Insulin stabilisation in artificial pancreas: a positive control approach

Abstract

In the therapy of type 1 diabetes, artificial pancreas (AP) involves the automatic insulin delivery. The control problem in AP has been formulated to regulate glucose into its physiological range without accounting for dynamical effects of the delivered insulin. To address this problem, a control scheme to stabilise the insulin is proposed. The method shows that insulin stabilisation is reached and it is further improved while glucose remains into its range. Glucose metabolism is represented by a physiological and compartmental mathematical model, which consists of three interconnected subsystems called glucose, insulin and glucagon subsystems. In particular, the insulin subsystem is a positive linear system, thus it is possible to exploit its properties to propose a stabilisation scheme via positive control. Two approaches are presented: one based on sliding mode theory, and other based on control Lyapunov function theory. Some conditions are stated for the existence of stabilising controllers that improve the stabilisation rate while they take advantage of the cascade structure of the physiological model to maintain glucose into its range. A further application of these schemes is regarding safety of AP, preventing hypoglycaemia and/or hyperinsulinemia induced by a possible overreaction of AP's control schemes.