Low-dimensional approximation and control of periodic solutions in spatially extended systems

S. Y. Shvartsman, I. G. Kevrekidis

Research output: Contribution to journalArticlepeer-review

25 Scopus citations

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-Loève 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.

Original languageEnglish (US)
Pages (from-to)361-368
Number of pages8
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume58
Issue number1
DOIs
StatePublished - Jan 1 1998

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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