American Institute of Mathematical Sciences

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

Glucose level regulation via integral high-order sliding modes

Lela Dorel 1,

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.
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

[1]

Cecilia Cavaterra, Denis Enăchescu, Gabriela Marinoschi. Sliding mode control of the Hodgkin–Huxley mathematical model. Evolution Equations & Control Theory, 2019, 8 (4) : 883-902. doi: 10.3934/eect.2019043
[2]

Ellina Grigorieva, Evgenii Khailov. Chattering and its approximation in control of psoriasis treatment. Discrete & Continuous Dynamical Systems - B, 2019, 24 (5) : 2251-2280. doi: 10.3934/dcdsb.2019094
[3]

Saloni Rathee, Nilam. Quantitative analysis of time delays of glucose - insulin dynamics using artificial pancreas. Discrete & Continuous Dynamical Systems - B, 2015, 20 (9) : 3115-3129. doi: 10.3934/dcdsb.2015.20.3115
[4]

Hooton Edward, Balanov Zalman, Krawcewicz Wieslaw, Rachinskii Dmitrii. Sliding Hopf bifurcation in interval systems. Discrete & Continuous Dynamical Systems - A, 2017, 37 (7) : 3545-3566. doi: 10.3934/dcds.2017152
[5]

Jiamin Zhu, Emmanuel Trélat, Max Cerf. Planar tilting maneuver of a spacecraft: Singular arcs in the minimum time problem and chattering. Discrete & Continuous Dynamical Systems - B, 2016, 21 (4) : 1347-1388. doi: 10.3934/dcdsb.2016.21.1347
[6]

Siwei Yu, Jianwei Ma, Stanley Osher. Geometric mode decomposition. Inverse Problems & Imaging, 2018, 12 (4) : 831-852. doi: 10.3934/ipi.2018035
[7]

Jonathan H. Tu, Clarence W. Rowley, Dirk M. Luchtenburg, Steven L. Brunton, J. Nathan Kutz. On dynamic mode decomposition: Theory and applications. Journal of Computational Dynamics, 2014, 1 (2) : 391-421. doi: 10.3934/jcd.2014.1.391
[8]

Steven L. Brunton, Joshua L. Proctor, Jonathan H. Tu, J. Nathan Kutz. Compressed sensing and dynamic mode decomposition. Journal of Computational Dynamics, 2015, 2 (2) : 165-191. doi: 10.3934/jcd.2015002
[9]

Hao Zhang, Scott T. M. Dawson, Clarence W. Rowley, Eric A. Deem, Louis N. Cattafesta. Evaluating the accuracy of the dynamic mode decomposition. Journal of Computational Dynamics, 2019, 0 (0) : 0-0. doi: 10.3934/jcd.2020002
[10]

Hernán Cendra, María Etchechoury, Sebastián J. Ferraro. Impulsive control of a symmetric ball rolling without sliding or spinning. Journal of Geometric Mechanics, 2010, 2 (4) : 321-342. doi: 10.3934/jgm.2010.2.321
[11]

D. J. W. Simpson, R. Kuske. Stochastically perturbed sliding motion in piecewise-smooth systems. Discrete & Continuous Dynamical Systems - B, 2014, 19 (9) : 2889-2913. doi: 10.3934/dcdsb.2014.19.2889
[12]

Shu Zhang, Yuan Yuan. The Filippov equilibrium and sliding motion in an internet congestion control model. Discrete & Continuous Dynamical Systems - B, 2017, 22 (3) : 1189-1206. doi: 10.3934/dcdsb.2017058
[13]

Laura Levaggi. Existence of sliding motions for nonlinear evolution equations in Banach spaces. Conference Publications, 2013, 2013 (special) : 477-487. doi: 10.3934/proc.2013.2013.477
[14]

Tomáš Roubíček, V. Mantič, C. G. Panagiotopoulos. A quasistatic mixed-mode delamination model. Discrete & Continuous Dynamical Systems - S, 2013, 6 (2) : 591-610. doi: 10.3934/dcdss.2013.6.591
[15]

Clelia Marchionna. Free vibrations in space of the single mode for the Kirchhoff string. Communications on Pure & Applied Analysis, 2013, 12 (6) : 2947-2971. doi: 10.3934/cpaa.2013.12.2947
[16]

Xinpeng Wang, Bingo Wing-Kuen Ling, Wei-Chao Kuang, Zhijing Yang. Orthogonal intrinsic mode functions via optimization approach. Journal of Industrial & Management Optimization, 2017, 13 (5) : 1-16. doi: 10.3934/jimo.2019098
[17]

Piotr Słowiński, Bernd Krauskopf, Sebastian Wieczorek. Mode structure of a semiconductor laser with feedback from two external filters. Discrete & Continuous Dynamical Systems - B, 2015, 20 (2) : 519-586. doi: 10.3934/dcdsb.2015.20.519
[18]

Bo Lu, Shenquan Liu, Xiaofang Jiang, Jing Wang, Xiaohui Wang. The mixed-mode oscillations in Av-Ron-Parnas-Segel model. Discrete & Continuous Dynamical Systems - S, 2017, 10 (3) : 487-504. doi: 10.3934/dcdss.2017024
[19]

Theodore Vo, Richard Bertram, Martin Wechselberger. Bifurcations of canard-induced mixed mode oscillations in a pituitary Lactotroph model. Discrete & Continuous Dynamical Systems - A, 2012, 32 (8) : 2879-2912. doi: 10.3934/dcds.2012.32.2879
[20]

Qi Lü, Enrique Zuazua. Robust null controllability for heat equations with unknown switching control mode. Discrete & Continuous Dynamical Systems - A, 2014, 34 (10) : 4183-4210. doi: 10.3934/dcds.2014.34.4183

2018 Impact Factor: 1.313

Tools

Metrics

  • PDF downloads (6)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences