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.
KeywordsModel Predictive Control Endogenous Glucose Production Artificial Pancreas Linear Controller Exact Linearization
Unable to display preview. Download preview PDF.
- 1.Wild, S., Roglic, G., Green, A., Sicree, R., King, H.: Global prevalence of diabetes - Estimates for the year 2000 and projections for 2030. Diab Care 27(5), 1047–1053 (2004)Google Scholar
- 3.Fonyó, A., Ligeti, E.: Physiology. Medicina, Budapest (2008) (in Hungarian)Google Scholar
- 5.Harvey, R., Wang, Y., Grossman, B., Percival, M., Bevier, W., Finan, D., Zisser, H., Seborg, D., Jovanovic, L., Doyle, J.F., Dassau, E.: Quest for the artificial pancreas. IEEE Eng. Med. Biol. Mag. 29(2), 53–62 (2010)Google Scholar
- 6.Chee, F., Tyrone, F.: Closed-loop control of blood glucose. LNCS, vol. 368. Springer, Heidelberg (2007)Google Scholar
- 7.Bergman, B.N., Ider, Y.Z., Bowden, C.R., Cobelli, C.: Quantitative estimation of insulin sensitivity. Am. J. Physiol. 236, 667–677 (1979)Google Scholar
- 10.Hovorka, R., Canonico, V., Chassin, L.J., Haueter, U., Massi-Benedetti, M., Federici, M.O., Pieber, T.R., Schaller, H.C., Schaupp, L., Vering, T., Wilinska, M.E.: Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes. Physiol. Meas. 25, 905–920 (2004)CrossRefGoogle Scholar
- 12.Sorensen, J.T.: A physiologic model of glucose metabolism in man and its use to design and assess improved insulin therapies for diabetes. PhD Thesis, Dept. of Chemical Engineering Massachusetts Institute of Technology, USA (1985)Google Scholar
- 13.Palumbo, P., Pepe, P., Panunzi, S., Gaetano, A.: Glucose control by subcutaneous insulin administration: a DDE modeling approach. In: Proc. 18th IFAC World Congress, Milano, Italy, pp. 1471–1476 (2011)Google Scholar
- 14.Kovács, L., Szalay, P., Benyó, B., Chase, G.J.: Asymptotic output tracking in blood glucose control. A case study. In: 50th IEEE CDC & ECC Conf., Orlando, USA (2011) (in press)Google Scholar
- 15.Szalay, P., Kovács, L.: Applicability of asymptotic tracking in case of Type 1 Diabetes. In: Proc. 6th. IEEE Int. Symp. Appl. Comput. Intell. and Inform., Timisoara, Romania, pp. 623–628 (2011)Google Scholar
- 17.Lantos, B.: Theory and design of control systems II. Akademia Press, Budapest (2003) (in Hungarian)Google Scholar