µ Analysis for Robust Blood Glucose Regulation in T1DM Patients

The idea of an integrated system called Artificial Pancreas (AP) has become a research area for multiple disciplines such as biomedical and automatic control. The AP gives a promising approach for the Type 1 Diabetes Mellitus (T1DM) treatment since an automatic insulin infusion device is expected. This system consists of three parts: control algorithm, insulin pump and glucose sensor. Scientific community has treated these elements separately and some agree that the most challenging part is related to the control algorithm. Initial proposals for this algorithm have appeared, based on classical and well-known control techniques. Nevertheless, the aim of this AP is to reduce disease complications despite variability of internal/external body conditions. From a control point of view this variability can be treated as perturbations or parametric uncertainties. Therefore, robust control techniques should be applied in order to propose more realistic approaches. A sensitivity analysis [18] performed on Sorensen nonlinear model was able to identify three parameters as the most responsible for changes in blood glucose and insulin dynamics. Previous work have suggested unstructured uncertainties on these parameters and proposed H8 control algorithms as the case of Ruiz-Velázquez et. al. [20] and Femat et. al. [21]. In the present paper the same uncertain parameters are structured in the linearized Sorensen model in such a manner μ-analysis is applied. Thus, the aim of this analysis is to verify if robust stability and robust performance are preserved when the H8 control algorithms were designed on a different scenario. The results attempt to justify the use structured uncertainties in a T1DM patient model as a more appropriate approach. This work can be considered as a preliminary in development of new control algorithms for blood glucose regulation based on the μ-synthesis technique.