Simultaneous model predictive control and moving horizon estimation for blood glucose regulation in Type 1 diabetes

A new estimation and control approach for the feedback control of an artificial pancreas to treat Type 1 diabetes mellitus is proposed. In particular, we present a new output-feedback predictive control approach that simultaneously solves the state estimation and control objectives by means of a single min-max optimization problem. This involves optimizing a cost function with both finite forward and backward horizons with respect to the unknown initial state, unmeasured disturbances and noise, and future control inputs and is similar to simultaneously solving a model predictive control (MPC) problem and a moving horizon estimation (MHE) problem. We incorporate a novel asymmetric output cost to penalize dangerous low blood glucose values more severely than less harmful high blood glucose values. We compare this combined MPC/MHE approach to a control strategy that uses state-feedback MPC preceded by a Luenberger observer for state estimation. In-silico results showcase several advantages of this new simultaneous MPC/MHE approach, including fewer hypoglycemic events without increasing the number of hyperglycemic events, faster insulin delivery in response to a meal consumption, and shorter insulin pump suspensions, resulting in smoother blood glucose trajectories.