title: Phase-reduction-theory-based treatment of extended delayed feedback control algorithm in the presence of a small time delay mismatch.
abstract: The delayed feedback control (DFC) methods are noninvasive, which means that the control signal vanishes if the delay time is adjusted to be equal to the period of a target unstable periodic orbit (UPO). If the delay time differs slightly from the UPO period, a nonvanishing periodic control signal is observed. We derive an analytical expression for this period for a general class of multiple-input multiple-output systems controlled by an extended DFC algorithm. Our approach is based on the phase-reduction theory adapted to systems with time delay. The analytical results are supported by numerical simulations of the controlled Rössler system.
authors.affiliation: Center for Physical Sciences and Technology, Vilnius, Lithuania.
authors.forename: Viktor
authors.initials: V
authors.lastname: Novičenko
authors.forename: Kestutis
authors.initials: K
authors.lastname: Pyragas
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D005246:Feedback; D016014:Linear Models; D015233:Models, Statistical; D008962:Models, Theoretical; D009991:Oscillometry; D010825:Physics / Q000379:methods*; D013598:Systems Theory; D013995:Time; D013997:Time Factors