Skip to main content
SpringerLink
Log in

Fuzzy type-2 fractional Backstepping blood glucose control based on sliding mode observer

  • Published:
International Journal of Dynamics and Control Aims and scope Submit manuscript

Abstract

A new combination of fractional order (FO) nonlinear control and sliding mode observer (SMO) for blood glucose regulation in type 1 diabetes mellitus is proposed in this paper. An observer estimates the difficult-to-measure process variables that are significant to control law design and to prevent failures. A SMO is proposed to estimate non-measurable states variables of Bergman minimal model by data acquired from a continuous glucose monitoring sensor. At first based on Backstepping method with FO sliding surface a control signal is proposed, and then interval type 2 fuzzy logic is utilized to reduce the chattering phenomenon in control signal. The FO sliding mode control provides robust performance and the Backstepping algorithm protects the controller in front of mismatched and matched uncertainties. Simulation results of the proposed controller are compared with its integer counterpart.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

Notes

  1. High Order SMC.

  2. Backstepping SMC.

  3. Bergman minimal model.

  4. Interval type 2 fuzzy logic control.

  5. Sliding mode control.

  6. FO Backstepping SMC.

  7. Fuzzy logic control.

  8. Type 2 fuzzy sets.

  9. Footprint Of uncertainty.

  10. IT2FL system.

References

  1. Tucker ME (2015) IDF Atlas: about 415 million adults worldwide have diabetes. In: International Diabetes Federation (IDF) 2015 World Congress

  2. Colmegna P, Sanchez Pèna RS, Gondhalekar R, Dassau E, Doyle FJ (2014) Reducing risks in type 1 diabetes using H\(\infty \) control. IEEE Trans Biomed Eng 61(12):2939–2947

    Article  Google Scholar 

  3. Goharimanesh M, Lashkaripour A, Abouei Mehrizi A (2015) FO PID controller for diabetes patients. J Comput Appl Mech 46(1):69–76

    Google Scholar 

  4. Allam F, Nossair Z, Gomma H, Ibrahim I, Abdelsalam M (2012) Evaluation of using a recurrent neural network (RNN) and a fuzzy logic controller (FLC) in closed loop system to regulate blood glucose for type-1 diabetic patients. Int J Intell Syst Appl 10:58–71

    Google Scholar 

  5. Leon BS, Alanis AY, Sanchez EN, Ornelas-Tellez F, Ruiz-Velazquez E (2012) Inverse optimal neural control of blood glucose level for type 1 diabetes mellitus patients. J Frankl Inst 349(5):1851–1870

    Article  MathSciNet  MATH  Google Scholar 

  6. Hernández AGG, Fridman L, Levant A, Shtessel YB, Leder R, Monsalve CR, Andrade SI (2013) High-order sliding-mode control for blood glucose: practical relative. Control Eng Pract 21(5):747–758

    Article  Google Scholar 

  7. Parsa NT, Vali AR, Ghasemi R (2014) Back stepping sliding mode control of blood glucose for type I diabetes. Int J Med Health Biomed Pharm Eng 8(11):749–753

    Google Scholar 

  8. Zeighami A, Ayoubi A (2017) The regulation of the blood glucose levels by type-2 fuzzy controller. Biomed Eng Appl Basis Commun 29(3):1750022

    Article  Google Scholar 

  9. Ahmad S, Ahmed N, Ilyas M, Khan W (2017) Super twisting sliding mode control algorithm for developing artificial pancreas in type 1 diabetes patients. Biomed Signal Process Control 38:200–211

    Article  Google Scholar 

  10. Toffanin C, Visentin R, Messori M, Di Palma F, Magni L, Cobelli C (2018) Toward a run-to-run adaptive artificial pancreas. in silico results. IEEE Trans Biomed Eng 65(3):479–488

    Article  Google Scholar 

  11. N’doye I, Voos H, Darouach M, Schneider JG (2015) Static output feedback H\(_{\infty }\) control for a fractional-order glucose-insulin system. Int J Control Autom Syst 13(4):798–807

    Article  Google Scholar 

  12. León-Vargasa F, Garellib F, De Battistab H, Vehía J (2013) Postprandial blood glucose control using a hybrid adaptive PD controller with insulin-on-board limitation. Biomed Signal Process Control 8(6):724–732

    Article  Google Scholar 

  13. Heydarinejad H, Delavari H (2016) FO back stepping sliding mode control for blood glucose regulation in type I diabetes patients. In: Babiarz A, Czornik A, Klamka J, Niezabitowski M (eds) Theory and applications of non-integer order systems. Springer, Zakopane, pp 187–202

    Google Scholar 

  14. Delavari H, Heydarinejad H, Baleanu D (2018) Adaptive fractional order blood glucose regulator based on high order sliding mode observer. Submitted to IET systems biology

  15. Mandal S, Sutradhar A (2017) Multi-objective control of blood glucose with H\(\infty \) and pole-placement constraint. Int J Dyn Control 5(2):357–366

    Article  MathSciNet  Google Scholar 

  16. Bergman RN, Philips LS, Cobelli C (1981) Physiological evaluation of factors controlling glucose tolerance in man. J Clin Investig 68(6):1456–1467

    Article  Google Scholar 

  17. Delavari H (2017) A novel fractional adaptive active sliding mode controller for synchronization of non-identical chaotic systems with disturbance and uncertainty. Int J Dyn Control 5(1):102–114

    Article  MathSciNet  Google Scholar 

  18. Delavari H, Senejohnny D, Baleanu D (2014) Sliding observer for synchronization of fractional order chaotic systems with mismatched parameter. Cent Eur J Phys 10(5):1095–1101

    Google Scholar 

  19. Mohadeszadeh M, Delavari H (2017) Synchronization of fractional-order hyper-chaotic systems based on a new adaptive sliding mode control. Int J Dyn Control 5(1):124–134

    Article  MathSciNet  Google Scholar 

  20. Faieghi MR, Delavari H, Baleanu D (2012) Control of an uncertain fractional-order Liu system via fuzzy fractional-order sliding mode control. J Vib Control 18(9):1366–1374

    Article  MathSciNet  Google Scholar 

  21. Song X, Song S, Liu L, Inés Tejado B (2017) Adaptive interval type-2 fuzzy sliding mode control for fractional-order systems based on finite-time scheme. J Intell Fuzzy Syst 32(3):1903–1915

    Article  MATH  Google Scholar 

  22. Hamza MF, Yap HJ, Choudhury IA, Chiroma H, Kumbasar T (2017) A survey on advancement of hybrid type 2 fuzzy sliding mode control. Neural Comput Appl 8(1):1–23

    Google Scholar 

  23. Akbarzadeh-T MR, Hosseini SA, Naghibi-Sistani MB (2017) Stable indirect adaptive interval type-2 fuzzy sliding-based control and synchronization of two different chaotic systems. Appl Soft Comput 55:576–578

    Article  Google Scholar 

  24. Chen SH, Fu LC (2015) Observer-based Backstepping control of a 6-dof parallel hydraulic manipulator. Control Eng Pract 36:100–112

    Article  Google Scholar 

  25. Ginoya D, Shendge PD, Patre BM, Phadke SB (2016) A new state and perturbation observer based sliding mode controller for uncertain systems. Int J Dyn Control 4(1):92–103

    Article  MathSciNet  Google Scholar 

  26. Machado JT, Kiryakova V, Mainardi F (2011) Recent history of fractional calculus. Commun Nonlinear Sci Numer Simul 16(3):1140–1153

    Article  MathSciNet  MATH  Google Scholar 

  27. Podlubny I (1999) Fractional differential equations. Academic Press, San Diego

    MATH  Google Scholar 

  28. Li Y, Chen YQ, Podlubny I (2010) Stability of fractional-order nonlinear dynamic systems: Lyapunov direct method and generalized Mittag–Leffler stability. Comput Math Appl 59(5):1810–1821

    Article  MathSciNet  MATH  Google Scholar 

  29. Li Y, Chen YQ, Podlubny I (2009) Mittag–Leffler stability of FO nonlinear dynamic systems. Automatica 45(8):1965–1969

    Article  MathSciNet  MATH  Google Scholar 

  30. Trigeassou V, Maamri N, Sabatier J, Oustaloup A (2011) A Lyapunov approach to the stability of fractional differential equations. Signal Process 91(3):437–445

    Article  MATH  Google Scholar 

  31. Li C, Deng W (2007) Remarks on fractional derivatives. Appl Math Comput 187(2):777–784

    MathSciNet  MATH  Google Scholar 

  32. Aguila-Camacho N, Duarte-Mermoud MA, Gallegos JA (2014) Lyapunov functions for fractional order systems. Commun Nonlinear Sci Numer Simul 19(9):2951–2957

    Article  MathSciNet  Google Scholar 

  33. Palumbo P, Ditlevsen S, Bertuzzi A, De Gaetano A (2013) mathematical modeling of the glucose-insulin system: a review. Math Biosci 244(2):69–81

    Article  MathSciNet  MATH  Google Scholar 

  34. Balakrishnan NP, Rangaiah GP, Samavedham L (2011) Review and analysis of blood glucose (BG) models for type 1 diabetic patients. Ind Eng Chem Res 50(21):12041–12066

    Article  Google Scholar 

  35. Ghosh S (2014) A differential evolution based approach for estimating minimal model parameters from IVGTT data. Comput Biol Med 45:51–60

    Article  Google Scholar 

  36. Cobelli C, Dalla Man C, Toffolo G, Basu R, Vella A, Rizza R (2014) The oral minimal model method. Diabetes 63(4):1203–1213

    Article  Google Scholar 

  37. Mohadeszadeh M, Delavari H (2017) Synchronization of uncertain fractional-order hyper-chaotic systems via a novel adaptive interval type-2 fuzzy active sliding mode controller. Int J Dyn Control 5(1):135–144

    Article  MathSciNet  Google Scholar 

  38. Niknam T, Khooban MH, Kavousifard A, Soltanpour MR (2014) An optimal type II fuzzy sliding mode control design for a class of nonlinear systems. Nonlinear Dyn 75(2):73–83

    Article  MathSciNet  Google Scholar 

  39. Wu D, Mendel JM (2009) Enhanced Karnik–Mendel algorithms. IEEE Trans Fuzzy Syst 17(4):923–934

    Article  Google Scholar 

  40. Deng W, Li C, Lu J (2007) Stability analysis of linear fractional differential system with multiple time delays. Nonlinear Dyn 48(4):409–416

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Hamedan University of Technology, Hamedan, 65155, Iran

    Hamid Heydarinejad & Hadi Delavari

  2. Department of Mathematics, Cankya University, Ankara, Turkey

    Dumitru Baleanu

  3. Institute of Space Science, Magurele, Bucharest, Romania

    Dumitru Baleanu

Authors
  1. Hamid Heydarinejad
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hadi Delavari
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dumitru Baleanu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hadi Delavari.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Heydarinejad, H., Delavari, H. & Baleanu, D. Fuzzy type-2 fractional Backstepping blood glucose control based on sliding mode observer. Int. J. Dynam. Control 7, 341–354 (2019). https://doi.org/10.1007/s40435-018-0445-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40435-018-0445-8

Keywords

Search

Navigation