Delayed feedback control and phase reduction of unstable quasi-periodic orbits | Zendy

Natsuhiro Ichinose | Zendy; Motomasa Komuro | Zendy

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Delayed feedback control and phase reduction of unstable quasi-periodic orbits

Author(s) -

Natsuhiro Ichinose,

Motomasa Komuro

Publication year - 2014

Publication title -

chaos an interdisciplinary journal of nonlinear science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.971

H-Index - 113

eISSN - 1089-7682

pISSN - 1054-1500

DOI - 10.1063/1.4896219

Subject(s) - reduction (mathematics) , control theory (sociology) , phase (matter) , physics , phase difference , state (computer science) , periodic orbits , feedback control , orbit (dynamics) , quasi periodic , control (management) , mathematics , computer science , astrophysics , algorithm , classical mechanics , quantum mechanics , geometry , artificial intelligence , control engineering , aerospace engineering , engineering

The delayed feedback control (DFC) is applied to stabilize unstable quasi-periodic orbits (QPOs) in discrete-time systems. The feedback input is given by the difference between the current state and a time-delayed state in the DFC. However, there is an inevitable time-delay mismatch in QPOs. To evaluate the influence of the time-delay mismatch on the DFC, we propose a phase reduction method for QPOs and construct a phase response curve (PRC) from unstable QPOs directly. Using the PRC, we estimate the rotation number of QPO stabilized by the DFC. We show that the orbit of the DFC is consistent with the unstable QPO perturbed by a small state difference resulting from the time-delay mismatch, implying that the DFC can certainly stabilize the unstable QPO

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