Description of the Positively Invariant Sets of a Type 1 Diabetic Patient Model

PABLO S. RIVADENEIRA; TAGHREED MOHAMMARIDHA; MICHEL CARDELLI; JUAN E. SERENO

Medellín

Congreso; XVII Clca Latin American Conference of Automatic Control; 2016

Positive invariant sets of a biological mathematical model of type-1 diabetes arecharacterized in this paper. Glycemia is physically a non-negative variable but the presentedmathematical model does not guarantee positive trajectories of this state variable for t 0.Therefore, to give a better mathematical representation of the blood glucose-insulin interaction,invariance conditions of the positivity of the open-loop free-system response are rstly found.Secondly, closed-loop positive invariance is investigated for the ultimate goal of regulatingglycemia within normal levels using automated exogenous insulin infusions. The conditions fora standard state feedback control that guarantees a positiveness and stability of the input/statesolutions are presented. The resulting non-negative control is virtually tested on diabetic patientsto illustrate the theoretical results.