Fejer and Suffridge polynomials in the delayed feedback control theory
Dmitriy Dmitrishin, Anna Khamitova, Anatolii Korenovskyi, Alex, Stokolos
TL;DR
This paper uncovers a link between optimal delayed feedback control and complex polynomial mappings, revealing that extremal polynomials are related to Fejer polynomials, which can stabilize cycles in nonlinear discrete systems.
Contribution
It establishes a novel connection between DFC and Fejer polynomials, providing explicit extremal polynomials for stabilization in nonlinear systems.
Findings
Optimal DFC is connected to Fejer polynomial structures.
Explicit extremal polynomials are derived for control.
The approach stabilizes cycles in nonlinear discrete systems.
Abstract
A remarkable connection between optimal delayed feedback control (DFC) and complex polynomial mappings of the unit disc is established. The explicit form of extremal polynomials turns out to be related with the Fejer polynomials. The constructed DFC can be used to stabilize cycles of one-dimensional non-linear discrete systems.
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Taxonomy
TopicsQuantum chaos and dynamical systems · Advanced Differential Equations and Dynamical Systems · Chaos control and synchronization