APPLICATION OF COMPUTER ALGEBRA FOR GLUCOSE-INSULIN CONTROL IN H<I>₂</I>/H<I>_inf</I> SPACE USING MATHEMATICA

Abstract

In this case study, an optimal control in H₂/H_inf 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 γ_crit 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.