Robust Control Algorithms for Blood Glucose Control Using Mathematica

Application of modern robust control methods using Mathematica are presented in this case-study for blood glucose control of Type I diabetic patients under intensive care. The methods are applied on the minimal model of Bergman [1], using computer algebra. Two modern robust control methods are exemplified: the disturbance rejection LQ control or minimax control (as an extension of the classical LQ control) and the robust H∞ control. It is shown the minimax control has limitations in practice, but employing reduced Gröbner basis on rational field, it is possible to approximate the theoretical solution and so getting a better solution than LQ does. In case of H∞ control, the graphical method in frequency domain – implemented under Mathematica by [2] – is extended with a disturbance rejection constraint and the robustness of the resulted high-order linear controller is demonstrated by nonlinear closed loop simulation in state-space, in case of standard meal disturbances. The symbolic and numeric computations were carried out with Mathematica 5.2 and with its CSPS Application, as well as with MATLAB 6.5.