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Modelling and optimal control of blood glucose levels in the human body
1. | Department of Mathematics and Statistics, Curtin University, GPO Box U1987 Perth, Western Australia 6845, Australia, Australia, Australia |
References:
[1] |
F. Chee and T. Fernando, Closed Loop Control of Blood Glucose, Springer, Berlin, 2007. |
[2] |
R. Hovorka, V. Canonico, L. J. Chassin, U. Haueter, M. Massi-Benedetti, M. O. Federici, T. R. Pieber, H. C. Schaller, L. Schaupp, T. Vering and M. E. Wilinska, Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes, Physiological Measurement, 25 (2004), 905-920.
doi: 10.1088/0967-3334/25/4/010. |
[3] |
IDF Diabetes Atlas, 5th Edition, International Diabetes Federation, Brussels, 2011. |
[4] |
L. S. Jennings, M. E. Fisher, K. L. Teo and C. J. Goh, MISER3 Optimal Control Software: Theory and User Manual Version 3, University of Western Australia, Perth, 2004. |
[5] |
M. Korach-André, H. Roth, D. Barnoud, M. Péan, F. Péronnent and X. Leverve, Glucose appearance in the peripheral circulation and liver glucose output in men after a large C starch meal, The American Journal of Clinical Nutrition, 80 (2004), 881-886. |
[6] |
L. Kovács, B. Kulcsár, A. György and Z. Benyó, Robust servo control of a novel type 1 diabetic model, Optimal Control Applications and Methods, 32 (2011), 215-238.
doi: 10.1002/oca.963. |
[7] |
Q. Lin, R. Loxton and K. L. Teo, The control parameterization method for nonlinear optimal control: A survey, Journal of Industrial and Management Optimization, 10 (2014), 275-309.
doi: 10.3934/jimo.2014.10.275. |
[8] |
W. Liu and F. Tang, Modelling a simplified regulatory system of blood glucose at molecular levels, Journal of Theoretical Biology, 252 (2008), 608-620.
doi: 10.1016/j.jtbi.2008.02.021. |
[9] |
R. Loxton, K. L. Teo and V. Rehbock, Optimal control problems with multiple characteristic time points in the objective and constraints, Automatica, 44 (2008), 2923-2929.
doi: 10.1016/j.automatica.2008.04.011. |
[10] |
G. Marchetti, M. Barolo, L. Jovanovic and H. Zisser, An improved PID switching control strategy for type 1 diabetes, In Proceeding of the 28th IEEE EMBS Annual International Conference, New York, (2006), 5041-5044.
doi: 10.1109/IEMBS.2006.259541. |
[11] |
R. Martin and K. L. Teo, Optimal Control of Drug Administration in Cancer Chemotherapy, World Scientific, Singapore, 1993.
doi: 10.1142/9789812832542. |
[12] |
K. L. Teo, C. J. Goh and K. H. Wong, A Unified Computational Approach to Optimal Control Problems, Longman Scientific and Technical, Essex, 1991. |
show all references
References:
[1] |
F. Chee and T. Fernando, Closed Loop Control of Blood Glucose, Springer, Berlin, 2007. |
[2] |
R. Hovorka, V. Canonico, L. J. Chassin, U. Haueter, M. Massi-Benedetti, M. O. Federici, T. R. Pieber, H. C. Schaller, L. Schaupp, T. Vering and M. E. Wilinska, Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes, Physiological Measurement, 25 (2004), 905-920.
doi: 10.1088/0967-3334/25/4/010. |
[3] |
IDF Diabetes Atlas, 5th Edition, International Diabetes Federation, Brussels, 2011. |
[4] |
L. S. Jennings, M. E. Fisher, K. L. Teo and C. J. Goh, MISER3 Optimal Control Software: Theory and User Manual Version 3, University of Western Australia, Perth, 2004. |
[5] |
M. Korach-André, H. Roth, D. Barnoud, M. Péan, F. Péronnent and X. Leverve, Glucose appearance in the peripheral circulation and liver glucose output in men after a large C starch meal, The American Journal of Clinical Nutrition, 80 (2004), 881-886. |
[6] |
L. Kovács, B. Kulcsár, A. György and Z. Benyó, Robust servo control of a novel type 1 diabetic model, Optimal Control Applications and Methods, 32 (2011), 215-238.
doi: 10.1002/oca.963. |
[7] |
Q. Lin, R. Loxton and K. L. Teo, The control parameterization method for nonlinear optimal control: A survey, Journal of Industrial and Management Optimization, 10 (2014), 275-309.
doi: 10.3934/jimo.2014.10.275. |
[8] |
W. Liu and F. Tang, Modelling a simplified regulatory system of blood glucose at molecular levels, Journal of Theoretical Biology, 252 (2008), 608-620.
doi: 10.1016/j.jtbi.2008.02.021. |
[9] |
R. Loxton, K. L. Teo and V. Rehbock, Optimal control problems with multiple characteristic time points in the objective and constraints, Automatica, 44 (2008), 2923-2929.
doi: 10.1016/j.automatica.2008.04.011. |
[10] |
G. Marchetti, M. Barolo, L. Jovanovic and H. Zisser, An improved PID switching control strategy for type 1 diabetes, In Proceeding of the 28th IEEE EMBS Annual International Conference, New York, (2006), 5041-5044.
doi: 10.1109/IEMBS.2006.259541. |
[11] |
R. Martin and K. L. Teo, Optimal Control of Drug Administration in Cancer Chemotherapy, World Scientific, Singapore, 1993.
doi: 10.1142/9789812832542. |
[12] |
K. L. Teo, C. J. Goh and K. H. Wong, A Unified Computational Approach to Optimal Control Problems, Longman Scientific and Technical, Essex, 1991. |
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