Luenberger observer with nonlinear structure applied to diabetes type 1

Abstract

In this work a Luenberger observer (LO) for type 1 diabetes is established using the Hovorka’s model (HM). The HM is linearized around an operating point and the eigenvalues are calculated.  The LO is designed relocating the HM eigenvalues through the Ackermann’s methodology for linear observers where the proposed LO keeps the nonlinear structure of the model system. The LO is parameterized and tuned with the mean from six virtual patients of HM. Once the observer performance is reliable estimating the state space variables for HM, the virtual patients are changed by patients of Bergman’s model in order to test the observer behavior under unknown dynamics. These estimated variables constitute the ones corresponding to HM. The variables are estimated by the data computational processing which correspond    to the insulin (input) and glucose (output) of the virtual patients. The estimated variables by the LO are very similar for virtual patients generated by both models, where the parameter FIT is used to quantify    the performance of the observer. The computational implementation of the LO is useful tool to estimate the unmeasured variables in diabetic patients so they can be used in the artificial   pancreas.