Optimal feedback control strategies for periodic delayed systems

Morad Nazari, Eric Butcher, Oleg A. Bobrenkov

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

In this study, three strategies based on infinite-dimensional Floquet theory, Chebyshev spectral collocation, and the Lyapunov–Floquet transformation (LFT) are proposed for optimal feedback control of linear time periodic delay differential equations using periodic control gains. First, a periodic-gain discrete-delayed feedback control is implemented where optimization of the control gains is included to obtain the minimum spectral radius of the closed-loop response. Second, a large set of ODEs is obtained using the Chebyshev spectral continuous time approximation, after which optimal (time-varying LQR) control is used to obtain a periodic-gain distributed-delayed feedback control. The third strategy involves the use of both CSCTA and the reduced LFT, along with either pole-placement or time-invariant LQR used on a linear time invariant auxiliary system, to obtain a periodic-gain non-delayed feedback control that asymptotically stabilizes the original system. The delayed Mathieu equation is used as an illustrative example for all three control strategies.

Original languageEnglish (US)
Pages (from-to)102-118
Number of pages17
JournalInternational Journal of Dynamics and Control
Volume2
Issue number1
DOIs
StatePublished - Mar 1 2014

Keywords

  • Chebyshev spectral collocation
  • Floquet theory
  • Lyapunov–Floquet transformation
  • Optimal feedback control
  • Periodic delay differential equations

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Control and Systems Engineering
  • Electrical and Electronic Engineering
  • Mechanical Engineering
  • Control and Optimization
  • Modeling and Simulation

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