@article{39036,
  keywords = {feedback, equation, models, patterns, stabilization, coherent   structures, chaos, karhunen-loeve decomposition, reaction-diffusion system, tracking},
  author = {Shvartsman and Kevrekidis},
  title = {Low-dimensional approximation and control of periodic solutions in spatially extended systems},
  abstract = { Nonlinear model reduction is combined with numerical continuation and linear state-space control techniques to design regulators for periodic solutions in a spatially extended system. We address issues of construction and systematic evaluation of low-dimensional dynamic models using Galerkin projections on empirical orthogonal eigenfunctions (also known as proper orthogonal decomposition modes or Karhunen-Loeve modes). The reduced order dynamical systems are used first to compute the open-loop bifurcation diagrams and then to design feedback controllers stabilizing unstable limit cycles. We outline the steps for discrete-time controller design and computational linear stability analysis of the resulting hybrid (continuous-discrete) closed-loop systems. },
  year = {1998},
  journal = {Physical Review EPhysical Review E},
  volume = {58},
  pages = {361-368},
  month = {07/1998},
  isbn = {1063-651X},
  language = {English},
}