A closed-loop optimal control of the plasma glycemia

The paper investigates the problem of the optimal tracking of a desired plasma glucose evolution by means of a continuous intravenous infusion. The model for the glucose-insulin system here adopted, and recently published, belongs to the class of nonlinear single-distributed delay models. The closed-loop control law is performed according to the feedback linearization theory: a state-feedback is designed in order to exactly linearize the model with respect to a suitably defined change of coordinates. Then, the optimal tracking is achieved by minimizing a performance index. The methodology here proposed allows both to decrease and increase the glycemia. Simulations support theoretical results and show the physical reliability of the approach proposed.