Adaptive Estimation for an Insulin-Glucose Model

Resumen: In this article, an adaptive observer is designed for patients affected by Type 1 Diabetes Mellitus. The adaptive observer, synthesized using the Bergman minimal model, simultaneously estimates the states and the parameter corresponding to the insulin-dependent glucose disappearance rate. The adaptive observer considers parameter uncertainties, whereas food intake is considered an external disturbance. The state estimation error converges to a neighborhood of the origin in the presence of external disturbances and uncertainties, whereas the parameter identification error converges in fixed time to a neighborhood of the origin. The synthesis of the adaptive observer is given by a constructive method based on Linear Matrix Inequalities. Simulation results show the feasibility of the proposed scheme for different classes of patients.

¿Cómo citar?

R. Franco , H. Rios, A. Ferreira de Loza, L. Cassany, D. Gucik-Derigny, J. Cieslak & D. Henry. Adaptive Estimation for an Insulin-Glucose Model. Memorias del Congreso Nacional de Control Automático, pp. 1-6, 2021.

Palabras clave

Adaptive Observer, Diabetes Mellitus, Sliding-Modes

• Astolfi, A., Karaglannis, D., and Ortega, R. (2008). Nonlinear and Adaptive Control with Applications. SpringerVerlang London UK.
• Bergman, R. (2005). Minimal model: Perspective from 2005. Hormon Research in Paediatrics, 64, 8–15.
• Bergman, R., Phillips, L., and Cobelli, C. (1981). Physiologic evaluation of factors controlling glucose tolerance in man: measurement of insulin sensitivity and betacell glucose sensitivity from the response to intravenous glucose. Journal of Clinical Investigation, 68, 1456– 1467.
• Bernuau, E., Polyakov, A., Efimov, D., and Perruqueti, W. (2013). Verification of ISS, iISS and IOSS properties applying weighted homogeneity. System & Control Letters, 62, 1159–1167.
• Borri, A., Cacace, F., Gaetano, A., Germani, A., Manes, C., Palumbo, P., Panunzi, S., and Pepe, P. (2017). Luenberger-like observers for nonlinear time-delay systems with application to the artificial pancreas. IEEE Control Systems Magazine, 37, 33–49.
• Chakrabarty, A., Healey, E., Shi, D., Zavitsanou, S., Doyle, F., and Dassau, E. (2020). Embedded model predictive control for a wearable artificial pancreas. IEEE Transactions on Control Systems Technology, 28, 2600–2607.
• Fisher, M. (1991). A semi closed-loop algorithm for the control of blood glucose levels in diabetics. IEEE Transactions on Biomedical Engineering, 38, 57–61.
• Franco, R., R´ıos, H., Efimov, D., and Perruquetti, W. (2020). Adaptive estimation for uncertain nonlinear systems with measurement noise: A sliding-mode observer approach. International Journal of Robust and Nonlinear Control, 31, 3809–3826.
• Gallardo, A., Gonzalez, M., Revilla, C., Escobar, J., Castellanos, M., and Leder, R. (2019). Rapid automatic identification of parameters of the Bergman minimal model in sprague-dawley rats with experimental diabetes for adaptive insulin delivery. Computers in Biology and Medicine, 108, 242–248.
• Jiang, Z., Mareels, I., and Wang, Y. (1996). A Lyapunov formulation of the nonlinear small-gain theorem for interconnected ISS systems. Automatica, 32, 1211– 1215.
• Khalil, H.K. (2002). Nonlinear Systems. Prentice Hall, third edition.
• Morettini, M., Di-Nardo, F., and Burattini, L. (2018). Assessment of glucose effectiveness from short IVGTT in individuals with different degrees of glucose tolerance. Acta Diabetol, 55, 1011–1018.
• Nitalla, A., Ghosh, S., Stefanovski, D., Bergman, R., and Wang, X. (2006). Dimensional analysis of minmod leads to definition of the disposition index of glucose regulation and improved simulation algorithm. Biomedical Engineering Online, 5, 44.
• Novara, C., Rabbone, I., and Tinti, D. (2020). DataDriven Disturbance Estimation and Control with Application to Blood Glucose Regulation. IEEE Transactions on Control Systems Technology, 28, 48–62.
• Pacini, G. and Ahren, B. (2017). Glucagon-like peptide1 and glucose-dependent insulinotropic peptide: effects alone and in combination on insulin secretion and glucose disappearance in mice. Physiological Reports, 5, 1–8.
• Palumbo, P., Pizzichelli, G., Panunzi, S., Pepe, P., and Gaetano, A. (2014). Model-based control of plasma glycemia: Tests on populations of virtual patients. Mathematical Biosciences, 257, 2–10.
• Rueda-Escobedo, J., Moreno, J., and Schiffer, J. (2016). Discontinuous gradient algorithm for finite-time estimation of time-varying parameters. International Journal of Control, 89, 1838–1848.
• Turksoy, K., Quinn, L., Littlejohn, E., and Cinar, A. (2014). Multivariable adaptive identification and control for artificial pancreas systems. IEEE Transactions on Biomedical Engineering, 61, 883–891.
• Turksoy, K., Samadi, S., Feng, J., Littlejohn, E., Quinn, L., and Cinar, A. (2016). Meal-detection in patients with type 1 diabetes: A new module for the multivariable adaptive artificial pancreas control system. IEEE Journal of Biomedical and Health Informatics, 20, 47– 54.
• Xie, J. and Wang, Q. (2017). A variable state dimension approach to meal detection and meal size estimation: In silico evaluation through basal-bolus insulin therapy for type 1 diabetes. IEEE Journal of Biomedical Engineering, 64, 1249–1260.