Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Intelligent Industrial Systems
Erschienen in: Intelligent Industrial Systems 2/2017

18.11.2016 | Original Paper

A Nonlinear Optimal Control Approach of Insulin Infusion for Blood Glucose Levels Regulation

verfasst von: G. Rigatos, P. Siano, A. Melkikh

Erschienen in: Intelligent Industrial Systems | Ausgabe 2/2017

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The article proposes a nonlinear optimal control method for the administered infusion of insulin, aiming at regulation of patients’ blood glucose levels. The dynamic model of blood glucose concentration which receives as control input the insulin’s infusion rate, undergoes approximate linearization through Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization takes place round a temporary equilibrium which is updated at each iteration of the control method and which is defined by the last value of the system’s state vector and the last value of the control inputs vector exerted on it. For the linearized model, a robust H-infinity feedback controller is designed. To find the feedback control gain of the controller, an algebraic Riccati equation is solved at each iteration of the control algorithm. Through Lyapunov stability analysis it is first proven that the control loop satisfies the H-infinity tracking performance criterion, which signifies elevated robustness to model uncertainty and external perturbations. Moreover, the global asymptotic stability of the control loop is proven. The proposed control method can contribute to the treatment of diabetes patients and to blood glucose levels regulation in patients of intensive care units.
Vorheriger Artikel Flatness-Based Control in Successive Loops for Business Cycles of Finance Agents
Nächster Artikel Highway Traffic Estimation using Nonlinear Kalman Filtering

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Anhänge
Nur mit Berechtigung zugänglich
Literatur
1.
Leelarathna, L., English, S.W., Thabit, H., Caldwell, K., Allen, J.M., Kumareswaran, K., Wilinska, M.E., Nodele, M., Mangat, J., Evans, M.L., Bernstein, R., Havorka, R.: Feasibility of fully automated closed-loop glucose control using continuous subcutaneous glucose measurements in critical illness: a randomized control trial. J. Crit. Care 17, 1 (2013)
2.
Wang, Q., Molenaar, P., Harsh, S., Freeman, K., Xie, J., Gold, C., Rovine, M., Ulbrecht, J.: Personalized state-space modeling of glucose dynamics for type 1 diabetes using continuously monitored glucose, insulin dose, and meal intake an extended kalman filter approach. J. Diabetes Sci. Technol. 8(2), 331345 (2014)CrossRef
3.
Kalfon, P.: Automatisation du contrôle strict de la glycémie en réanimation (Computer protocols for tight glycaemic control in critically ill patients). Réanimation, 18, 532–537 (2009)
4.
Bridges, B.C., Preissig, C.M., Maher, K.O., Rigby, M.R.: Continuous glucose monitors prove highly accurate in critically ill children. J. Crit. Care 14, 1 (2010)
5.
Chase, J., Shaw, G.M., Wong, X.W., Lotz, T., Lin, J., Hann, C.E.: Model-based Glycaemic Control in Critical Care—a review of the state of the possible. Biomed. Signal Process. Control 1(1), 321 (2006)CrossRef
6.
Chee, F., Fernando, T., Vernon van Heerden, P.: Closed-loop glucose control in critically ill patients using continuous glucose monitoring system (CGMS) in real time. IEEE Trans. Inf. Technol. Biomed. 7(1), 43–53 (2003)CrossRef
7.
Lunze, K., Singh, T., Walter, M., Brendel, M.D., Leonhardt, S.: Blood glucose control algorithms for type 1 diabetic patients: a methodological review. Biomed. Signal Process. Control 8(2m), 107–119 (2011)
8.
Bhattacharjee, A., Sengupta, A., Sutradhar, A.: Nonparametric modelling of glucose-insulin process in IDDM patient using Hammerstein-Wiener model. In: 2010 11th Interantional. Conference on Control, Automation, Robotics and Vision, Singapore, (December 2010)
9.
Ting, C.W., Chek, C.: A novel blood glucose regulation using TSK-FCMAC: A Fuzzy CMAC based on the zero-ordered TSK fuzzy inference scheme. IEEE Trans. Neural Netw. 20(5), 856–871 (2009)CrossRef
10.
Makroglou, A., Li, J., Kuang, Y.: Mathematical models and software tools for the glucose-insulin regulatory system and diabetes: an overview. Appl. Numer. Math. 56, 559–573 (2006)MathSciNetCrossRefMATH
11.
Chee, F., Savkin, A.V., Fernando, T.L., Nahavandi, S.: Optimal \(H_{\infty }\) insulin injection control for blood glucose regulation in diabetic patients. IEEE Trans. Biomed. Eng. 52(10), 1625–1631 (2005)CrossRef
12.
Al-Helal, Z., Rehbock, V., Loxton, R.: Modellling and optimal control of blood glucose in the human body. J. Ind. Manag. Optim. 11(4), 1149–1164 (2015)MathSciNetCrossRefMATH
13.
Ridha, T.M., Moog, C., Delaleau, E., Fliess, M., Join, C.: A variable reference trajectory for model-free glycemia regulation. In: SIAM Conference on Control & its Applications (SIAM CT15), Jul 2015, Paris, France (2015)
14.
Liu, W., Tang, F.: Modeling a simplified regulatory system of blood glucose at molecular levels. J. Theor. Biol. 252, 608–620 (2008)MathSciNetCrossRef
15.
Marheineke, N., Cibis, T.M., Schiessl, S., Pielmeier, U.: Optimal control of glucose balance in ICU patients based on GlucoSafe model. J. Math. Ind. 4(3), 1–13 (2014)MathSciNet
16.
Boiroux, D., Finan, D.A., Jrgensen, J.B., Poulsen, N.K., Madsen, H.: Optimal Insulin Administration for People with Type 1 Diabetes. In: 9th International Symposium on Dynamics and Control of Process Systems (DYCOPS 2010), Leuven, Belgium, (July 2010)
17.
Kovacs, L., Szaloy, P., Benyo, B., Chase, J.G.: Optimal tight glycaemic control supported by differential geometric methods. In: IFBME Proceedings of the 5th European Medical and Biological Engineering Conference vol. 37, pp. 351–354 (2011)
18.
Kovacs, L., Szolay, P., Alamassy, Z., Benyo, Z., Bankai, L.: Quasi in-silico validations of a nonlinear LPV model-based robust glucose control algorirthm for Type I diabetes. In: 18th IFAC World Congress. Milano, Italy, (Sept. 2011)
19.
Kovacs, L., Kucsur, B., Bokor, J, Benyo, Z.: LPV fault detection of glucose-insulin system. In: IEEE MED 2006, 14th Mediterranean Conference on Control and Automation, Ancona, Italy (June 2006)
20.
Palumbo, P., Pepe, P., Panunzi, S., de Gaetano, A.: Glucose control by subcutaneous insulin administration: a DDE modelling approach. In: 18th IFAC World Control Conference, Milano, Italy, September, (2011)
21.
Palumbo, P., Pizzichelli, G., Panunzi, S., Pepe, P., de Gaetano, A.: Tests on virtual patient for an observer-based closed-loop of plasma glycaemia. In: 2011 50th IEEE Conference on Decision and Control and European Control Conference, Orlando, Florida, (Dec. 2011)
22.
Rigatos, G., Rigatou, E., Zervos, N.: A nonlinear H-infinity approach to optimal control of the depth of anaesthesia. In: 12th International Conference of Computational Methods in Sciences and Engineering (ICCMSE 2016), Athems, Greece, (March 2016)
23.
Rigatos, G.G., Tzafestas, S.G.: Extended Kalman filtering for fuzzy modelling and multi-sensor fusion. Math. Comput. Model. Dyn. Syst. 13, 251–266 (2007)MathSciNetCrossRefMATH
24.
Basseville, M., Nikiforov, I.: Detection of Abrupt Changes: Theory and Applications. Prentice-Hall, Upper Saddle River (1993)
25.
Rigatos, G., Zhang, Q.: Fuzzy model validation using the local statistical approach. Fuzzy Sets Syst. 60(7), 882–904 (2009)MathSciNetCrossRefMATH
26.
Rigatos, G.G.: Modelling and Control for Intelligent Industrial Systems: Adaptive Algorithms in Robotcs and Industrial engineering. Springer, Heidelberg (2011)CrossRefMATH
27.
Rigatos, G.: Nonlinear Control and Filtering Using Differential Flatness Approaches: Applications to Electromechanicsl Systems. Springer, Berlin (2015)CrossRefMATH
28.
Rigatos, G.: Intelligent Renewable Energy Systems: Modelling and Control. Springer, New York (2017)
29.
Toussaint, G.J., Basar, T., Bullo, F.: \(H_{\infty }\) optimal tracking control techniques for nonlinear underactuated systems. In: Proceedings of the IEEE CDC 2000, 39th IEEE Conference on Decision and Control. Sydney Australia (Dec. 2000)
30.
Lublin, L., Athans, M.: An experimental comparison of and designs for interferometer testbed. In: Francis, B., Tannenbaum, A. (eds.) Lectures Notes in Control and Information Sciences: Feedback Control, Nonlinear Systems and Complexity, pp. 150–177. Springer, London (1995)
31.
Doyle, J.C., Glover, K., Khargonekar, P.P., Francis, B.A.: State-space solutions to standard \(H_2\) and \(H_{\infty }\) control problems. IEEE Trans. Autom. Control 34, 831–847 (1989)CrossRefMATH
32.
Gibbs, B.P.: Advanced Kalman Filtering, Least Squares and Modelling, A practical handbook. Wiley, New York (2011)
33.
Simon, D.: A game theory approach to constrained minimax state estimation. IEEE Trans. Signal Process. 54(2), 405–412 (2006)CrossRef
34.
Kovacs, L., Kulesar, B., Gyorgy, A., Benyo, Z.: Robust servo control of a novel type I diabetic model. Optim Control Appl. Methods 32, 215–238 (2011)MathSciNetCrossRefMATH
35.
Magni, L., Raimondo, D., Bassi, L., Dalla Man, C., De Nicolao, G., Kovatchev, B., Cobelli, C.: Model-predictive control of typeI diabetes. J. Diabetes Sci. Technol. 1, 804–812 (2007)CrossRef
36.
Chase, J., Shaw, G., Wang, X., Lotz, T., Lin, J., Hann, C.: Model-based glycaemia control in critical care: a review of the state of the possible. Biomed. Signal Process. Control 1, 3–21 (2006)CrossRef
37.
Eren-Oruklu, M., Cinar, A., Quino, L., Smith, D.: Adaptive control strategy for regulation of blood-glucose levels in patients with type I diabetes. J. Process Control 19, 1333–1346 (2009)CrossRef
Metadaten
Titel
A Nonlinear Optimal Control Approach of Insulin Infusion for Blood Glucose Levels Regulation
verfasst von
G. Rigatos
P. Siano
A. Melkikh
Publikationsdatum
18.11.2016
Verlag
Springer Singapore
Erschienen in
Intelligent Industrial Systems / Ausgabe 2/2017
Print ISSN: 2363-6912
Elektronische ISSN: 2199-854X
DOI
https://doi.org/10.1007/s40903-016-0063-8

Weitere Artikel der Ausgabe 2/2017

Intelligent Industrial Systems 2/2017 Zur Ausgabe

Original Paper

TFS: Towards Fuzzy Rule-Based Feedback Scheduling in Networked Control Systems

Retraction Note

Retraction Note to: A Survey on Recent Vision-Based Gesture Recognition

Original Paper

An H-infinity Approach to Optimal Control of Oxygen and Carbon Dioxide Contents in Blood

Original Paper

A Nonlinear H-Infinity Control Approach for Three-Phase Voltage Inverters

Original Paper

Flatness-Based Control in Successive Loops for Business Cycles of Finance Agents

Original Paper

Highway Traffic Estimation using Nonlinear Kalman Filtering

Neuer Inhalt

    Bildnachweise