2011, 8(2): 549-560. doi: 10.3934/mbe.2011.8.549

Glucose level regulation via integral high-order sliding modes

1. 

School of Math Sciences, Tel Aviv University, Tel Aviv, Ramat Aviv, 69978, Israel

Received  March 2010 Revised  October 2010 Published  April 2011

Diabetes is a condition in which the body either does not produce enough insulin, or does not properly respond to it. This causes the glucose level in blood to increase. An algorithm based on Integral High-Order Sliding Mode technique is proposed, which keeps the normal blood glucose level automatically releasing insulin into the blood. The system is highly insensitive to inevitable parametric and model uncertainties, measurement noises and small delays.
Citation: Lela Dorel. Glucose level regulation via integral high-order sliding modes. Mathematical Biosciences & Engineering, 2011, 8 (2) : 549-560. doi: 10.3934/mbe.2011.8.549
References:
[1]

R. N. Bergman, S. Phillips and C. Cobelli, Physiologic evaluation of factors controlling glucose tolerance in man,, J. Clin. Invest, 68 (1981), 1456. doi: 10.1172/JCI110398.

[2]

F. Chee, T. L. Fernando and V. V. Heerden, Closed-loop glucose control in critically ill patients using continuous glucose monitoring system(CGMS) in real time,, IEEE Trans. Information Technology in Biomedicine, 7 (2003), 419.

[3]

L. Dorel, "Transient features of High Order Sliding Modes,", Ph.D thesis, (2010).

[4]

A. F. Fillipov, "Differential equations with Discontinuous Right-Hand Sides,", Kluwer academic Publishers, (1988).

[5]

U. Fisher, E. Salzsieder, E. J. Freyse and G. Albrecht, Experimental validation of a glucose-insulin control model to simulate patterns in glucose turnover,, Comput. Methods Programs, 7 (1990), 249.

[6]

A. Isidori, "Nonlinear Control Systems,", Springer Verlag, (1989).

[7]

K. H. Kienitz and T. A. Yoneyama, Robust controller for insulin pumps based on H-Infinity theory,, IEEETrans. Inf. Biomed. Eng, 40 (1993), 1133. doi: 10.1109/10.245631.

[8]

A. Levant, Sliding order and sliding accuracy in sliding mode control,, Int. Journal of Control, 58 (1993), 1247. doi: 10.1080/00207179308923053.

[9]

A. Levant, Higher order sliding modes, differentiation and output-feedback control,, Int. Journal of Control, 76 (2003), 924.

[10]

A. Levant, Homogeneity approach to high-order sliding mode design,, Automatica, 41 (2005), 823. doi: 10.1016/j.automatica.2004.11.029.

[11]

A. Levant and L. Alelishvili, Integral high-order sliding modes,, IEEE Trans. Automat. Control, 52 (2007), 1278. doi: 10.1109/TAC.2007.900830.

[12]

F. Lewis and V. Syrmos, "Optimal Control," 2nd edition,, John Wiley, (1995).

[13]

R. S. Parker, F. J. Doyle and N. A. Peppas, A Model-Based algorithm for Blood Glucose Concentration in Type I Diabetic Patients, IEEE Trans. Biomed. Eng., 46 (1999), 148. doi: 10.1109/10.740877.

[14]

Y. B. Shtessel and P. Kaveh, Blood glucose regulation using higher-order sliding mode control,, Int.J. of Robust and Nonlinear Control, 18 (2008), 557. doi: 10.1002/rnc.1223.

[15]

V. Utkin, "Sliding Modes in Control and Optimization,", Springer-Verlag, (1992).

show all references

References:
[1]

R. N. Bergman, S. Phillips and C. Cobelli, Physiologic evaluation of factors controlling glucose tolerance in man,, J. Clin. Invest, 68 (1981), 1456. doi: 10.1172/JCI110398.

[2]

F. Chee, T. L. Fernando and V. V. Heerden, Closed-loop glucose control in critically ill patients using continuous glucose monitoring system(CGMS) in real time,, IEEE Trans. Information Technology in Biomedicine, 7 (2003), 419.

[3]

L. Dorel, "Transient features of High Order Sliding Modes,", Ph.D thesis, (2010).

[4]

A. F. Fillipov, "Differential equations with Discontinuous Right-Hand Sides,", Kluwer academic Publishers, (1988).

[5]

U. Fisher, E. Salzsieder, E. J. Freyse and G. Albrecht, Experimental validation of a glucose-insulin control model to simulate patterns in glucose turnover,, Comput. Methods Programs, 7 (1990), 249.

[6]

A. Isidori, "Nonlinear Control Systems,", Springer Verlag, (1989).

[7]

K. H. Kienitz and T. A. Yoneyama, Robust controller for insulin pumps based on H-Infinity theory,, IEEETrans. Inf. Biomed. Eng, 40 (1993), 1133. doi: 10.1109/10.245631.

[8]

A. Levant, Sliding order and sliding accuracy in sliding mode control,, Int. Journal of Control, 58 (1993), 1247. doi: 10.1080/00207179308923053.

[9]

A. Levant, Higher order sliding modes, differentiation and output-feedback control,, Int. Journal of Control, 76 (2003), 924.

[10]

A. Levant, Homogeneity approach to high-order sliding mode design,, Automatica, 41 (2005), 823. doi: 10.1016/j.automatica.2004.11.029.

[11]

A. Levant and L. Alelishvili, Integral high-order sliding modes,, IEEE Trans. Automat. Control, 52 (2007), 1278. doi: 10.1109/TAC.2007.900830.

[12]

F. Lewis and V. Syrmos, "Optimal Control," 2nd edition,, John Wiley, (1995).

[13]

R. S. Parker, F. J. Doyle and N. A. Peppas, A Model-Based algorithm for Blood Glucose Concentration in Type I Diabetic Patients, IEEE Trans. Biomed. Eng., 46 (1999), 148. doi: 10.1109/10.740877.

[14]

Y. B. Shtessel and P. Kaveh, Blood glucose regulation using higher-order sliding mode control,, Int.J. of Robust and Nonlinear Control, 18 (2008), 557. doi: 10.1002/rnc.1223.

[15]

V. Utkin, "Sliding Modes in Control and Optimization,", Springer-Verlag, (1992).

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