@article{Paláncz_Kovács_2006, title={APPLICATION OF COMPUTER ALGEBRA FOR GLUCOSE-INSULIN CONTROL IN H<I><sub>2</sub></I>/H<I><sub>inf</sub></I> SPACE USING MATHEMATICA}, volume={50}, url={https://pp.bme.hu/ee/article/view/890}, DOI={N/A}, abstractNote={In this case study, an optimal control in H<I><sub>2</sub></I>/H<I><sub>inf</sub></I> 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 <I>γ<sub>crit</sub></I> is determined by symbolic solution of the
modified Riccati equation. The numeric evaluation of the symbolic
computation for <I>γ > γ <sub>crit</sub></I> leads to two different solutions, but the norms of
the vectors <I>λ<sub>1</sub>, λ<sub>2</sub></I> 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 <I>μ</I>-Toolbox of MATLAB. One of the gain matrices
with increasing <I>γ </I>, approaches the gain matrix computed with the traditional
LQ optimal control design. The symbolic and numerical computations were
carried out with \textitMathematica 5, and with the CSPS Application 2 as well as with MATLAB
6.5.
}, number={1-2}, journal={Periodica Polytechnica Electrical Engineering}, author={Paláncz, Béla and Kovács, Levente}, year={2006}, pages={33–45} }