Optimal Insulin Administration for People with Type 1 Diabetes

In this paper we apply receding horizon constrained optimal control to the computation of insulin administration for people with type 1 diabetes. The study is based on the Hovorka model, which describes a virtual subject with type 1 diabetes. First of all, we compute the optimal insulin administration for the linearized system using quadratic programming (QP) for optimization. The optimization problem is a discrete-time problem with soft state constraints and hard input constraints. The computed insulin administration is applied to the nonlinear model, which represents the virtual patient. Then, a nonlinear discrete-time Bolza problem is stated and solved using sequential quadratic programming (SQP) for optimization and an explicit Dormand-Prince Runge-Kutta method (DOPRI54) for numerical integration and sensitivity computation. Finally, the effects of faster acting insulin on the postprandial (i.e., post-meal) blood glucose peak are discussed.