The significance of LPV modeling of a widely used T1DM model

Abstract

The paper investigates the specificity of Linear Parameter Varying (LPV) modeling and robust controller design on a widely used Type 1 Diabetes Mellitus model. LPV systems can be seen as an extension of linear time invariant systems, which allows us to extend some powerful control methodologies to the highly nonlinear and uncertain models of the human metabolism. Different LPV models are proposed with their own advantages and disadvantages. The possible choices are separately analyzed for both controller and observer design perspective.

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

“…State variables x 1 (t) and x 2 (t) are also candidates for scheduling variables replacing Q 1 (t) and Q 2 (t), which is more advantageous for observer design Szalay et al (2013).…”

LPV-based quality interpretations on modeling and control of diabetes

“…From the aforementioned consideration it can be derived that the LPV-type diabetes models have the following form which can be observed in several studies [8,9,14]:…”

“…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.…”

System Engineering Approach of Diabetes Treatment

“…Modern robust control methods like L2-or H∞-based ones were introduced in the AP researches in order to stave off the determinative uncertainties coming from inter-and intra patient variability. Supplemented by Linear Parameter Variability (LPV) methodology (providing the opportunity to handle the original nonlinear system/model as a linear one; hence, to give access using the original nonlinear model for linear control methods enumerated above), modern robust control successfully deals with the quality and quantity requirements [40][41][42][43].…”