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Extended Kalman filter state estimation–based nonlinear explicit model predictive control design for blood glucose regulation of type 1 diabetic patient

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Abstract

The computational burden of iterative online optimization–based model predictive control (MPC) process is solved by adapting off-line optimization-based nonlinear explicit model predictive control (NEMPC). In this paper, the application of NEMPC is verified to regulate blood glucose level in type 1 diabetes mellitus (T1DM) patients. The objective of glucose regulation is to avoid hyperglycemia (> 180 mg/dl) and hypoglycemia (< 50 mg/dl) by maintaining glucose level in the range of 70 to 180 mg/dl. It helps to avoid time complexity of iterative process during solution of optimization stage in MPC. In the nonlinear T1DM model, only the state dynamic of sugar is measurable with low complexity and high cost among other states of the model. Therefore, an extended Kalman filter (EKF) is used developed to estimate unavailable states. The information of the estimated states are used to develop the proposed control approach for the T1DM patients. The simulation results of the NEMPC along with EKF-based state estimator for T1DM model shows the regulation of blood glucose-level (BGL) within 70 to 180 mg/dl within 120 min. The robustness of the proposed scheme is also verified under the change in parameters and food disturbance. The control variability grid analysis (CVGA) of NEMPC for 50 numbers of virtual T1DM patients under random parametric changes and meal disturbances shows the avoidance of hypoglycemia and hyperglycemia in type 1 diabetic patients. The proposed control method is simple, robust and efficient to regulate glucose level in T1DM patients.

Extended Kalman filter state estimator based nonlinear explicit model predictive control for blood glucose regulation in Type 1 diabetic patients

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References

  1. Abdelrahem M, Hackl C, Kennel R (2015) Application of extended Kalman filter to parameter estimation of doubly-fed induction generators in variable-speed wind turbine systems. In: 2015 International conference on clean electrical power (ICCEP), p 226–233. IEEE

  2. Acharya D, Das DK (2021) Non linear back stepping based sliding mode controller design with real-time simulator for regulating glucose in type-1 diabetic patient. In: 2021 1St odisha international conference on electrical power engineering, communication and computing technology (ODICON), p 1–5. IEEE

  3. Acharya D, Gurumurthy G, Das DK (2020) Linearized receding horizon model predictive controller design to regulate glucose in type 1 diabetic patients. In: 2020 IEEE Applied signal processing conference (ASPCON), p 203–207. IEEE

  4. Ahmad S, Ahmed N, Ilyas M, Khan W, et al. (2017) Super twisting sliding mode control algorithm for developing artificial pancreas in type 1 diabetes patients. Biomedical Signal Processing and Control 38:200–211

    Article  Google Scholar 

  5. Aleppo G (2019) Insulin pump overview https://www.endocrineweb.com/guides/insulin/insulin-pump-overview

  6. Ali SF, Padhi R (2011) Optimal blood glucose regulation of diabetic patients using single network adaptive critics. Optimal Control Applications and Methods 32(2):196–214

    Article  Google Scholar 

  7. Bahremand S, Ko HS, Balouchzadeh R, Lee HF, Park S, Kwon G (2019) Neural network-based model predictive control for type 1 diabetic rats on artificial pancreas system. Medical & biological engineering & computing 57(1):177–191

    Article  Google Scholar 

  8. Batmani Y (2017) Blood glucose concentration control for type 1 diabetic patients: a non-linear suboptimal approach. IET systems biology 11(4):119–125

    Article  PubMed  PubMed Central  Google Scholar 

  9. Bavdekar VA, Deshpande AP, Patwardhan SC (2011) Identification of process and measurement noise covariance for state and parameter estimation using extended Kalman filter. Journal of Process control 21(4):585–601

    Article  CAS  Google Scholar 

  10. Bergman RN, Ider YZ, Bowden CR, Cobelli C (1979) Quantitative estimation of insulin sensitivity. American Journal of Physiology-Endocrinology And Metabolism 236(6):E667

    Article  CAS  Google Scholar 

  11. Bhattacharjee A, Sutradhar A (2016) Data driven nonparametric identification and model based control of glucose-insulin process in type 1 diabetics. J Process Control 41:14–25

    Article  CAS  Google Scholar 

  12. Boiroux D, Duun-Henriksen AK, Schmidt S, Nørgaard K, Poulsen NK, Madsen H, Jø rgensen JB (2017) Adaptive control in an artificial pancreas for people with type 1 diabetes. Control Engineering Practice 58:332–342

  13. Bolognani S, Tubiana L, Zigliotto M (2003) Extended Kalman filter tuning in sensorless pmsm drives. IEEE Trans Ind Appl 39(6):1741–1747

    Article  Google Scholar 

  14. Borri A, Cacace F, De Gaetano A, Germani A, Manes C, Palumbo P, Panunzi S, Pepe P (2017) Luenberger-like observers for nonlinear time-delay systems with application to the artificial pancreas: the attainment of good performance. IEEE Control Syst Mag 37(4):33–49

    Article  Google Scholar 

  15. Van den Bossche W (2013) Data assimilation toolbox for matlab

  16. Bruttomesso D, Farret A, Costa S, Marescotti MC, Vettore M, Avogaro A, Tiengo A, Dalla Man C, Place J, Facchinetti A et al (2009) Closed-loop artificial pancreas using subcutaneous glucose sensing and insulin delivery and a model predictive control algorithm: preliminary studies in padova and montpellier

  17. Campos-Delgado DU, Hernández-Ordoñez M., Femat R, Gordillo-Moscoso A (2006) Fuzzy-based controller for glucose regulation in type-1 diabetic patients by subcutaneous route. IEEE Trans Biomed Eng 53(11):2201–2210

    Article  CAS  PubMed  Google Scholar 

  18. Copp DA, Gondhalekar R, Hespanha JP (2018) Simultaneous model predictive control and moving horizon estimation for blood glucose regulation in type 1 diabetes. Optimal Control Applications and Methods 39(2):904–918

    Article  Google Scholar 

  19. De Wit CC, Youssef A, Barbot J, Martin P, Malrait F (2000) Observability conditions of induction motors at low frequencies. In: Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No. 00CH37187), vol 3, p 2044–2049. IEEE

  20. Dinani ST, Zekri M, Kamali M (2015) Regulation of blood glucose concentration in type 1 diabetics using single order sliding mode control combined with fuzzy on-line tunable gain, a simulation study. Journal of medical signals and sensors 5(3):131

    Article  PubMed  PubMed Central  Google Scholar 

  21. Dutta L, Das DK (2021) A new adaptive explicit nonlinear model predictive control design for a nonlinear mimo system: an application to twin rotor mimo system. International Journal of Control, Automation and Systems p 1–14

  22. Eberle C, Ament C (2011) The unscented Kalman filter estimates the plasma insulin from glucose measurement. Biosystems 103(1):67–72

    Article  CAS  PubMed  Google Scholar 

  23. Farahmand B, Dehghani M, Vafamand N (2019) Fuzzy model-based controller for blood glucose control in type 1 diabetes: an lmi approach. Biomedical Signal Processing and Control 54(101):627

    Google Scholar 

  24. Girardin CM, Huot C, Gonthier M, Delvin E (2009) Continuous glucose monitoring: a review of biochemical perspectives and clinical use in type 1 diabetes. Clinical biochemistry 42(3):136–142

    Article  CAS  PubMed  Google Scholar 

  25. Gondhalekar R, Dassau E, Doyle III (2016) F.j.: Periodic zone-mpc with asymmetric costs for outpatient-ready safety of an artificial pancreas to treat type 1 diabetes. Automatica 71:237–246

    Article  PubMed  PubMed Central  Google Scholar 

  26. Gondhalekar R, Dassau E, Zisser H, Doyle III (2013) F.J.:Periodic-zone model predictive control for diurnal closed-loop operation of an artificial pancreas

  27. Hariri A, et al. (2011) Observer-based state feedback for enhanced insulin control of type 1 diabetic patients. The open biomedical engineering journal 5:98

    Article  PubMed  PubMed Central  Google Scholar 

  28. Hariri AM (2011) Identification, state estimation and adaptive control of type i diabetic patients

  29. Hovorka R, Canonico V, Chassin LJ, Haueter U, Massi-Benedetti M, Federici MO, Pieber TR, Schaller HC, Schaupp L, Vering T et al (2004) Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes. Physiological measurement 25(4):905

    Article  PubMed  Google Scholar 

  30. Kaveh P, Shtessel YB (2008) Blood glucose regulation using higher-order sliding mode control. International Journal of Robust and Nonlinear Control:, IFAC-Affiliated Journal 18(4-5):557–569

    Article  Google Scholar 

  31. Khodakaramzadeh S, Batmani Y, Meskin N (2019) Automatic blood glucose control for type 1 diabetes: a trade-off between postprandial hyperglycemia and hypoglycemia. Biomedical Signal Processing and Control 54(101):603

    Google Scholar 

  32. 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  Google Scholar 

  33. León-Vargas F, Garelli F, De Battista H, Vehí J (2013) Postprandial blood glucose control using a hybrid adaptive pd controller with insulin-on-board limitation. Biomedical Signal Processing and Control 8(6):724–732

    Article  Google Scholar 

  34. Li C, Hu R (2007) Pid control based on bp neural network for the regulation of blood glucose level in diabetes. In: 2007 IEEE 7Th international symposium on bioinformatics and bioengineering, p 1168–1172. IEEE

  35. Liu W, Tang F (2008) Modeling a simplified regulatory system of blood glucose at molecular levels. J Theor Biol 252(4):608–620

    Article  CAS  PubMed  Google Scholar 

  36. Lunze K, Singh T, Walter M, Brendel MD, Leonhardt S (2013) Blood glucose control algorithms for type 1 diabetic patients: a methodological review. Biomedical signal processing and control 8(2):107–119

    Article  Google Scholar 

  37. Maahs DM, Horton LA, Chase HP (2010) The use of insulin pumps in youth with type 1 diabetes, vol 12, pp S–59

  38. Magni L, Raimondo DM, Dalla Man C, De Nicolao G, Kovatchev B, Cobelli C (2009) Model predictive control of glucose concentration in type i diabetic patients: an in silico trial. Biomedical Signal Processing and Control 4(4):338–346

    Article  Google Scholar 

  39. Mandal S, Sutradhar A (2019) Robust multi-objective blood glucose control in type-1 diabetic patient. IET systems biology 13(3):136–146

    Article  PubMed  PubMed Central  Google Scholar 

  40. Mosquera-Lopez C, Dodier R, Tyler N, Resalat N, Jacobs P (2019) Leveraging a big dataset to develop a recurrent neural network to predict adverse glycemic events in type 1 diabetes IEEE journal of biomedical and health informatics

  41. Nath A, Deb D, Dey R (2020) An augmented subcutaneous type 1 diabetic patient modelling and design of adaptive glucose control. J Process Control 86:94–105

    Article  CAS  Google Scholar 

  42. Nath A, Deb D, Dey R, Das S (2018) Blood glucose regulation in type 1 diabetic patients: an adaptive parametric compensation control-based approach. IET systems biology 12(5):219–225

    Article  PubMed  PubMed Central  Google Scholar 

  43. Nath A, Dey R, Aguilar-Avelar C (2019) Observer based nonlinear control design for glucose regulation in type 1 diabetic patients: an lmi approach. Biomedical Signal Processing and Control 47:7–15

    Article  Google Scholar 

  44. Paiva HM, Keller WS, da Cunha LGR (2020) Blood-glucose regulation using fractional-order pid control. Journal of Control Automation and Electrical Systems 31(1):1–9

    Article  Google Scholar 

  45. Palerm CC, Zisser H, Jovanovič L, Doyle III (2008) F.J.: A run-to-run control strategy to adjust basal insulin infusion rates in type 1 diabetes. Journal of process control 18(3-4):258–265

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  46. Parker RS, Doyle FJ, Peppas NA (1999) A model-based algorithm for blood glucose control in type i diabetic patients. IEEE Transactions on biomedical engineering 46(2):148–157

    Article  CAS  PubMed  Google Scholar 

  47. Parsa NT, Vali A, Ghasemi R (2014) Back stepping sliding mode control of blood glucose for type i diabetes. World Academy of Science, Engineering and Technology, International Journal of Medical, Health, Biomedical Bioengineering and Pharmaceutical Engineering 8(11):779–783

    Google Scholar 

  48. Ramprasad Y, Rangaiah G, Lakshminarayanan S (2004) Robust pid controller for blood glucose regulation in type i diabetics. Industrial & engineering chemistry research 43(26):8257–8268

    Article  CAS  Google Scholar 

  49. Rivadeneira PS, Godoy JL, Sereno J, Abuin P, Ferramosca A, González A. H. (2020) Impulsive mpc schemes for biomedical processes: application to type 1 diabetes. In: Control applications for biomedical engineering systems, p 55–87. Elsevier

  50. Shen JC (2002) New tuning method for pid controller. ISA transactions 41(4):473–484

    Article  PubMed  Google Scholar 

  51. Sorensen JT (1985) A physiologic model of glucose metabolism in man and its use to design and assess improved insulin therapies for diabetes. Ph.D. thesis Massachusetts Institute of Technology

  52. Steil G, Clark B, Kanderian S, Rebrin K (2005) Modeling insulin action for development of a closed-loop artificial pancreas. Diabetes technology & therapeutics 7(1):94–108

    Article  CAS  Google Scholar 

  53. Walsh J, Roberts R, Heinemann L (2014) Confusion regarding duration of insulin action a potential source for major insulin dose errors by bolus calculators. Journal of diabetes science and technology 8 (1):170–178

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  54. Wen Y, Chen L, Wang Y, Sun D, Duan D, Liu J (2018) Nonlinear dob-based explicit nmpc for station-keeping of a multi-vectored propeller airship with thrust saturation. The Aeronautical Journal 122(1257):1753–1774

    Article  Google Scholar 

  55. Zhao D, Liu C, Stobart R, Deng J, Winward E, Dong G (2013) An explicit model predictive control framework for turbocharged diesel engines. IEEE Trans Ind Electron 61(7):3540–3552

    Article  Google Scholar 

  56. Ziegler JG, Nichols NB et al (1942) Optimum settings for automatic controllers. trans ASME 64 (11)

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  1. National Institute of Technology Nagaland, Dimapur, India

    Debasis Acharya & Dushmanta Kumar Das

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  1. Debasis Acharya
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Correspondence to Dushmanta Kumar Das.

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Acharya, D., Das, D.K. Extended Kalman filter state estimation–based nonlinear explicit model predictive control design for blood glucose regulation of type 1 diabetic patient. Med Biol Eng Comput 60, 1347–1361 (2022). https://doi.org/10.1007/s11517-022-02511-5

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