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

• Autorzy: Grabowski P.
• Języki publikacji: EN

Abstrakty

EN

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 Zołopa and the author.

Słowa kluczowe

EN

control of infinite-dimensional systems; semigroups; infinite-time lq-control problem

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2013
• Tom: Vol. 33, no. 1
• Strony: 29--79
• Opis fizyczny: Bibliogr. 26 poz.

Twórcy

autor

Grabowski P.

• 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,

Bibliografia

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