Glucose-insulin control of typel diabetic patients in H2/H space via computer algebra

Levente Kovács, Béla Paláncz

Research output: Chapter in Book/Report/Conference proceedingConference contribution

26 Citations (Scopus)

Abstract

This article presents the H2/H control (disurbance rejection LQ method) of the Bergman minimal model [2] for Typel diabetic patients under intensive care using computer algebra. To design the optimal controller, the disturbance rejection LQ method based on the minimax differential game is applied. The critical, minimax value of the scaling parameter γcrit is determined by using the Modified Riccati Control Algebraic (MCARE) equation employing reduced Gröbner basis solution on rational field. The numerical results are in good agreement with those of the Control Toolbox of MATLAB. It turned out, that in order to get positive definite solution stabilizing the closed loop, γ should be greater than γcrit. The obtained results are compared with the classical LQ technique on the original non-linear system, using a standard meal disturbance situation. It is also demonstrated that for γ Gt; γcrit, the gain matrix approaches the traditional LQ optimal control design solution. The symbolic and numerical computations were carried out with Mathematica 5.2, and with the CSPS Application 2, as well as with MATLAB 6.5.

Original languageEnglish
Title of host publicationAlgebraic Biology - Second International Conference, AB 2007, Proceedings
PublisherSpringer Verlag
Pages95-109
Number of pages15
ISBN (Print)9783540734321
DOIs
Publication statusPublished - 2007
Event2nd International Conference on Algebraic Biology, AB 2007 - Castle of Hagenberg, Austria
Duration: Jul 2 2007Jul 4 2007

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4545 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other2nd International Conference on Algebraic Biology, AB 2007
CountryAustria
CityCastle of Hagenberg
Period7/2/077/4/07

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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    Kovács, L., & Paláncz, B. (2007). Glucose-insulin control of typel diabetic patients in H2/H space via computer algebra. In Algebraic Biology - Second International Conference, AB 2007, Proceedings (pp. 95-109). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4545 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-540-73433-8_8