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Optimal Control in H2 space

Béla Paláncz
Organization: Budapest University of Technology and Economics
Department: Photogrammetry and Geoinformatics
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In this case study, an optimal control in a space is presented for glucose - insulin system of diabetic patients under intensive care. The analysis is based on a modified two-compartment model. To design optimal controller, the disturbance rejection, LQR method based on minimax differential game is applied. The critical, minimax value of the scaling parameter a, is determined by symbolic solution of the modified Ricatti equation. The numeric evaluation of the symbolic computation for γ > a leads two different solutions, but the norms of the vectors {a, a} 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, however this latest gives only one of the two solutions. 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 Mathematica 5. and with the CSPS Application 2. as well as with MATLAB 6.5

*Engineering > Control Theory
*Wolfram Technology > Application Packages > Wolfram Research Applications > Control System Professional

Optimal control, Hardy space, Ricatti equation, symbolic-numeric solution, Bela Palancz
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LQRM.nb (538.7 KB) - Mathematica Notebook [for Mathematica 5.0]