3.8 Proceedings Paper

Qualitative resonance of feedback-controlled chaotic oscillators

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IFAC PAPERSONLINE
卷 51, 期 33, 页码 1-6

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ELSEVIER SCIENCE BV
DOI: 10.1016/j.ifacol.2018.12.075

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Chaos control; Nonlinear systems; Qualitative resonance; Stability; Synchronization

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The qualitative resonance of feedback-controlled chaotic oscillators is the ability of the control system to qualitatively synchronize with a reference signal similar to one of the unstable periodic orbits embedded in the open-loop attractor. This property, discovered by 0. De Feo (2004a; 2004b) while studying Shilnikov-type attractors, was explained in terms of the random-like rephasing mechanism characterizing the oscillator's dynamics, so to guarantee the eventual in-phase looking with the reference forcing. We experimentally show that the phenomenon works more in general, even in the absence of a rephasing mechanism. Intuitively, the forcing by the target cycle, or by a qualitative approximation of it, is sufficient to bring in the in-phase condition. Our results can make chaos control more practicable than so far imagined, as a qualitative control can be achieved with no a-priori knowledge about the target solution. (C) 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.

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