Design tools to stabilize and to synchronize fractional-order energy resources system based on fractional-order control approaches: a review

In this work, a review of fractional-order calculus (F-oC), fractional-order systems (F-oSs), fractional-order chaotic and hyperchaotic systems (F-oCHSs) as a special case of F-oSs is considered. Modeling, simulation and control using the concept of F-oC, as advanced control technique, of F-oCHSs and stability analysis strategies are addressed. As a case study, the paper proposes a stable feedback control strategy based on the so called fractional-order PD controller (F-oPDC) with an adequate knowledge base for synchronization and/or stabilization a large class of F-oCHSs. The stability analysis is performed using Lyapunov stability theories and a recent stability hypothesis and assumptions of F-oSs. The 'optimal' knowledge base of the proposed F-oPDC, while meeting design requirements, is obtained based on a nature-inspired optimization method named gazelle optimization algorithm inspired from the 'gazelles' survival ability in their predator-dominated environment. Accordingly, the proposed design approach offers a good compromise between simplicity of implementation, faster convergence speed, higher tracking precision, robustness to uncertainties and energy efficiency, computational time, stability and accuracy for the case of controlling F-oCHSs. Ultimately, results of simulations are presented to illustrate both the feasibility and efficacy of the proposed strategy, by taking the fractional-order energy resources demand-supply (FoER-DS) hyperchaotic system as an example.