Recent Results on Glucose–Insulin Predictions by Means of a State Observer for Time Delay Systems

Abstract

To achieve accurate and affordable predictions of glucose and insulin plasma concentrations is of paramount importance, especially in the field of the artificial pancreas, where real-time measurements could be properly exploited in model-based glucose control algorithms. This note focuses on a recently developed research line that makes use of a state observer to estimate insulin in real-time from glucose measurements, since it is known that insulin measurements are slower and more cumbersome to obtain, more expensive and also less accurate. Based on these predictions, glucose control algorithms can be designed, and can be exploited for both intra-venous and subcutaneous insulin infusions. The safety, robustness and efficacy of the observer-based control algorithms have been validated on a population of rather heterogenous virtual patients, modeled by a different, comprehensive model of the glucose-insulin system, recently accepted by the Food and Drug Administration as a substitute of animal trials.

Luenberger-Like Observers for Nonlinear Time-Delay Systems with Application to the Artificial Pancreas: The Attainment of Good Performance

“…From a control engineering perspective, glucose and insulin real-time predictions are of great importance for the AP, since they could be required in closed-loop algorithms whenever the complete knowledge of the state of the system is needed to design the control law [14]. Differently from plasma glycemia, which can be straightforwardly measured with relatively low cost devices and affordable algorithms, plasma insulinemia is slower and more cumbersome to obtain, more expensive and also less accurate.…”

“…From a control engineering perspective, realtime predictions of both glucose and insulin blood concentrations (glycemia and insulinemia, respectively) are of great importance for the AP, since they could be required in closedloop algorithms whenever the complete knowledge of the state of the system is needed to implement the control law. Differently from insulinemia, plasma glucose measurements are currently affordable with relatively low cost devices and effective algorithms, thus the control problem of designing suitable closed-loop regulators by means of only glucose measurements is well posed, and the use of a state observer to compensate for the lack of direct insulin measurements deserves interest in the AP community [14].…”

Sampled-data Observer-based Glucose Control for the Artificial Pancreas

“…In this framework, the theory on the artificial control of glycemia has had to address a number of problems, stemming from the nonlinear and delayed insulin response [4,5], the availability of observations on glucose only, and the high variability of the insulin determinations that can be obtained with radio-immunological methods [6]. One fruitful way to address these problems has been through the shift from modelless to model-based control algorithms, in which the controller is synthesized using the model equations themselves.…”

Glucose control with incomplete information

“…Diabetes Mellitus (DM) is a widespread disease (affecting millions of people worldwide) characterized by the lack of insulin production or resistance to insulin action. As a consequence, a number of techniques have been made available in the last few years for the automatic control of glucose levels, which need to cope with the several nonidealities of the underlying dynamics, among which we recall the nonlinear and delayed insulin response [3], [4] and the difficulty in obtaining precise and frequent measurements of the current levels of insulin [5].…”