Control of an artificial human pancreas using the SDRE method

Diabetes mellitus is a condition where the human body can no longer produce the insulin needed to sufficiently regulate the amount of blood glucose and use it for energy and metabolism. An automatic control system would be able to lessen long term adverse health affects resulting from elevated blood glucose levels. We are interested in regulating blood glucose around a safe equilibrium value by the injection of insulin. This paper examines the use of nonlinear regulation for controlling the amount of insulin delivered to a diabetic person based on measuring their blood glucose level. Specifically, the nonlinear method using the state dependent Riccati equation (SDRE) developed by Cloutier, D'Souza, and Mracek [1], will be applied and examined under numerical simulations. It must be emphasized that this paper examines only a theoretical study of SDRE as a control methodology, and does not imply that the modelling of the human body is correct nor the resulting controller safe. The biological equations and disturbances modelled are taken from Hodel and Naylor [2] so that a comparison between this methodology and previous work can be made. Significant advances in the accurate modelling of the human body would have to be made before any real controller could be considered. Our concern is with the following problem: assuming these dynamics, what kind of performance can we achieve with a nonlinear regulator?