Local sampled-data control of the glucose-insulin system

Abstract

In this work we consider the local sampleddata stabilization of human plasma glycemia. It is proved theoretically that the implementation by sampling and holding, for suitable small sampling period, of a state feedback which is shown in the literature to yield local stabilization when applied in a continuous time basis, yields local practical stabilization, with arbitrarily small final target ball. The model of the system is given by a nonlinear retarded functional differential equation and the above state feedback is provided by standard tools of differential geometry for time-delay systems. The proposed theoretical result proves an important property for the digital implementation of the controller, which has been shown in past literature to perform very well when checked in closed-loop with well known computer simulators of diabetic patients approved by the Food and Drug Administration as a substitute of animal trials.

Sample-data output-feedback parameter variable control of glucose for type 1 diabetes mellitus patients

“…Estimating the states of BMM without linearization and observer-based controllers was proposed using an unscented Kalman filter in Eberle and Ament (2011) and an extended Kalman filter in Eberle and Ament (2012). Using the sampled-data control theory in Di Ferdinando et al (2020), Pepe et al (2017), and Di et al (2017), sampled-data controllers for T2DM patients are presented, in which measurements of glucose and insulin concentrations are utilized. For real-time control of the BGC in the AP system, insulin measurement is not possible.…”

Semiglobal Sampled-Data Dynamic Output Feedback Controller for the Glucose–Insulin System

“…Differently from [32], [33], here the proposed regulator is synthesized according to a novel control design architecture, on the ground of sampled-data measurements (sampled-data regulator). Preliminary results have been proposed in [39] where a local sampled-data control law for the nonlinear DDE model is presented. In [13] a semi-global sampleddata controller for the glucose-insulin system is provided.…”

“…In [13] a semi-global sampleddata controller for the glucose-insulin system is provided. In [39] and [13] both measurements of glucose and insulin concentrations are required by the controller, thus making these works just a proof of concept since, unfortunately, insulin measurements cannot be exploited in real-time closed-loop algorithms because they are time-consuming and cumbersome to achieve. This drawback is, here, overcome since the design of the proposed semi-global nonlinear sampled-data control law makes use of only plasma glucose measurements.…”

Robust global nonlinear sampled-data regulator for the Glucose-Insulin system

“…Differently from [22], [24], here the proposed regulator is synthesized according to a different control design architecture, on the ground of sampled-data measurements (sampled-data regulator). Preliminary results have been proposed in [31] where a local sampled-data control law for the nonlinear DDE model is presented, whilst here the problem to consider a global sampled-data control law is investigated. To the best of our knowledge, this problem has not been addressed in the literature.…”