[1] Vahidi, O., Bhushan Gopaluni, R. and Kwok, E., “Detection of abnormalities in type II diabetic patients using particle filters”, Journal of Medical and Biological Engineering,35 (2), 188 (2015).
[2] Boden, G., Sargrad, K., Homko, C., Mozzoli, M. and Stein, T. P., “Effect of a low-carbohydrate diet on appetite, blood glucose levels, and insulin resistance in obese patients with type 2 diabetes”, Annals of Internal Medicine,142 (6), 403 (2005).
[3] Parker, R. S., Doyle, F. J. and Peppas, N. A., “A model-based algorithm for blood glucose control in type I diabetic patients”, IEEE Transactions on Biomedical Engineering,46 (2), 148 (1999).
[4] Ramprasad, Y., Rangaiah, G. P. and Lakshminarayanan, S., “Robust PID controller for blood glucose regulation in type I diabetics”, Industrial & Engineering Chemistry Research,43 (26), 8257 (2004).
[5] Cryer, P., “Hypoglycaemia: The limiting factor in the glycaemic management of type I and type II diabetes”, Diabetologia,45 (7), 937 (2002).
[6] Cryer, P. E., Davis, S. N. and Shamoon, H., “Hypoglycemia in diabetes”, Diabetes Care,26 (6), 1902 (2003).
[7] Fowler, M. J., “Hypoglycemia”, Clinical Diabetes,26 (4), 170 (2008).
[8] Weinstock, R. S., “Closing the loop: Another step forward”, Diabetes Care,34 (9), 2136 (2011).
[9] El-Khatib, F. H., Russell, S. J., Nathan, D. M., Sutherlin, R. G. and Damiano, E. R., “A bihormonal closed-loop artificial pancreas for type 1 diabetes”, Science Translational Medicine,2 (27), 27ra27 (2010).
[10] Castle, J. R., Engle, J. M., Youssef, J. E., Massoud, R. G., Yuen, K. C. J., Kagan, R., et al., “Novel use of glucagon in a closed-loop system for prevention of hypoglycemia in type 1 diabetes”, Diabetes Care,33 (6), 1282 (2010).
[11] Weinzimer, S. A., Steil, G. M., Swan, K. L., Dziura, J., Kurtz, N. and Tamborlane, W. V., “Fully automated closed-loop insulin delivery versus semiautomated hybrid control in pediatric patients with type 1 diabetes using an artificial pancreas”, Diabetes Care,31 (5), 934 (2008).
[12] Steil, G. M., Palerm, C. C., Kurtz, N., Voskanyan, G., Roy, A., Paz, S., et al., “The effect of insulin feedback on closed loop glucose control”, The Journal of Clinical Endocrinology & Metabolism,96 (5), 1402 (2011).
[13] Ekram, F., Sun, L., Vahidi, O., Kwok, E. and Gopaluni, R. B., “A feedback glucose control strategy for type II diabetes mellitus based on fuzzy logic”, The Canadian Journal of Chemical Engineering,90 (6), 1411 (2012).
[14] León-Vargas, F., Garelli, F., De Battista, H. and Vehí, J., “Postprandial blood glucose control using a hybrid adaptive PD controller with insulin-on-board limitation”, Biomedical Signal Processing and Control,8 (6), 724 (2013).
[15] Garcia-Gabin, W., Vehí, J., Bondia, J., Tarín, C. and Calm, R., “Robust sliding mode closed-loop glucose control with meal compensation in type 1 diabetes mellitus”, IFAC Proceedings Volumes,41 (2), 4240 (2008).
[16] Kaveh, P. and Shtessel, Y. B., “Blood glucose regulation using higher-order sliding mode control”, International Journal of Robust and Nonlinear Control,18 (4-5), 557 (2008).
[17] Magni, L., Raimondo, D. M., Dalla Man, C., De Nicolao, G., Kovatchev, B. and Cobelli, C., “Model predictive control of glucose concentration in type I diabetic patients: An in silico trial”, Biomedical Signal Processing and Control,4 (4), 338 (2009).
[18] Abedini Najafabadi, H. and Shahrokhi, M., “Model predictive control of blood sugar in patients with type-1 diabetes”, Optimal Control Applications and Methods,37 (4), 559 (2016).
[19] Palumbo, P., Pizzichelli, G., Panunzi, S., Pepe, P. and De Gaetano, A., “Model-based control of plasma glycemia: Tests on populations of virtual patients”, Mathematical Biosciences,257, 2 (2014).
[20] Ruiz-Velázquez, E., Femat, R. and Campos-Delgado, D. U., “Blood glucose control for type I diabetes mellitus: A robust tracking H∞ problem”, Control Engineering Practice,12 (9), 1179 (2004).
[21] Chee, F., Savkin, A. V., Fernando, T. L. and Nahavandi, S., “Optimal H infinity insulin injection control for blood glucose regulation in diabetic patients”, IEEE Trans. Biomed. Eng.,52 (10), 1625 (2005).
[22] Chase, J. G., Shaw, G. M., Wong, X. W., Lotz, T., Lin, J. and Hann, C. E., “Model-based glycaemic control in critical care: A review of the state of the possible”, Biomedical Signal Processing and Control,1 (1), 3 (2006).
[23] Lunze, K., Singh, T., Walter, M., Brendel, M. D. and Leonhardt, S., “Blood glucose control algorithms for type 1 diabetic patients: A methodological review”, Biomedical Signal Processing and Control,8 (2), 107 (2013).
[24] Bequette, B. W., “2- Control in physiology and medicine”, in Modelling methodology for physiology and medicine, 2nd ed., E. C. Cobelli, ed., Oxford, Elsevier, pp. 13-44, (2014).
[25] Shalitin, S. and Phillip, M., “Hypoglycemia in type 1 diabetes: A still unresolved problem in the era of insulin analogs and pump therapy”, Diabetes Care,31 (Supplement 2), S121 (2008).
[26] Karges, B., Rosenbauer, J., Kapellen, T., Wagner, V. M., Schober, E., Karges, W., et al., “Hemoglobin A1c levels and risk of severe hypoglycemia in children and young adults with type 1 diabetes from Germany and Austria: A trend analysis in a cohort of 37,539 patients between 1995 and 2012”, PLoS Med.,11 (10), e1001742 (2014).
[27] Vahidi, O., Kwok, K. E., Gopaluni, R. B. and Knop, F. K., “A comprehensive compartmental model of blood glucose regulation for healthy and type 2 diabetic subjects”, Medical & Biological Engineering & Computing, 1 (2015).
[28] Farmer, T. G., Edgar, T. F. and Peppas, N. A., “Effectiveness of intravenous infusion algorithms for glucose control in diabetic patients using different simulation models”, Industrial & Engineering Chemistry Research,48 (9), 4402 (2009).
[29] Dua, P., Doyle, F. and Pistikopoulos, E., “Multi-objective blood glucose control for type 1 diabetes”, Medical & Biological Engineering & Computing,47 (3), 343 (2009).
[30] Bolie, V. W., “Coefficients of normal blood glucose regulation”, Journal of Applied Physiology,16, 783 (1961).
[31] Ackerman, E., Gatewood, L. C., Rosevear, J. W. and Molnar, G. D., “Model studies of blood-glucose regulation”, The Bulletin of Mathematical Biophysics,27, Suppl: 21 (1965).
[32] Cobelli, C. and Mari, A., “Validation of mathematical models of complex endocrine-metabolic systems: A case study on a model of glucose regulation”, Medical & Biological Engineering & Computing,21 (4), 390 (1983).
[33] Sorensen, J. T., “A physiological model of glucose metabolism in man and its use to design and assess improved insulin therapies for diabetes”, Dissertation/Thesis, Massachusetts Institute of Technology, (1985).
[34] Hovorka, R., Canonico, V., Chassin, L. J., Haueter, U., Massi-Benedetti, M., Orsini Federici, M., et al., “Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes”, Physiological Measurement,25 (4), 905 (2004).
[35] Fessel, K., Gaither, J. B., Bower, J. K., Gaillard, T., Osei, K. and Rempala, G. A., “Mathematical analysis of a model for glucose regulation”, Math. Biosci. Eng.,13 (1), 83 (2016).
[36] Vahidi, O., Kwok, K. E., Gopaluni, R. B. and Sun, L., “Developing a physiological model for type II diabetes mellitus”, Biochemical Engineering Journal,55 (1), 7 (2011).
[37] Charef, A., Sun, H., Tsao, Y. and Onaral, B., “Fractal system as represented by singularity function”, Automatic Control, IEEE Transactions,37 (9), 1465 (1992).
[38] Ahmad, W. M. and Sprott, J., “Chaos in fractional-order autonomous nonlinear systems”, Chaos, Solitons & Fractals,16 (2), 339 (2003).
[39] Valério, D. and da Costa, J. S., “Tuning of fractional PID controllers with Ziegler–Nichols-type rules”, Signal Processing,86 (10), 2771 (2006).
[40] Chen, Y., Bhaskaran, T. and Xue, D., “Practical tuning rule development for fractional order proportional and integral controllers”, Journal of Computational and Nonlinear Dynamics,3 (2), 021403 (2008).
[41] Gude, J. J. and Kahoraho, E., “Simple tuning rules for fractional PI controllers”, in Emerging Technologies & Factory Automation, ETFA 2009, IEEE Conference, pp. 1-8, (2009).
[42] Padula, F. and Visioli, A., “Tuning rules for optimal PID and fractional-order PID controllers”, Journal of Process Control,21 (1), 69 (2011).
[43] Thiebaud, D., Jacot, E., Defronzo, R. A., Maeder, E., Jequier, E. and Felber, J.-P., “The Effect of graded doses of insulin on total glucose uptake, glucose oxidation and glucose storage in man”, Diabetes,31 (11), 957 (1982).
[44] NIDDK, Hypoglycemia, Available: http://www.niddk.nih.gov/ health-information/health-topics/Diabetes/ hypoglycemia/Pages/index.aspx, (2008).
[45] Dalla Man, C., Camilleri, M. and Cobelli, C., “A system model of oral glucose absorption: validation on gold standard data”, IEEE Transactions on Bio-medical Engineering,53 (12 Pt 1), 2472 (2006).
[1] Vahidi, O., Bhushan Gopaluni, R. and Kwok, E., “Detection of abnormalities in type II diabetic patients using particle filters”, Journal of Medical and Biological Engineering,35 (2), 188 (2015).
[2] Boden, G., Sargrad, K., Homko, C., Mozzoli, M. and Stein, T. P., “Effect of a low-carbohydrate diet on appetite, blood glucose levels, and insulin resistance in obese patients with type 2 diabetes”, Annals of Internal Medicine,142 (6), 403 (2005).
[3] Parker, R. S., Doyle, F. J. and Peppas, N. A., “A model-based algorithm for blood glucose control in type I diabetic patients”, IEEE Transactions on Biomedical Engineering,46 (2), 148 (1999).
[4] Ramprasad, Y., Rangaiah, G. P. and Lakshminarayanan, S., “Robust PID controller for blood glucose regulation in type I diabetics”, Industrial & Engineering Chemistry Research,43 (26), 8257 (2004).
[5] Cryer, P., “Hypoglycaemia: The limiting factor in the glycaemic management of type I and type II diabetes”, Diabetologia,45 (7), 937 (2002).
[6] Cryer, P. E., Davis, S. N. and Shamoon, H., “Hypoglycemia in diabetes”, Diabetes Care,26 (6), 1902 (2003).
[7] Fowler, M. J., “Hypoglycemia”, Clinical Diabetes,26 (4), 170 (2008).
[8] Weinstock, R. S., “Closing the loop: Another step forward”, Diabetes Care,34 (9), 2136 (2011).
[9] El-Khatib, F. H., Russell, S. J., Nathan, D. M., Sutherlin, R. G. and Damiano, E. R., “A bihormonal closed-loop artificial pancreas for type 1 diabetes”, Science Translational Medicine,2 (27), 27ra27 (2010).
[10] Castle, J. R., Engle, J. M., Youssef, J. E., Massoud, R. G., Yuen, K. C. J., Kagan, R., et al., “Novel use of glucagon in a closed-loop system for prevention of hypoglycemia in type 1 diabetes”, Diabetes Care,33 (6), 1282 (2010).
[11] Weinzimer, S. A., Steil, G. M., Swan, K. L., Dziura, J., Kurtz, N. and Tamborlane, W. V., “Fully automated closed-loop insulin delivery versus semiautomated hybrid control in pediatric patients with type 1 diabetes using an artificial pancreas”, Diabetes Care,31 (5), 934 (2008).
[12] Steil, G. M., Palerm, C. C., Kurtz, N., Voskanyan, G., Roy, A., Paz, S., et al., “The effect of insulin feedback on closed loop glucose control”, The Journal of Clinical Endocrinology & Metabolism,96 (5), 1402 (2011).
[13] Ekram, F., Sun, L., Vahidi, O., Kwok, E. and Gopaluni, R. B., “A feedback glucose control strategy for type II diabetes mellitus based on fuzzy logic”, The Canadian Journal of Chemical Engineering,90 (6), 1411 (2012).
[14] León-Vargas, F., Garelli, F., De Battista, H. and Vehí, J., “Postprandial blood glucose control using a hybrid adaptive PD controller with insulin-on-board limitation”, Biomedical Signal Processing and Control,8 (6), 724 (2013).
[15] Garcia-Gabin, W., Vehí, J., Bondia, J., Tarín, C. and Calm, R., “Robust sliding mode closed-loop glucose control with meal compensation in type 1 diabetes mellitus”, IFAC Proceedings Volumes,41 (2), 4240 (2008).
[16] Kaveh, P. and Shtessel, Y. B., “Blood glucose regulation using higher-order sliding mode control”, International Journal of Robust and Nonlinear Control,18 (4-5), 557 (2008).
[17] Magni, L., Raimondo, D. M., Dalla Man, C., De Nicolao, G., Kovatchev, B. and Cobelli, C., “Model predictive control of glucose concentration in type I diabetic patients: An in silico trial”, Biomedical Signal Processing and Control,4 (4), 338 (2009).
[18] Abedini Najafabadi, H. and Shahrokhi, M., “Model predictive control of blood sugar in patients with type-1 diabetes”, Optimal Control Applications and Methods,37 (4), 559 (2016).
[19] Palumbo, P., Pizzichelli, G., Panunzi, S., Pepe, P. and De Gaetano, A., “Model-based control of plasma glycemia: Tests on populations of virtual patients”, Mathematical Biosciences,257, 2 (2014).
[20] Ruiz-Velázquez, E., Femat, R. and Campos-Delgado, D. U., “Blood glucose control for type I diabetes mellitus: A robust tracking H∞ problem”, Control Engineering Practice,12 (9), 1179 (2004).
[21] Chee, F., Savkin, A. V., Fernando, T. L. and Nahavandi, S., “Optimal H infinity insulin injection control for blood glucose regulation in diabetic patients”, IEEE Trans. Biomed. Eng.,52 (10), 1625 (2005).
[22] Chase, J. G., Shaw, G. M., Wong, X. W., Lotz, T., Lin, J. and Hann, C. E., “Model-based glycaemic control in critical care: A review of the state of the possible”, Biomedical Signal Processing and Control,1 (1), 3 (2006).
[23] Lunze, K., Singh, T., Walter, M., Brendel, M. D. and Leonhardt, S., “Blood glucose control algorithms for type 1 diabetic patients: A methodological review”, Biomedical Signal Processing and Control,8 (2), 107 (2013).
[24] Bequette, B. W., “2- Control in physiology and medicine”, in Modelling methodology for physiology and medicine, 2nd ed., E. C. Cobelli, ed., Oxford, Elsevier, pp. 13-44, (2014).
[25] Shalitin, S. and Phillip, M., “Hypoglycemia in type 1 diabetes: A still unresolved problem in the era of insulin analogs and pump therapy”, Diabetes Care,31 (Supplement 2), S121 (2008).
[26] Karges, B., Rosenbauer, J., Kapellen, T., Wagner, V. M., Schober, E., Karges, W., et al., “Hemoglobin A1c levels and risk of severe hypoglycemia in children and young adults with type 1 diabetes from Germany and Austria: A trend analysis in a cohort of 37,539 patients between 1995 and 2012”, PLoS Med.,11 (10), e1001742 (2014).
[27] Vahidi, O., Kwok, K. E., Gopaluni, R. B. and Knop, F. K., “A comprehensive compartmental model of blood glucose regulation for healthy and type 2 diabetic subjects”, Medical & Biological Engineering & Computing, 1 (2015).
[28] Farmer, T. G., Edgar, T. F. and Peppas, N. A., “Effectiveness of intravenous infusion algorithms for glucose control in diabetic patients using different simulation models”, Industrial & Engineering Chemistry Research,48 (9), 4402 (2009).
[29] Dua, P., Doyle, F. and Pistikopoulos, E., “Multi-objective blood glucose control for type 1 diabetes”, Medical & Biological Engineering & Computing,47 (3), 343 (2009).
[30] Bolie, V. W., “Coefficients of normal blood glucose regulation”, Journal of Applied Physiology,16, 783 (1961).
[31] Ackerman, E., Gatewood, L. C., Rosevear, J. W. and Molnar, G. D., “Model studies of blood-glucose regulation”, The Bulletin of Mathematical Biophysics,27, Suppl: 21 (1965).
[32] Cobelli, C. and Mari, A., “Validation of mathematical models of complex endocrine-metabolic systems: A case study on a model of glucose regulation”, Medical & Biological Engineering & Computing,21 (4), 390 (1983).
[33] Sorensen, J. T., “A physiological model of glucose metabolism in man and its use to design and assess improved insulin therapies for diabetes”, Dissertation/Thesis, Massachusetts Institute of Technology, (1985).
[34] Hovorka, R., Canonico, V., Chassin, L. J., Haueter, U., Massi-Benedetti, M., Orsini Federici, M., et al., “Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes”, Physiological Measurement,25 (4), 905 (2004).
[35] Fessel, K., Gaither, J. B., Bower, J. K., Gaillard, T., Osei, K. and Rempala, G. A., “Mathematical analysis of a model for glucose regulation”, Math. Biosci. Eng.,13 (1), 83 (2016).
[36] Vahidi, O., Kwok, K. E., Gopaluni, R. B. and Sun, L., “Developing a physiological model for type II diabetes mellitus”, Biochemical Engineering Journal,55 (1), 7 (2011).
[37] Charef, A., Sun, H., Tsao, Y. and Onaral, B., “Fractal system as represented by singularity function”, Automatic Control, IEEE Transactions,37 (9), 1465 (1992).
[38] Ahmad, W. M. and Sprott, J., “Chaos in fractional-order autonomous nonlinear systems”, Chaos, Solitons & Fractals,16 (2), 339 (2003).
[39] Valério, D. and da Costa, J. S., “Tuning of fractional PID controllers with Ziegler–Nichols-type rules”, Signal Processing,86 (10), 2771 (2006).
[40] Chen, Y., Bhaskaran, T. and Xue, D., “Practical tuning rule development for fractional order proportional and integral controllers”, Journal of Computational and Nonlinear Dynamics,3 (2), 021403 (2008).
[41] Gude, J. J. and Kahoraho, E., “Simple tuning rules for fractional PI controllers”, in Emerging Technologies & Factory Automation, ETFA 2009, IEEE Conference, pp. 1-8, (2009).
[42] Padula, F. and Visioli, A., “Tuning rules for optimal PID and fractional-order PID controllers”, Journal of Process Control,21 (1), 69 (2011).
[43] Thiebaud, D., Jacot, E., Defronzo, R. A., Maeder, E., Jequier, E. and Felber, J.-P., “The Effect of graded doses of insulin on total glucose uptake, glucose oxidation and glucose storage in man”, Diabetes,31 (11), 957 (1982).
[44] NIDDK, Hypoglycemia, Available: http://www.niddk.nih.gov/ health-information/health-topics/Diabetes/ hypoglycemia/Pages/index.aspx, (2008).
[45] Dalla Man, C., Camilleri, M. and Cobelli, C., “A system model of oral glucose absorption: validation on gold standard data”, IEEE Transactions on Bio-medical Engineering,53 (12 Pt 1), 2472 (2006).