the positioning and point cloud problems - and the solution of application problems does not allow purism in methodology but, rather, has to embrace different approaches with different benefits in different circumstances. The reason why this project manages to bring the algebraic and the numerical aspect together is because it is strictly goal-oriented towards the solution of fundamental problems in the areas of geosciences,- e.g. The project points to the recent combination of algebraic and numerical methods (“hybrid” methods), which is currently one of the most promising directions in the area of computer mathematics and geosciences in general. The project employs both algebraic (“exact ”, e.g., Groebner basis and Multiresultant techniques) and numerical (“approximate”, e.g., Homotopy and Extended Newton-Raphson) methods. The goal of this project is to use mathematical methods for the solution of multi-variable polynomial equations that are often encountered in geosciences. Keywords: symbolic computation, diabetes mellitus, blood glucose control and modeling with Mathematica, nonlinear control, Pontryagin's maximum principle. The results are in good agreement with the earlier presented symbolic-numeric analysis by. The effectivity of the applied symbolic -numeric procedures being mostly built-in the new version of Control System Professional Suite (CSPS) of Mathematica 5, have been demonstrated for controller design in case of a glucose control for treatment of diabetes mellitus. In case of nonlinear approach, the nonlinear optimal control law based on the Pontryagin's maximum principle has been developed assuming that glucose injection is the only control variable.
In the case of linear approach, the applied feedback control law decoupling even the nonlinear model leads to a fully symbolic solution of the closed loop equations. The analysis is based on a modified two-compartment model proposed by. In this case study two symbolic-numeric design and modeling methods are compared for blood glucose control of diabetic patients under intensive care.
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