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

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.