The Inverse Problem of Analytic Interpolation With Degree Constraint and Weight Selection for Control Synthesis
2010 (English)In: IEEE Transactions on Automatic Control, ISSN 0018-9286, E-ISSN 1558-2523, Vol. 55, no 2, 405-418 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2010. Vol. 55, no 2, 405-418 p.
Analytic interpolation, controller synthesis, degree constraint, loop, shaping, model reduction, robust control, weight selection, nevanlinna-pick interpolation, convex-optimization approach, h-infinity, control design, approximation, sensitivity, continuity, feedback
IdentifiersURN: urn:nbn:se:kth:diva-19190DOI: 10.1109/tac.2009.2037280ISI: 000274383400009ScopusID: 2-s2.0-76949096444OAI: oai:DiVA.org:kth-19190DiVA: diva2:337237
FunderSwedish Research Council
QC 20100525 QC 201201182010-08-052010-08-052012-01-18Bibliographically approved