Investigation of the TP modeling possibilities of the Hovorka T1DM model

Abstract

Controller design based on Linear Parameter Varying (LPV) and Linear Matrix Inequality (LMI) combination can be extremely useful in modeling and controller design for patient specific physiological systems, which are generally nonlinear, time varying systems. These methods allow us the usage of considerations which come from the linear controller design theorems, but require advanced mathematics and high computational capacity also. In this research we exhibit the usage of the Tensor Product (TP) model transformation regarding diabetes researches as a means to realize a Tensor Product based Type 1 Diabetes Mellitus model, whose basis is a control oriented, deviation based qLPV model. Our primary goal is to realize all possible TP models, derived by choosing different combination of parameters for the qLPV model, and to validate all of them, confirming that all the derived TP models approximately mimic the behavior of the original, nonlinear system having only numeric error.