Nonlinear analysis of Type 1 Diabetes Models by Differential Geometric Approach

The control of physiological systems is a highly demanding task. The requirements are strict and there is a little margin of error, since failure can directly endanger the patient's life. In the same time the performance of the available sensors and actuators are limited in most cases, leaving even higher burden on the control algorithm. Finally the models themselves, which can describe the biophysical and biochemical processes that are most significantly linked to the system we wish to regulate, are rather complex and nonlinear in nature. In general, linear model-based approaches are used, but linearization gives a first source of errors in the further development. The aim of this paper is to investigate two frequently used models describing the metabolism of the human body in case of Type 1 Diabetes Mellitus (T1DM) from nonlinear control perspective: the model presented by Magni et al. (2009) and Hovorka et al. (2004). These models will be investigated using differential geometric approach for the first time.