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

In this paper, an event-based quantized sampled-data 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 event-based 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.