Asymptotic output tracking in blood glucose control. A case study

Glucose is the primary source of energy for the human body. Keeping the blood glucose level between certain thresholds is essential for the proper energy transport. Insulin plays a key role in maintaining the glucose homeostasis. Because of its great importance, many models were published on either to describe the glucose-insulin interaction in case of patients under Intensive Care Unit (ICU), or to model Type 1 Diabetes Mellitus (T1DM). Currently for most of the models linear control concepts are used in order to design an appropriate controller. The aim of the current paper is to investigate applicability of nonlinear control theory providing exact mathematical background in the control problem of glucose-insulin interaction. Both ICU and T1DM cases are analyzed on well-known models with different complexity. Our aim is to hide the nonlinearity of the models by transforming the input signal so that the response of the model would mimic the behavior of a linear system; hence extending the validity of linear controllers. The asymptotic tracking problem needs the value of the state variables; therefore extended Kalman-filter is applied. The capabilities of this approach are examined through classical control algorithms and input data recorded in clinical environment.