Résumé
One of the main limiting factors in improving glucose control for type 1 diabetes mellitus (T1DM) subjects is the lack of a precise description of meal and insulin intake effects on blood glucose. Knowing the magnitude and duration of such effects would be useful not only for patients and physicians, but also for the development of a controller targeting glycaemia regulation. Therefore, in this paper we focus on estimating low-complexity yet physiologically sound and individualised multi-input single-output (MISO) models of the glucose metabolism in T1DM able to reflect the basic dynamical features of the glucose-insulin metabolic system in response to a meal intake or an insulin injection. The models are continuous-time second-order transfer functions relating the amount of carbohydrate of a meal and the insulin units of the accordingly administered dose (inputs) to plasma glucose evolution (output) and consist of few parameters clinically relevant to be estimated. The estimation strategy is continuous-time data-driven system identification and exploits a database in which meals and insulin boluses are separated in time, allowing the unique identification of the model parameters.