Positive input observer‐based controller design for blood glucose regulation for type 1 diabetic patients: A backstepping approach

Abstract

Abstract In practice, there are many physical systems that can have only positive inputs, such as physiological systems. Most conventional control methods cannot ensure that the main system input is positive. A positive input observer‐based controller is designed for an intravenous glucose tolerance test model of type 1 diabetes mellitus (T1DM). The backstepping (BS) approach is employed to design the feedback controller for artificial pancreas (AP) systems, based on the Extended Bergman's Minimal Model (EBMM). The EBMM represents the T1DM in terms of the blood glucose concentration (BGC), insulin concentration, and plasma level and the disturbance of insulin during medication due to either meal intake or burning sugar by doing some physical exercise. The insulin concentration and plasma level are estimated using observers, and these estimations are applied as feedback to the controller. The asymptotic stability of the observer‐based controller is proved using the Lyapunov theorem. Moreover, it is proved that the system is bounded input‐bounded output (BIBO) stable in the presence of uncertainties generated by uncertain parameters and external disturbance. For realistic situations, we consider only the BGC to be available for measurement and additionally inter‐and intra‐patient variability of system parameters is considered.

Keywords

• asymptotic stability
• backstepping approach
• blood glucose concentration
• extended Bergman's minimal model
• Lyapunov theorem
• observer design