Controlling and synchronizing of fractional-order chaotic systems via simple and optimal fractional-order feedback controller

Abstract

In this paper, a simple and optimal form of fractional-order feedback approach assigned for the control and synchronization of a class of fractional-order chaotic systems is proposed. The proposed control law can be viewed as a distributed network of linear regulators wherein each node is modeled by a PI controller with moderate gains. The multi-objective genetic algorithm with chaotic mutation, adopted in this work, can be visualized as a combination of structural and parametric genes of a controller orchestrated in a hierarchical fashion. Then, it is applied to select an optimal knowledge base, which characterizes the developed controller, and satisfies various design specifications. The proposed design and optimization of the developed controller represents a simple powerful approach to provide a reasonable tradeoff between computational overhead, storage space, numerical accuracy and stability criterion in control and synchronization of a class of fractional-order chaotic systems. Simulation results show the satisfactory performance of the proposed approach.