Applicability of Asymptotic Tracking in Case of Type 1 Diabetes

The alarming increasing tendency of diabetes population attracts technological interest too. From an engineering point of view, the treatment of diabetes mellitus can be represented by an outer control loop, to replace the partially or totally deficient blood glucose control system of the human body. To acquire this “artificial pancreas” a reliable glucose sensor and an insulin pump is needed as hardware, and a control algorithm to ensure the proper blood glucose regulation is needed as software. The latter is a key point of the diabetes “closing the loop” problem and its primary prerequisite is a valid model able to describe the blood glucose system. In the current chapter one of the most widely used and complex nonlinear model will be investigated with a dual purpose. Specific control aspects are discussed in the literature only on linearized versions; however, differential geometric approaches give more general formalization. As a result our first aim is to hide the nonlinearity of the physiological model by transforming the control input provided by a linear controller so that the response of the model would mimic the behavior of a linear system. Hence, the validity of linear controllers can be extended from the neighborhood of a working point to a larger subset of the state-space bounded by specific constraints. On the other hand, applicability of the nonlinear methodology is tested on a simple PID control based algorithm compared with LQG optimal method. Simulations are done under MATLAB on realistic input scenarios. Since the values of the state variables are needed Kalman filtering is used for state estimation.