Optimal Responses to Constrained Bolus Inputs to Models of T1D

We characterise the bolus insulin input which minimises the maximum plasma glucose concentration predicted by the Magdelaine and Bergman minimal models in response to any positive bounded disturbance whilst remaining above a fixed lower plasma glucose concentration. This characterisation is in terms of the maxima and minima of the plasma glucose concentration and limits the controllability of such systems. Any further attempt to lower the maximum plasma glucose concentration will result in hypoglycaemia.