The inverse problem of analytic interpolation with degree constraint and weight selection for control synthesis

Johan Karlsson, Tryphon T. Georgiou, Anders G. Lindquist

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

The minimizers of certain weighted entropy functionals are the solutions to an analytic interpolation problem with a degree constraint, and all solutions to this interpolation problem arise in this way by a suitable choice of weights. Selecting appropriate weights is pertinent to feedback control synthesis, where interpolants represent closed-loop transfer functions. In this paper we consider the correspondence between weights and interpolants in order to systematize feedback control synthesis with a constraint on the degree. There are two basic issues that we address: we first characterize admissible shapes of minimizers by studying the corresponding inverse problem, and then we develop effective ways of shaping minimizers via suitable choices of weights. This leads to a new procedure for feedback control synthesis.

Original languageEnglish (US)
Article number5378470
Pages (from-to)405-418
Number of pages14
JournalIEEE Transactions on Automatic Control
Volume55
Issue number2
DOIs
StatePublished - Feb 1 2010

Keywords

  • Analytic interpolation
  • Controller synthesis
  • Degree constraint
  • Loop shaping
  • Model reduction
  • Robust control
  • Weight selection

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