Abstract: We propose a novel approach called the robust fractional-order proportional-integral-derivative (FOPID) controller, to stabilize a perturbed nonlinear chaotic system on one of its unstable fixed points. The stability analysis of the nonlinear chaotic system is made based on the proportional-integral-derivative actions using the bifurcation diagram. We extract an initial set of controller parameters, which are subsequently optimized using a quadratic criterion. The integral and derivative fractional orders are also identified by this quadratic criterion. By applying numerical simulations on two nonlinear systems, namely the multi-scroll Chen system and the Genesio-Tesi system, we show that the fractional PI^λD^μ controller provides the best closed-loop system performance in stabilizing the unstable fixed points, even in the presence of random perturbation.

Key words: Fractional order system, Bifurcation diagram, Fractional PI^λD^μ, Multi-scroll Chen chaotic system, Genesio-Tesi chaotic system

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