This paper will establish the importance and significance of studying the fractional-order control of nonlinear dynamical systems. The foundation and the sources related to this research scope is going to be set. Then, the paper incorporates a brief overview on how this study is performed and present the organization of this study. The present work investigates the effectiveness of the physical-fractional and biological-genetic operators to develop an Optimal Form of Fractional-order PID Controller (O2Fo-PIDC). The newly developed Fo-PIDC with optimal structure and parameters can, also, improve the performances required in the modeling and control of modern manufacturing-industrial process (MIP). The synthesis methodology of the proposed O2Fo-PIDC can be viewed as a multi-level design approach. The hierarchical Multiobjective genetic algorithm (MGA), 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 structure and knowledge base of the developed fractional controller to satisfy the various design specification contradictories (simplicity, accuracy, stability and robustness).

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 multiobjective 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.