Opuscula Math. 33, no. 1 (2013), 29-79

Opuscula Mathematica

The lq-controller synthesis problem for infinite-dimensional systems in factor form

Piotr Grabowski

Abstract. The general lq-problem with infinite time horizon for well-posed infinite-dimensional systems has been investigated by George Weiss and Martin Weiss and by Olof Staffans with a complement by Kalle Mikkola and Olof Staffans. Our aim in this paper is to present a solution of a general lq-optimal controller synthesis problem for infinite-dimensional systems in factor form. The systems in factor form are an alternative to additive models, used in the theory of well-posed systems, which rely on leading the analysis exclusively within the basic state space. As a result of applying the simplified analysis in terms of the factor systems and an another derivation technique, we obtain an equivalent, however, astonishingly not the same formulae expressing the optimal controller in the time-domain and the method of spectral factorization. The results are illustrated by two examples of the construction of both the optimal control and optimal controller for some standard lq-problems met in literature: a control problem for a class of boundary controlled hyperbolic equations initiated by Chapelon and Xu, to which we give full solution and an example of the synthesis of the optimal control/controller for the standard lq-problem with infinite-time horizon met in the problem of improving a river water quality by artificial aeration, proposed by Żołopa and the author.

Keywords: control of infinite-dimensional systems, semigroups, infinite-time lq-control problem.

Mathematics Subject Classification: 49N10, 93B05, 93C25.

Full text (pdf)

  • Piotr Grabowski
  • AGH University of Science and Technology, Faculty of Electrical Engineering, Automatics, Biomedical Engineering and Computer Science, Institute of Control and Biomedical Engineering, al. Mickiewicza 30, 30-059 Krakow, Poland
  • Received: 2011-10-13.
  • Revised: 2012-03-23.
  • Accepted: 2012-03-29.
Opuscula Mathematica - cover

Cite this article as:
Piotr Grabowski, The lq-controller synthesis problem for infinite-dimensional systems in factor form, Opuscula Math. 33, no. 1 (2013), 29-79, http://dx.doi.org/10.7494/OpMath.2013.33.1.29

Download this article's citation as:
a .bib file (BibTeX),
a .ris file (RefMan),
a .enw file (EndNote)
or export to RefWorks.

In accordance with EU legislation we advise you this website uses cookies to allow us to see how the site is used. All data is anonymized.
All recent versions of popular browsers give users a level of control over cookies. Users can set their browsers to accept or reject all, or certain, cookies.