This article presents the H2/Hinf control (disturbance rejection LQ method) of the
Bergman minimal model [1] for Type1 diabetic patients under intensive care using computer
algebra. 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 gamma_crit is determined by using the Modified Riccati Control Algebraic
(MCARE) equation employing reduced Groebner basis solution on rational field. The
numerical results are in good agreement with those of the Control Toolbox of MATLAB.
It turned out, that in order to get positive definite solution stabilizing the closed
loop, should be greater than gamma_crit. The obtained results are compared with the
classical LQ technique on the original non-linear system, using a standard meal disturbance
situation. It is also demonstrated that for gamma >> gamma_crit, the gain matrix approaches
the traditional LQ optimal control design solution. The symbolic and numerical computations
were carried out with Mathematica 5.2, and with the CSPS Application 2, as well as
with MATLAB 6.5.
