Luenberger observer with nonlinear structure applied to diabetes type 1

  • Onofre Orozco Universidad de Guadalajara Centro Universitario de los Lagos
  • Carlos Eduardo Castañeda Universidad de Guadalajara Centro Universitario de los Lagos
  • Agustín Rodríguez-Herrero University of Madrid, Biomedical Research Networking Centre in Bioengineering Biomaterials and Nanomedicine (CIBER-BBN)
  • Gema García-Saéz University of Madrid, Biomedical Research Networking Centre in Bioengineering Biomaterials and Nanomedicine (CIBER-BBN)
  • María Elena Hernando University of Madrid, Biomedical Research Networking Centre in Bioengineering Biomaterials and Nanomedicine (CIBER-BBN)
Keywords: Luenberger observer, state space estimator, diabetes type 1, artificial pancreas

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.

Published
2018-02-02
How to Cite
Orozco, O., Castañeda, C., Rodríguez-Herrero, A., García-Saéz, G., & Hernando, M. (2018). Luenberger observer with nonlinear structure applied to diabetes type 1. International Journal of Combinatorial Optimization Problems and Informatics, 9(1), 68-80. Retrieved from https://ijcopi.org/index.php/ojs/article/view/81
Section
Articles