Observer-based controller design for blood glucose regulation for type 1 diabetic patients with disturbance estimation: A backstepping approach

Abstract

In this paper, an observer-based nonlinear controller is proposed to regulate blood glucose concentration (BGC) in type 1 diabetes mellitus (T1DM). The considered virtual patient model is the extended Bergmann minimal model, which is augmented by a meal disturbance and adapted to represent the insulin–glucose homeostasis of T1DM. The backstepping (BS) technique is used to design a closed-loop feedback controller. The proposed controller does not need to measure insulin, plasma concentrations, and external disturbances while improving control performance and robustness against uncertainty. Insulin concentrations and plasma levels are estimated using state observers and disturbance using a disturbance estimator. These estimations are used as feedback to the controller. The asymptotic stability of the observer-based controller is proved using the Lyapunov theorem. Furthermore, it is proven that the system is bounded input–bounded output (BIBO) stable in the presence of uncertainties caused by uncertain parameters and external disturbances. For real situations, we consider only the BGC available for measurement, and in addition, inter- and intra-patient variability of system parameters is considered. The results confirm that the proposed controller can asymptotically regulate BGC through appropriate injection of insulin under meal disturbance and $\pm 25\%$ of variations in system parameters.