Model Predictive Control of glucose concentration based on Signal Temporal Logic specifications

Insulin is a peptide hormone produced by the pancreas to regulate the cells intake of glucose in the blood. Type 1 diabetes compromises this particular capacity of the pancreas. Patients with this disease inject insulin to regulate the level of glucose in the blood, thus reducing the risk of longterm complications. Artificial Pancreas (AP) is a wearable device developed to provide automatic delivery of insuline, allowing a potentially significant improvement in the quality of life of patients. In this paper we apply to the AP a Model Predictive Controller able to generate state trajectories that meet constraints expressed through Signal Temporal Logic (STL). Such a form of constraints is indeed appropriate for the AP, in which some requirements result in hard constraints (absolutely avoid hypoglycaemia) and some other in soft constraints (avoid a prolonged hyperglycaemia). We rely on the BluSTL toolbox, which allows to automatically generate controllers using STL specifications. We perform simulations on two different scenarios: an MPC controller that uses the same constraints as [1] and an MPC-STL controller in both deterministic and adversarial environment (robust control). We show that the soft constraints permitted by STL avoid unnecessary restriction, providing safe trajectories in correspondence of higher disturbance.