and control of fractional discrete-time systems in chaos theory have been only recently investigated. So far, few control techniques have been designed for stabilizing at zero the chaotic dynamic of fractional maps. Based on this consideration, this chapter investigates the stabilization for a class of fractional chaotic discrete-time systems proposed recently. Firstly, a 1D nonlinear control law is proposed for stabilizing at the origin the chaotic dynamics of the fractional Lozi map using the µ-Caputo difference definitions. The design of this control law is derived and based on the linearization method. Secondly, based on the Lyapunov method we derive a new 2D control law to stabilize the chaotic trajectories of the fractional h-Caputo difference form of Wang maps. Finally, simulation results are presented to show the effectiveness of the proposed linear and nonlinear control approaches.