Control methods on unstable periodic orbits of a chaotic dynamical system — control chaos in buck converter

Abstract

Recently, there has been an extensive interest in research on the analysis and control of chaotic behavior in nonlinear systems. Various control problems can be defined for such systems, such as targeting the trajectories to a desired point, stabilizing unstable periodic orbits etc. In this paper we present the necessity and possibility to control chaotic dynamic systems. The first part of this paper describes the methods for the identification of Unstable Periodic Orbits (UPO) of a chaotic dynamic system. Some methods of control are applied to stabilize UPO embedded in the dynamics of the system. The chaos control was first advanced by Ott, Grebogi and York (OGY method). Finally, the resonant parametric perturbation method is applied to control chaos in buck converter. In particular, the effect of phase shift in the perturbing signal is studied.