Glucose level regulation via integral high-order sliding modes

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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

Abstract
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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.

Keywords: artifical pancreas., chattering effect, Sliding mode.

Mathematics Subject Classification: Primary: 93C10, 92C50; Secondary: 93D0.

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. Google Scholar
[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. Google Scholar
[3]	L. Dorel, "Transient features of High Order Sliding Modes,", Ph.D thesis, (2010). Google Scholar
[4]	A. F. Fillipov, "Differential equations with Discontinuous Right-Hand Sides,", Kluwer academic Publishers, (1988). Google Scholar
[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. Google Scholar
[6]	A. Isidori, "Nonlinear Control Systems,", Springer Verlag, (1989). Google Scholar
[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. Google Scholar
[8]	A. Levant, Sliding order and sliding accuracy in sliding mode control,, Int. Journal of Control, 58 (1993), 1247. doi: 10.1080/00207179308923053. Google Scholar
[9]	A. Levant, Higher order sliding modes, differentiation and output-feedback control,, Int. Journal of Control, 76 (2003), 924. Google Scholar
[10]	A. Levant, Homogeneity approach to high-order sliding mode design,, Automatica, 41 (2005), 823. doi: 10.1016/j.automatica.2004.11.029. Google Scholar
[11]	A. Levant and L. Alelishvili, Integral high-order sliding modes,, IEEE Trans. Automat. Control, 52 (2007), 1278. doi: 10.1109/TAC.2007.900830. Google Scholar
[12]	F. Lewis and V. Syrmos, "Optimal Control," 2nd edition,, John Wiley, (1995). Google Scholar
[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. Google Scholar
[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. Google Scholar
[15]	V. Utkin, "Sliding Modes in Control and Optimization,", Springer-Verlag, (1992). Google Scholar

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. Google Scholar
[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. Google Scholar
[3]	L. Dorel, "Transient features of High Order Sliding Modes,", Ph.D thesis, (2010). Google Scholar
[4]	A. F. Fillipov, "Differential equations with Discontinuous Right-Hand Sides,", Kluwer academic Publishers, (1988). Google Scholar
[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. Google Scholar
[6]	A. Isidori, "Nonlinear Control Systems,", Springer Verlag, (1989). Google Scholar
[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. Google Scholar
[8]	A. Levant, Sliding order and sliding accuracy in sliding mode control,, Int. Journal of Control, 58 (1993), 1247. doi: 10.1080/00207179308923053. Google Scholar
[9]	A. Levant, Higher order sliding modes, differentiation and output-feedback control,, Int. Journal of Control, 76 (2003), 924. Google Scholar
[10]	A. Levant, Homogeneity approach to high-order sliding mode design,, Automatica, 41 (2005), 823. doi: 10.1016/j.automatica.2004.11.029. Google Scholar
[11]	A. Levant and L. Alelishvili, Integral high-order sliding modes,, IEEE Trans. Automat. Control, 52 (2007), 1278. doi: 10.1109/TAC.2007.900830. Google Scholar
[12]	F. Lewis and V. Syrmos, "Optimal Control," 2nd edition,, John Wiley, (1995). Google Scholar
[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. Google Scholar
[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. Google Scholar
[15]	V. Utkin, "Sliding Modes in Control and Optimization,", Springer-Verlag, (1992). Google Scholar

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