APPLICATION OF COMPUTER ALGEBRA FOR GLUCOSE-INSULIN CONTROL IN H<I><sub>2</sub></I>/H<I><sub>inf</sub></I> SPACE USING MATHEMATICA
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 > γ crit 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 \textitMathematica 5, and with the CSPS Application 2 as well as with MATLAB 6.5.