Meal Estimation in Nonlinear Model Predictive Control for Type 1 Diabetes

Abstract

In this paper we apply receding horizon constrained nonlinear optimal control to the computation of insulin administration for people with type 1 diabetes. In particular, the sizes and the times of the meals are assumed to be unknown, and have to be estimated using a continuous-discrete extended Kalman filter (EKF). The optimization problem is a discrete-time Bolza problem with soft state constraints and hard input constraints. This problem is solved using a sequential quadratic programming (SQP) algorithm. An explicit Dormand-Prince Runge-Kutta method (DOPRI54) is used for numerical integration, including integration of the mean-covariance pair, and sensitivity computation. The study is based on the Hovorka model, which is a continuous-time physiological model describing a virtual subject with type 1 diabetes. The paper describes the key aspects of the numerical implementation and provides quantitative insight into the factors limiting the achievement of acceptable closed-loop performance.