A ROBUST NONMODEL-BASED TECHNIQUE FOR STABILIZING CHAOTIC SYSTEMS WITH CONSTANT DISTURBANCE INPUT

Abstract

The stabilization of nonlinear systems that exhibit chaotic behavior is presented using notch-filter output feedback control. The effect of constant disturbance input and/or parametric uncertainty on the systems' performance is studied for a class of nonlinear systems where bifurcation analysis is used to illustrate the period-doubling route to chaos. The motivation for using the notch-filter in the feedback is to selectively damp-out portions of the closed-loop power spectrum, thus truncating period-doubling. Double-notch-filter feedback is introduced as a regulation scheme to bring the chaotic system to a steady state. The effect of using the fixed-parameters feedback on the equilibrium points is carefully studied, and a robust numerical parameter-tuning method is presented. The efficiency of this method is verified via simulations applied to a third-order uncertain nonlinear system that has typical applications in power generation and voltage control. A comparative study with a model-based recursive backstepping controller is carried out to highlight the advantages and limitations of the proposed control system.