Quasi model based optimal control of type 1 diabetes mellitus

The paper presents an optimal controller design framework to investigate the type 1 diabetes from control theory point of view. The starting point of the problem is based on a recently published glucose-insulin model (Liu and Tang [2008]). Based on this a Quasi Model (a type 1 diabetes linear model) with favorable control properties is developed minimizing the physiological states to be taken into account. Consequently, different optimal control strategies (LQ, minimax control) can be designed on the Quasi Model, and the obtained controller applicability is investigated on more sophisticated type 1 diabetic models. It has to be remarked that it is not the purpose of the Quasi Model to model precisely the glucose-glucagon-insulin interaction, only to grasp the characteristic behavior such that the designed controller can successfully regulate the unbalanced system. In order to validate the applicability of this method, absorption scenarios taken from the model of Dalla Man et al. [2007] are generated and the controller is tested on the modified Liu-Tang model (Liu and Tang [2008]) as well as on the modified Sorensen model (Parker et al. [2000]).