An LMI-based controller for the glucose-insulin system

Exogenous insulin administration is the standard way to regulate hyperglycemia in diabetic patients and, in the recent decades, the challenging task to design an artificial pancreas has been addressed with the aim to synthesize a closed-loop control law by means of sampled glucose measurements. Model-based control law allow to explicitly exploit the glucose-insulin mathematical model, but need to cope with different sources of uncertainties and disturbances affecting the system. The present note investigates the framework of the H∞ control as a tool to attenuate the effect of a meal, modeled as an unknown disturbance. To this end an LMI-based feedback control law is synthesized, by properly exploiting a Delay Differential Equation model of the glucose-insulin system, that makes use of only glucose measurements, to avoid the use of insulin measurements, known to be slower and more cumbersome to obtain, more expensive and also less accurate than glucose measurements. It is shown by simulations that, besides to regulate plasma glycemia onto a desired level starting from a hyperglycemic state, the control law efficiently constrains the post-prandial increase of glycemia on a very tight control, preventing dangerous oscillations.