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TitleGlucose-insulin control of type,1 diabetic patients in $H_2/H_ infty $ space via computer algebra.
Author(s) Levente Kovacs, Bela Palancz
TypeBook, Chapter in Book, Conference Proceeding
AbstractThis article presents the H 2/H  ∞  control (disturbance rejection LQ method) of the Bergman minimal model [2] 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 γ crit is determined by using the Modified Riccati Control Algebraic (MCARE) equation employing reduced Gröbner 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, γ should be greater than γ 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 γ ≫ γ 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.
ISBN978-3-540-73432-1/pbk
URL http://link.springer.com/chapter/10.1007%2F978-3-540-73433-8_8
LanguageEnglish
Pages95--109
PublisherBerlin: Springer
Year2007
Edition0
Translation No
Refereed No
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