Observer Design for a Nonlinear Minimal Model of Glucose Disappearance and Insulin Kinetics

Driss Boutat, Mohamed Darouach, Holger Voos

2014

Abstract

This work deals with an observer design for a nonlinear minimal dynamic model of glucose disappearance and insulin kinetics (GD-IK). At first, the model is transformed into a nonlinear observer normal form. Then, using the knowledge of the plasma blood glucose level, we estimate the state variables that are not directly available from the system, i.e. the remote compartment insulin utilization, the plasma insulin deviation and the infusion rate. In addition, we estimate the amount of absorbed glucose by means of the inverse dynamics.

References

  1. Bergman, R., Ider, Y., Bowden, C., and Cobelli, C. (1979). Quantitative estimation of insulin sensitivity. American Journal of Physiology-Endocrinology And Metabolism, 236(6):E667.
  2. Bhattacharyya, S. (1978). Observer design for linear systems with unknown inputs. Automatic Control, IEEE Transactions on, 23(3):483-484.
  3. Boutat, D. (2007). Geometrical conditions for observer error linearization viaR 0, 1, ..., (N - 2). In 7th IFAC Symposium on Nonlinear Control Systems Nolcos'07,.
  4. Boutat, D., Benali, A., Hammouri, H., and Busawon, K. (2009). New algorithm for observer error linearization with a diffeomorphism on the outputs. Automatica, 45(10):21872193.
  5. Boutat, D. and Busawon, K. (2011). On the transformation of nonlinear dynamical systems into the extended nonlinear observable canonical form. International Journal of Control, 84(1):94-106.
  6. Chee, F., Fernando, T., and van Heerden, P. V. (2003). Closed-loop glucose control in critically ill patients using continuous glucose monitoring system (cgms) in real time. Information Technology in Biomedicine, IEEE Transactions on, 7(1):43-53.
  7. Darouach, M., Zasadzinski, M., and Xu, S. (1994). Fullorder observers for linear systems with unknown inputs. Automatic Control, IEEE Transactions on, 39(3):606-609.
  8. Eberle, C. and Ament, C. (2012). Identifiability and online estimation of diagnostic parameters with in the glucose insulin homeostasis. Biosystems, 107(3):135 - 141.
  9. González, P. and Femat, R. (2011). Control of glucose concentration in type 1 diabetes mellitus with discretedelayed measurements. In 18th IFAC World Congress Milano (Italy), August.
  10. Hariri, A. and Wang, Y. (2011). Observer-based state feedback for enhanced insulin control of type idiabetic patients. The Open Biomedical Engineering Journal, 5:98.
  11. Hui, S. and Zak, S. (2005). Observer design for systems with unknown inputs. International Journal of Applied Mathematics and Computer Science, 15(4):431.
  12. Krener, A. and Isidori, A. (1983). Linearization by output injection and nonlinear observers. Systems & Control Letters,, 3(1):47-52.
  13. Kudva, P., Viswanadham, N., and Ramakrishna, A. (1980). Observers for linear systems with unknown inputs. IEEE Transactions on Automatic Control, 25:113- 115.
  14. L Kovcs, B Palncz, Z. B. (2007). Design of luenberger observer for glucose-insulin control via mathematica. In Engineering in Medicine and Biology Society, 29th Annual International Conference of the IEEE.
  15. Magni, L., Raimondo, D., Bossi, L., Dalla Man, C., De Nicolao, G., Kovatchev, B., and Cobelli, C. (2007). Artificial pancreas: Closed-loop control of glucose variability in diabetes: Model predictive control of type 1 diabetes: An in silico trial. Journal of diabetes science and technology (Online), 1(6):804.
  16. Parker, R., Doyle III, F., and Peppas, N. (1999). A modelbased algorithm for blood glucose control in type i diabetic patients. Biomedical Engineering, IEEE Transactions on, 46(2):148-157.
  17. Percival, M., Zisser, H., Jovanovic?, L., and Doyle III, F. (2008). Closed-loop control and advisory mode evaluation of an artificial pancreatic ß cell: Use of proportional-integral-derivative equivalent modelbased controllers. Journal of diabetes science and technology, 2(4):636.
  18. Respondek, W. and Pogromsky, A. & Nijmeijer, H. (2004). Time scaling for observer design with linearizable error dynamics. Automatica,, 40 (2):277-285.
  19. Villafaa-Rojas, J., Gonzlez-Reynoso, O., Alcaraz-Gonzlez, V., Gonzlez-Garca, Y., Gonzlez-?lvarez, V., SolsPacheco, J. R., Aguilar-Uscanga, B., and GmezHermosillo, C. (2013). Asymptotic observers a tool to estimate metabolite concentrations under transient state conditions in biological systems: Determination of intermediate metabolites in the pentose phosphate pathway of saccharomyces cerevisiae. Chemical Engineering Science, 104(0):73 - 81.
  20. Yang, F. and Wilde, R. (1988). Observers for linear systems with unknown inputs. Automatic Control, IEEE Transactions on, 33(7):677-681.
Download


Paper Citation


in Harvard Style

Boutat D., Darouach M. and Voos H. (2014). Observer Design for a Nonlinear Minimal Model of Glucose Disappearance and Insulin Kinetics . In Proceedings of the International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2014) ISBN 978-989-758-011-6, pages 21-26. DOI: 10.5220/0004747700210026


in Bibtex Style

@conference{biosignals14,
author={Driss Boutat and Mohamed Darouach and Holger Voos},
title={Observer Design for a Nonlinear Minimal Model of Glucose Disappearance and Insulin Kinetics},
booktitle={Proceedings of the International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2014)},
year={2014},
pages={21-26},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004747700210026},
isbn={978-989-758-011-6},
}


in EndNote Style

TY - CONF
JO - Proceedings of the International Conference on Bio-inspired Systems and Signal Processing - Volume 1: BIOSIGNALS, (BIOSTEC 2014)
TI - Observer Design for a Nonlinear Minimal Model of Glucose Disappearance and Insulin Kinetics
SN - 978-989-758-011-6
AU - Boutat D.
AU - Darouach M.
AU - Voos H.
PY - 2014
SP - 21
EP - 26
DO - 10.5220/0004747700210026