Glucose Estimation in A Diabetes Mellitus Virtual Patient with Sampled Signal and Input Delay

This paper presents a control strategy for blood glucose regulation in the presence of an unknown time-varying delayed input. The proposed control scheme is based on an observer-based linear parameter varying (LPV) control with an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$H$</tex> criterion, designed for the Bergman minimal model (BMM) for type 1 diabetes mellitus patients. This control strategy regulates glucose levels in response to meal intake. A novel LPV system representation is used to mitigate the inherent conservativeness of the nonlinear system. The observer employs an event-triggered (ET) strategy to avoid unnecessary signal updates, enabling the estimation of the current state vector despite the delayed input, even when the delay is relatively long. Consequently, the control law ensures good performance despite a long unknown delay. The observer-based control scheme is validated under various meal disturbances and unknown delay.