Application of computer algebra for glucose-insulin control in H 2/Hinf space using Mathematica

Béla Paláncz, L. Kovács

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

In this case study, an optimal control in H2/Hinf space is presented for glucose- insulin system of diabetic patients under intensive care. The analysis is based on a modified two-compartment Bergman model. 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 symbolic solution of the modified Riccati equation. The numeric evaluation of the symbolic computation for γ > γcrit leads to two different solutions, but the norms of the vectors {λ1, λ2} formed by the eigenvalues of the pair of the gain matrices are the same. The numerical results are in good agreement with that of the μ-Toolbox of MATLAB. One of the gain matrices with increasing γ, approaches the gain matrix computed with the traditional LQ optimal control design. The symbolic and numerical computations were carried out with Mathematica 5, and with the CSPS Application 2 as well as with MATLAB 6.5.

Original languageEnglish
Pages (from-to)33-45
Number of pages13
JournalPeriodica Polytechnica, Electrical Engineering
Volume50
Issue number1-2
Publication statusPublished - 2006

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Insulin
Algebra
Glucose
MATLAB
Riccati equations
Disturbance rejection
Controllers

Keywords

  • Disturbance rejection LQ method
  • Glucose-insulin control
  • LQ control
  • Mathematica
  • Symbolic computation

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

Cite this

Application of computer algebra for glucose-insulin control in H 2/Hinf space using Mathematica. / Paláncz, Béla; Kovács, L.

In: Periodica Polytechnica, Electrical Engineering, Vol. 50, No. 1-2, 2006, p. 33-45.

Research output: Contribution to journalArticle

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