Robust controller design for an artificial pancreas using Bernstein polynomial
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In this thesis, a robust nonlinear model predictive controller is proposed to regulate the blood glucose concentration in Type 1 diabetic patients. The virtual patient model considered is the minimal model of Bergman, augmented by a meal disturbance and adapted to represents the insulin-glucose homeostasis of Type 1 diabetes. Uncertainties in the model are quantified by a Polynomial Chaos expansion, with unknown parameters defined over a compact support. Using a linear matrix transformation to express the polynomial approximation in the Bernstein basis, tight bounds of the stochastic blood glucose concentration are easily computed. The knowledge on the range of this stochastic concentration allows the implementation of a Model Predictive Control which tends to prevent hypo- and hyperglycemia by controlling the upper or lower bound of the uncertain concentration. This Model Predictive Control uses a Sequential Linear Programming formulation to determine the required control insulin injection which minimize the difference between the stochastic controlled concentration and a target trajectory. Constraints on the blood glucose level and control infusion are prescribed. The procedure is experimented on the rest-to-rest maneuvers control of a two mass system and the results are compared with the literature to validate the method. The Model Predictive Control of the insulin-glucose homeostasis of Type 1 diabetes exhibits the desired behaviour to avoid hypo- and hyperglycemia. However the lack of real human subject data does not permit further comparison, but the closing presents the tools necessary to extend the present work to future research.