Optimality of Unconstrained Pulse Inputs to the Bergman Minimal Model

We characterise optimality of bolus insulin inputs, to the Bergman minimal model, by the predicted behaviour of the plasma glucose concentration for a given disturbance. The result is derived subject to the constraints that the plasma glucose concentration must attain but not go below a specified minimum value and the bolus input is rectangular. We give numerical examples of the results for the Hovorka model.