Insulin infusion rate control in type 1 diabetes patients using information-theoretic model predictive control

Abstract

The present paper examines the glucose regulation system in patients with type 1 diabetes. To this end, the nonlinear Bergman's minimal model with parametric uncertainty, which represents this system, is converted to a fractional-order model using Caputo’s definition. As the recent literature suggests, the noise in the interstitial glucose concentration continuous control sensors is considered non-Gaussian. With this in mind, first an optimal non-fragile H∞ observer is designed for a Lipschitz nonlinear fractional-order system including parametric uncertainty and input disturbance in order to estimate the unknown states. Second, feedback linearization method for nonlinear fractional-order system with parametric uncertainty is used, after which the linearized system is used to design controller for diabetes mellitus patients. Third, robust fractional model predictive control (RFMPC) with a minimax optimization approach is presented for closed-loop insulin delivery. Finally, the performance of the proposed controller under non-Gaussian measurement noise is enhanced with a suitable choice of a cost function based on generalized correntropy (GC), whereas the performance of a mean square error (MSE)-based controller is simulated. The results indicate that not only the proposed controller performs better under non-Gaussian conditions but also it effectively recovers and maintains the glucose concentration within the desired range by appropriately infusing insulin under parametric uncertainty and meal disturbances.