Imperial College London
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ProfessorGeorgePapadakis

Faculty of Engineering, Department of Aeronautics

Professor of Aerodynamics
 
 
 
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Contact

 

+44 (0)20 7594 5080g.papadakis

 
 
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Location

 

331City and Guilds BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Papadakis:2020:10.1098/rspa.2020.0322,
author = {Papadakis, G and Shawki, K},
doi = {10.1098/rspa.2020.0322},
journal = {Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences},
pages = {1--20},
title = {Feedback control of chaotic systems using Multiple Shooting Shadowing andapplication to Kuramoto Sivashinsky equation},
url = {http://dx.doi.org/10.1098/rspa.2020.0322},
volume = {476},
year = {2020}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We   propose   an   iterative   method   to   evaluate   thefeedback  control  kernel  of  a  chaotic  system  directlyfrom the system’s attractor. Such kernels are currentlycomputed   using   standard   linear   optimal   controltheory,  known  as  Linear  Quadratic  Regulator  (LQR)theory.  This  is  however  applicable  only  to  linearsystems,   which   are   obtained   by   linearising   thesystem  governing  equations  around  a  target  state.In the present paper, we employ the PreconditionedMultiple  Shooting  Shadowing  (PMSS)  algorithm  tocompute   the   kernel   directly   from   the   non-linear dynamics, thereby bypassing the linear approximation.Using  the  adjoint  version  of  the  PMSS  algorithm,we  show  that  we  can  compute  the  kernel  at  any point  of  the  domain  in  a  single  computation.  The algorithm replaces the standard adjoint equation (that is  ill-conditioned  for  chaotic  systems)  with  a  well-conditioned  adjoint,  producing  reliable  sensitivities which   are   used   to   evaluate   the   feedback   matrix elements.   We   apply   the   idea   to   the   Kuramoto Sivashinsky   equation.   We   compare   the   computed kernel   with   that   produced   by   the   standard   LQR algorithm and note similarities and differences. Bothkernels  are  stabilising,  have  compact  support  and similar shape. We explain the shape using two-point spatial correlations that capture the streaky structure of the solution of the uncontrolled system.
AU  - Papadakis,G
AU  - Shawki,K
DO  - 10.1098/rspa.2020.0322
EP  - 20
PY  - 2020///
SN  - 1364-5021
SP  - 1
TI  - Feedback control of chaotic systems using Multiple Shooting Shadowing andapplication to Kuramoto Sivashinsky equation
T2  - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
UR  - http://dx.doi.org/10.1098/rspa.2020.0322
UR  - https://royalsocietypublishing.org/doi/10.1098/rspa.2020.0322
UR  - http://hdl.handle.net/10044/1/81469
VL  - 476
ER  -
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