Quasi-continuous high order sliding modes controllers applied to glucose-insulin regulatory system models

Abstract

This paper analyzes two glucose-insulin models for diabetic patients: by Bergman and by Hovorka. Bergman's Model is nonlinear, and has relative degree three. It offers a good approximation of the system, but omits several important physiological functions, and insulin features, that are included in Hovorka's Model. This is a nonlinear model with relative degree five. It includes most of physiological parameters of glucose system and insulin action. It has two glucose and insulin compartments. It describes in details the insulin action and the rate of appearance of subcutaneously injected insulin. An intestinal glucose absorption function is proposed to describe better the process of glucose production from ingested food. A renal excretion function is proposed in order to model kidneys filtration excretion. Hovorka's non-insulin-dependent function has been smoothed to avoid discontinuities in the system. For both models Homogeneous Quasi-Continuous Controllers of order three and five are used giving a good performance from a medical point of view.

A variational characterization of the sliding mode control processes

“…Moreover, the developed analytic tool and results related to the variable structures systems (VSSs) constitute a valuable part of the modern systems theory. We refer to [9], [12], [13], [20], [25], [29], [30], [33], [35], [36], [37], [38], [39], [40] for the basic facts and also for some interesting real world uses of the sliding mode techniques.…”

“…The study of the general variable structures control processes in the framework of discontinuous dynamic models given by differential equations with discontinuous right hand sides or by the associated differential inclusions has gained lots of interest in recent years (see e.g., [5], [7], [9], [10], [12], [13], [17], [19], [20], [25], [26], [27], [29], [30], [34], [39]). An important case of the above-mentioned discontinuous dynamics is given by a class of the conventional firstorder sliding mode control systems [33].…”

A new framework for analyzing the performance of the glucose-insulin system

“…These models use embedded devices such as sensors [6][7][8][9], actuators [10] and controllers [11,12]. The treatment in the proposed models depends on the availability and wellfunctioning of the embedded devices.…”

Consistent approximations and variational description of some classes of sliding mode control processes

“…These sophisticated mathematical models are practically motivated by many modern engineering applications and constitute a valuable part of the recent progress in the systems theory. We refer to [12,16,17,27,35,40,41,43,45,46,47,48,49,50] for the basic theoretic facts and also for some interesting real world applications of the sliding mode control techniques.…”