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

Abstract

In this paper we deal with the problem of tracking a desired plasma glucose evolution by means of intravenous insulin administration, for Type 2 diabetic patients exhibiting basal hyperglycemia. A nonlinear time-delay model is used to describe the glucose-insulin regulatory system, and a modelbased approach is exploited in order to design a global sampleddata control law for such system. Sontag's universal formula is designed to obtain a steepest descent feedback induced by a suitable control Lyapunov-Krasovskii functional. Such a feedback is a stabilizer in the sample-and-hold sense. Furthermore, the input-to-state stability redesign method is used in order to attenuate the effects of bounded actuation disturbances and observation errors, which can appear for uncertainties in the instruments. The proposed control law depends on sampled glucose and insulin measurements. Theoretical results are validated through simulations.

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

“…In [13], a preliminary result on a global nonlinear sampleddata regulator for the glucose-insulin system is provided, with the drawback of a complete knowledge of the state of the system, i.e. the implementation of the control strategy provided in [13] requires both glucose and insulin measurements. Unfortunately, insulin measurements are less accurate than glucose measurements and time-consuming to obtain, thus inappropriate to be exploited in a real-time closed-loop control algorithm.…”

“…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 [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.…”

“…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.…”

FPGA-Based Implementation of a Digital Insulin-Glucose Regulator for Type 2 Diabetic Patients

“…A key aspect to be considered in designing a glucose regulator for an AP is the time sampling of the patient glucose concentration and its quantization in the implemented digital devices [10][11][12][13]. In this regard, sampled-data glucose regulators for T2DM patients have been proposed by exploiting both insulin and glucose measurements [14,15]. However, for real time AP operations, direct insulin measurements are not exploitable since they need the use of specific chemical reagents, a drawback that can be only overcome by measuring the blood glucose concentration [16,17].…”

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.…”