Browsing by Subject "Unstable periodic orbits"

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    Further stability results for a generalization of delayed feedback control
    (Springer, 2012-08-01) Morgül, Ö.
    In this paper, we consider the stabilization of unstable periodic orbits for one-dimensional and discrete time chaotic systems. Various control schemes for this problem are available and we consider a recent generalization of delayed control scheme. We prove that if a certain condition, which depends only on the period number, is satisfied then the stabilization is always possible. We will also present some simulation results.
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    A nonlinear control scheme for discrete time chaotic systems
    (The International Federation of Automatic Control, 2012-06) Morgül, Ömer
    In this paper we consider the stabilization problem of unstable periodic orbits of discrete time chaotic systems. We consider both one dimensional and higher dimensional cases. We propose a nonlinear feedback law and present some stability results. These results show that for period 1 all hyperbolic periodic orbits can be stabilized with the proposed method. By restricting the gain matrix to a special form we obtain some novel stability results. The stability proofs also give the possible feedback gains which achieve stabilization. We also present some simulation results.