Zone Model Predictive Control with Glucose- and Velocity-Dependent Control Penalty Adaptation for an Artificial Pancreas

An adaptive zone model predictive control design problem is considered for enhanced blood glucose regulation in patients with type 1 diabetes mellitus. The key contribution of this work is the development of a zone MPC with a dynamic cost function that updates its control penalty parameters based on the predicted glucose and its rate of change. A parameter adaptation law is proposed by explicitly constructing maps from glucose state and velocity spaces to control penalty parameter spaces. The proposed controller is tested on the to-patient cohort of the US Food and Drug Administration accepted Universities of Virginia/Padova simulator and compared with the zone model predictive control without parameter adaptation. The obtained in-silico results indicate that for unannounced meals, the controller leads to statistically significant improvements in terms of mean glucose level (154.2 mg/dL vs. 160.7 mg/dL; $\boldsymbol{p} < 0.001)$ and percentage time in the safe euglycemic range of [70, 180] mg/dL (72.7% vs. 67.5%; $\boldsymbol{p} < 0.001$) without increasing the risk of hypoglycemia (percentage time below 70 mg/dL, 0.0% vs. 0.0%; $\boldsymbol{p}=0.788$). For announced meals, the obtained performance is similar (and slightly superior) to that of the zone model predictive control without adaptation in terms of mean glucose level (135.6 mg/dL vs. 136.5 mg/dL; $\boldsymbol{p} < 0.001$), percentage time in [70, 180] mg/dL (91.2% vs. 90.9%; $\boldsymbol{p}=0.04$), and percentage time below 70 mg/dL (0.0% vs. 0.0%; $\boldsymbol{p}=0.346$).