Linear Matrix Inequality-based Robust Controller design for Type-1 Diabetes Model

Abstract

This paper investigates the capabilities of a sophisticated robust nonlinear controller designed directly for a widely known and used high-order nonlinear type 1 diabetes (T1DM) model to lessen the dependency from patient compliance and to answer practical requirements such as avoiding hypoglycaemia. The resulting controller can perform adequately in nominal conditions, but expected to keep this performance even in extreme situations, e.g. high carbohydrate intake, rejecting hypoglycaemic episodes.

Long-term prediction for T1DM model during state-feedback control

“…Therefore, hypoglycemia can occur. Finally, because of the max{} functions present in (2) one can define not one but four separate LPV models depending on the value of Q 1 (t) and x 3 (t) (or k a S IE S 2 (t)/(V I k e ) in the reduced model) as presented in [15]. 1) Endogenous glucose production (EGP) is active and there is no renal extraction of glucose: (x 3 (t) ≤ 1) and Q 1 (t) < R thr V G ; 2) EGP is active (x 3 (t) ≤ 1), and renal extraction is active…”

“…This modified controller will bring the simulated patient to hypoglycemia after every meal intake, which the predictor can detect. The model (2) can be transformed into an LPV system [15]. For the LPV form, let us introduce the following notation for the scheduling variables:…”

System Engineering Approach of Diabetes Treatment

“…Another useful direction in this domain proved to be the combination of LPV methodologies with Linear Matrix Inequalities (LMI)-based one [44], [45]. Its newest direction is connected to Tensor Product (TP) transformations based LMI controller design that is not validated yet in AP, but it can be useful in control of physiological systems [46][47][48].…”

LPV-based quality interpretations on modeling and control of diabetes

“…Robust control allows to handle these uncertainties in a natural way. With LPV modeling linear RC methods also can be used, besides that the properties of the original nonlinear model are still valid [8,14]. Usually, in the physiological models the nonlinearities occur within the system model and do not affect the output matrices.…”

“…There were attempts with the fusion of modern and classical control theory, like switching Proportional-Integral-Derivative (PID) control [2,3], with modern control theory, for example Model Predictive Control (MPC) [4,5], or Soft Computing-based Control (SCC) [6,7]. Moreover, Robust Control (RC) theory also were considered by researches [8][9][10] in this scientific discipline. In order to test and preliminarily validate the developed algorithms in silico models can be used.…”