Contractive Model Predictive Control for Insulin Delivery for Type 1 Diabetics

In this paper, a low complexity nonlinear model predictive control (NMPC) approach to blood glucose control is suggested, which is based on the nonlinear glucose-insulin dynamics model. It applies the idea of introducing a contractive constraint in the NMPC problem formulation, which would guarantee the closed-loop system stability when using a small prediction horizon. Particularly, the one step ahead NMPC problem is considered. Further, a quasi-NMPC method is developed, which is based on a sequential linearization of the nonlinear system dynamics and finding a suboptimal solution of the resulting convex Quadratically Constrained Quadratic Programming problem. The suggested approach would be appropriate to be embedded in an automatic blood glucose control system, since it will reduce the complexity of the on-line NMPC computations, simplify the software implementation, and reduce the requirements for available memory. The proposed method is illustrated with simulations on the nonlinear model of glucose-insulin dynamics.