Differential Flatness based Run-to-Run Control of Blood Glucose for People with Type 1 Diabetes

The objective of this paper is to develop an open loop insulin input profile over a span of 24 hours which makes the glucose trajectory of a Type 1 diabetic person track a target glucose trajectory. The Bergman minimal model is chosen to represent the glucose-insulin dynamics which is shown to be differentially flat. An optimal control problem is posed by parameterizing the differentially flat output of the Bergman model using Fourier series, to result in an input profile that can be repeatedly administered every day. The solution to the optimization problem is then shown to present acceptable performance in terms of tracking and adhering to imposed constraints.