Stability and causality constraints on frequency response coefficients applied for non-parametric H2 and H∞ control synthesis

A.J. Hamer, den, S. Weiland, M. Steinbuch, G.Z. Angelis

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

6 Citations (Scopus)

Abstract

The value of norm-based control synthesis methodologies heavily depends on the quality of the model at hand. The acquisition of low-order control oriented models however is often a non-trivial task. This paper pursuits the nonparametric synthesis of optimal controllers while omitting parametrization of the plant. As a result, the actual parametrization is performed on the controller such that no data-reduction is performed without knowledge of closed-loop relevant behavior. The synthesis of frequency response coefficients of an optimal controller for a sampled version of the mixed-sensitivity problem is considered. To convexify the problem, the actual optimization is performed over the frequency response coefficients of the Youla parameter Qi. Using the Youla parameter, the set of stabilizing controllers is mapped onto the set of stable transfer functions. The main contribution of this paper is the derivation of algebraic constraints over Qi that guarantee the existence of a rational stable interpolant over the points Qi. Simulations shows that the frequency response coefficients found via the proposed approach show similar behavior as model based methods. © 2008 IEEE.
Original languageEnglish
Title of host publicationProceedings of the 47th IEEE Conference on Decision and Control (CDC 2008) : Mexico, Cancún, 9 - 11 December 2008
Place of PublicationPiscataway, NJ
PublisherInstitute of Electrical and Electronics Engineers
Pages3670-3675
ISBN (Print)978-1-4244-3124-3
DOIs
Publication statusPublished - 2008

Fingerprint Dive into the research topics of 'Stability and causality constraints on frequency response coefficients applied for non-parametric H2 and H∞ control synthesis'. Together they form a unique fingerprint.

  • Cite this

    Hamer, den, A. J., Weiland, S., Steinbuch, M., & Angelis, G. Z. (2008). Stability and causality constraints on frequency response coefficients applied for non-parametric H2 and H∞ control synthesis. In Proceedings of the 47th IEEE Conference on Decision and Control (CDC 2008) : Mexico, Cancún, 9 - 11 December 2008 (pp. 3670-3675). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC.2008.4739015