TY - JOUR
AU - Paláncz, Béla
AU - Kovács, Levente
PY - 2006/01/01
Y2 - 2024/09/11
TI - APPLICATION OF COMPUTER ALGEBRA FOR GLUCOSE-INSULIN CONTROL IN H<I><sub>2</sub></I>/H<I><sub>inf</sub></I> SPACE USING MATHEMATICA
JF - Periodica Polytechnica Electrical Engineering
JA - Period. Polytech. Elec. Eng.
VL - 50
IS - 1-2
SE -
DO - N/A
UR - https://pp.bme.hu/ee/article/view/890
SP - 33-45
AB - In this case study, an optimal control in H<I><sub>2</sub></I>/H<I><sub>inf</sub></I> space ispresented for glucose- insulin system of diabetic patients under intensivecare. The analysis is based on a modified two-compartment Bergman model. Todesign the optimal controller, the disturbance rejection LQ method based onthe minimax differential game is applied. The critical, minimax value of thescaling parameter <I>γ<sub>crit</sub></I> is determined by symbolic solution of themodified Riccati equation. The numeric evaluation of the symboliccomputation for <I>γ > γ <sub>crit</sub></I> leads to two different solutions, but the norms ofthe vectors <I>λ<sub>1</sub>, λ<sub>2</sub></I> formed by the eigenvalues of the pair ofthe gain matrices are the same. The numerical results are in good agreementwith that of the <I>μ</I>-Toolbox of MATLAB. One of the gain matriceswith increasing <I>γ </I>, approaches the gain matrix computed with the traditionalLQ optimal control design. The symbolic and numerical computations werecarried out with \textitMathematica 5, and with the CSPS Application 2 as well as with MATLAB6.5.
ER -