On the Digital Event-Based Implementation of a Glucose Regulator via Subcutaneous Insulin Infusion

In this paper, an event-based quantized sampleddata control strategy is proposed for the plasma glucose regulation problem in Type 2 diabetic patients. In particular, the proposed event-triggered digital glucose regulator is designed by exploiting a nonlinear time-delay model of the glucose-insulin regulatory system which takes into account the subcutaneous infusion of insulin. It is proved that the provided quantized sampled-data glucose controller, updated via a proposed eventbased mechanism, guarantees the semi-global practical stability property of the related closed–loop tracking error system, with arbitrarily small steady–state tracking error. The stabilization in the sample–and–hold sense theory is used as a tool to prove the results. An approximation scheme based on first– order splines is used in order to cope with the problem of the possible non–availability in the buffer of the value of the system variables at some past times which are needed for the implementation of the proposed digital controller. The possible non-uniform quantization of the input/output channels as well as the case of time–varying sampling periods are included in the theory here developed. The validation of the proposed glucose control strategy is carried out via simulations.