Delay-Independent regulation of blood glucose for type-1 diabetes mellitus patients via an observer-based predictor feedback approach by considering quantization constraints

Abstract

Diabetes, as a widespread chronic disease, is caused by the increase of blood glucose concentration (BGC) due to pancreatic insulin production failure and/or insulin resistance in the body. The artificial pancreas (AP) known as a closed-loop insulin delivery control system consists of a glucose sensor for BGC measurement, a control algorithm for calculation of exogenous insulin delivery rate (IDR), and an insulin infusion pump. The AP provides a closed-loop glucose-insulin regulatory system for type-1 diabetes mellitus (T1DM) patients in order to effectively reduce the high BGC level. In this paper, we aim to design a controller in order to regulate the BGC of T1DM patients at its basal value with considering meal disturbance in the system. We confront with different problems for glucose control such as sampled and quantized glucose measurement by the sensor, quantized IDR by the insulin infusion pump, and an unknown input delay of the insulin infusion pump as the actuator of the control system. The bergman minimal model (BMM) as the most famous model for describing the glucose-insulin regulatory system is reviewed and the delay-independent observer for the estimation of the system’s state vector from the sensor output (sampled and quantized BGC) is considered. Moreover, the observer works on the basis of an event-triggered strategy in order to avoid unnecessary signal updating. At the end, the IDR calculated by the proposed delay-independent truncated predictor output feedback controller (based on the observer’s output) is delivered to the T1DM patient. A sufficient condition on the insulin infusion pump delay’s upper bound value in order to guarantee the ultimate boundedness of the glucose-insulin regulatory system under the mentioned constraints is derived. Also, the nonoccurrence of Zeno behavior in the proposed control system is proved. Numerical simulation results confirm the effectiveness of the designed controller in the presence of meal disturbance, unknown input delay, and quantization errors for blood glucose regulation of the glucose-insulin regulatory system in T1DM patients. Moreover, a pre-clinical verification of the applicability of the proposed glucose controller is carried out on a large-scale and multi-compartmental model that is the base of the UVA/PADOVA Type-1 Diabetes Simulator.