Tube-based Model Predictive Control of Blood Glucose for Multiple Meal Scenarios

Abstract

This paper aims to keep blood glucose levels within an acceptable range for any prior announced meal scenarios by a model predictive control approach. However, due to the nonlinearity of the system and the necessity to set decision variables for each meal scenario, a straightforward formulation of a mathematical optimization problem to determine insulin dose becomes a nonlinear optimization problem with many decision variables. To formulate the mathematical optimization problem as a convex quadratic programming problem, we approximate the nonlinear system with a linear one and apply a tube method by considering the linearization error as a disturbance. Furthermore, we suppress the increase in blood glucose levels due to meals by discrete-time LQ control for systems with exogenous inputs, which makes the number of decision variables independent of the number of the meal scenarios.