Imperial College London
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ProfessorSergeiChernyshenko

Faculty of Engineering, Department of Aeronautics

Chair in Aerodynamics
 
 
 
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Contact

 

+44 (0)20 7594 5548s.chernyshenko Website

 
 
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Location

 

211aCity and Guilds BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Lakshmi:2021:10.1016/j.physd.2021.133009,
author = {Lakshmi, MV and Fantuzzi, G and Chernyshenko, SI and Lasagna, D},
doi = {10.1016/j.physd.2021.133009},
journal = {Physica D: Nonlinear Phenomena},
title = {Finding unstable periodic orbits: A hybrid approach with polynomial optimization},
url = {http://dx.doi.org/10.1016/j.physd.2021.133009},
volume = {427},
year = {2021}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We present a novel method to compute unstable periodic orbits (UPOs) that optimize the infinite-time average of a given quantity for polynomial ODE systems. The UPO search procedure relies on polynomial optimization to construct nonnegative polynomials whose sublevel sets approximately localize parts of the optimal UPO, and that can be used to implement a simple yet effective control strategy to reduce the UPO's instability. Precisely, we construct a family of controlled ODE systems, parameterized by a scalar k, such that the original ODE system is recovered for k=0 and such that the optimal orbit is less unstable, or even stabilized, for k>0. Periodic orbits for the controlled system can often be more easily converged with traditional methods, and numerical continuation in k allows one to recover optimal UPOs for the original system. The effectiveness of this approach is illustrated on three low-dimensional ODE systems with chaotic dynamics.
AU  - Lakshmi,MV
AU  - Fantuzzi,G
AU  - Chernyshenko,SI
AU  - Lasagna,D
DO  - 10.1016/j.physd.2021.133009
PY  - 2021///
SN  - 0167-2789
TI  - Finding unstable periodic orbits: A hybrid approach with polynomial optimization
T2  - Physica D: Nonlinear Phenomena
UR  - http://dx.doi.org/10.1016/j.physd.2021.133009
UR  - http://hdl.handle.net/10044/1/92655
VL  - 427
ER  -
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