Periodic event-based regulation of blood glucose for type-1 diabetic patients in the presence of unknown actuation delay and quantization in BGC measurement and infused insulin

Abstract

In this paper, a delay-independent observer-based truncated predictor output feedback controller is considered to overcome the problem of glucose regulation in the normoglycemic band in type-1 diabetes mellitus (T1DM) patients. The proposed controller confronts with various difficulties such as unannounced meal intakes (modeled as disturbances), sampled and quantized measured blood glucose concentration (BGC) level due to the mechanism of the continuous glucose measurement (CGM) device as a digital glucose sensor, quantized infused insulin as the output of the digital insulin infusion pump, and an unknown input delay in the automated delivery system. The automated delivery system with three fundamental elements CGM device (as a glucose sensor), a controller for calculation of the required infused insulin, and an insulin infusion pump provides a closed-loop glucose–insulin regulatory framework for T1DM patients in order to effectively regulate the BGC level and keep it in the normoglycemic band (i.e., 70-180 (mg/dl)). An observer is applied for the estimation of the unmeasured state variables of the system. Furthermore, a periodic event-triggered strategy is introduced to specify whether it is required to send the information of the CGM device (as the sensor) for the controller. Moreover, another periodic event-triggered strategy is proposed to determine whether it is needed to change the infusion rate of the insulin pump (as the actuator). Benefiting from these periodic event-triggered strategies, the communication and energy consumptions of the automated delivery system are reduced. A sufficient condition on the delay’s upper bound value is obtained in order to assure the local exponential stability (LES) of the glucose–insulin regulatory system. Design of the controller has been done based on the nonlinear Bergman minimal model (BMM) as a so-called model for control design purposes in T1DM patients. Also, the proposed approach is validated on 10 adult virtual patients (VPs) with a large-scale and multi-compartmental model that is the base of the UVA/PADOVA Type-1 Diabetes Simulator in the presence of the unannounced meal intakes.