Document Type : Original Research Paper


1 MS.C Student, Faculty of Electrical, Biomedical and Mechatronics Engineering, Qazvin branch, Islamic Azad University, Qazvin, Iran

2 Assistant Professor, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran


In this paper, chaotic dynamic and nonlinear control in a glucose-insulin system in types I diabetic patients and a healthy person have been investigated. Chaotic analysis methods of the blood glucose system include Lyapunov exponent and power spectral density based on the time series derived from the clinical data. Wolf's algorithm is used to calculate the Lyapunov exponent, which positive values of the Lyapunov exponent mean the dynamical system is chaotic. Also, a wide range in frequency spectrum based on the power spectral density is also used to confirm the chaotic behavior. In order to control the chaotic system and reach the desired level of a healthy person's glucose, a novel fuzzy high-order sliding mode control method has been proposed. Thus, in the control algorithm of the high-order sliding mode controller, all of the control gains computed by the fuzzy inference system accurately. Then the novel control algorithm is applied to the Bergman's mathematical model that is verified using the clinical data set. In this system, the control input is the amount of insulin injected into the body and the control output is the amount of blood glucose level at any moment. The simulation results of the closed-loop system in various conditions, along with the performance of the control system in disturbance presence, indicate the proper functioning of this controller at the settling time, overshoot and the control inputs.


Main Subjects

[1] P. a. S. Cobelli, 1979, On a simple model of insulin secretion, Medical and Biological Engineering and Computing. vol. 18, pp. 457-463.
[2] Jutzi E, A. G. Salzsieder E, Fischer U, 1984, Estimation of individually adapted control parameters for an artificial beta cell. Biomed Biochim Acta. , vol.43, pp. 85-96.
[3] Alan Wolf, Jack B. SWIFT, Harry L.SWINNEY and John A. VASTANO, 1984, Determining Lyapanov exponents from a time series. Departments of Physics, University of Texas, Austin, Texas 78712, USA, October.
[4] A. Wolf, 1986, Quantifying chaos with Lyapunov exponents, in Chaos. Princeton University Press.
[5] ME.Fischer, 1991, A semi closed-loop algorithm for the control of blood glucose levels in diabetics. IEEE Transactions on Biomedical Engineering, Vol. 3, pp.157-61.
[6] Mendel, J. M., 2001, Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions. Prentice Hall PTR, ISBN 0-13-040969-3.
[7] J. Geoffry chase, ks. Hwang, Z-H. Lam, J-Y.lee, G.c. Wake and G. Shaw, 2002, Steady-state optimal insulin infusion for hyperglycemia ICU patients. Seventh international conference of control, Automation, Robotics and vision (ICARV02), Singapore.
[8] Tadashi Iokibe, Keiji kakita, Masaya Yoneda, 2003, Chaos based blood glucose prediction and insulin adjustment for diabetes mellttus. Research lnstitute of Application Technologies for Chaos & Complex Systems Co. Ltd., Japan.
[9] MM Bani Amer, MS Ibbini, MA Masadeh and MA Masadeh, 2004, A semiclosed-loop optimal control system for blood glucose level in diabetics. Journal of Medical Engineering & Technology, Vol. 28, No. 5, pp 189-196.
[10] Toshiro Katayama, Kotaro Minato, Tetsuo Sato, 2004, A blood glucose prediction system by chaos approach. Graduate School of Information Science, Nara Institute of Science and Technology, Nara, Japan.
[11] Parisa Kaveh, Yuri B. Shtessel, 2006, Higher order sliding mode control for bloodglucose regulation. IEEE Xplore.
[12] Parisa Kaveh, Yuri B. Shtessel, July 2008, Blood glucose regulation via double loop higher order sliding mode control and multiple sampling rate. 17th IFAC World Congress.
[13] Soudabeh Taghian Dinani, Maryam Zekri, Behzad Nazari, 2013, Fuzzy high-order sliding-mode control of blood glucose concentration, 3rd International Conference on Computer and Knowledge Engineering.
[14] Jessica C. Kichler, Laura Levin, Michele Polfuss, 2013, The relationship between hemoglobin A1C in youth with type 1 diabetes and chaos in the family household. From Medical College of Wisconsin, Milwaukee, Wisconsin.
[15] Luiz Carlos, Naiara Maria De Souza, M. Vanderlie, and David M. Garner, 2014, Risk evaluation of diabetes mellitus by relation of chaotic globals to HRV. Department of Physiotherapy, UNESP (Universidade Estadual Paulista), Presidente Prudente, Sao Paulo, Brazil; and Department of Biological and Medical Sciences, Faculty of Health and Life Sciences.
[16] Emmanuel S. Sánchez-Velarde, 2015, Determination of bermang’s minimal model parameters for diabetic mice treated with ibervillea sonorae. Springer International Publishing Switzerland.
[17] Xiao Peng, Li Wenshi, Feng Yejia, 2016, Chaos based blood glucose noninvasive measurement: concept, principle and case study. Department of Microelectronics Soochow University Suzhou, China.
[18] Véronique DI COSTANZO, Farhat FNAIECH, Takoua HAMDI, Eric MOREAU, Roomila NAECK and Jean-Marc GINOUX, 2016, Glycemic evolution of type 1 diabetic patients is a chaotic phenomenon. Department of University of Tunis, Higher National School of Engineering of Tunis (ENSIT), LR13ES03 SIME, 1008, Montfleury, Tunisia.
[19] Abdullah Idris Enagi, Musa Bawa, Abdullah Muhammad Sani, Mathematical Study of Diabetes and its Complication Using the Homotopy Perturbation Method, International Journal of Mathematics and Computer Science, 12(2017), no. 1, 43–63
[20] Sh. Asadi, V. Nekoukar, Adaptive fuzzy integral sliding mode control of blood glucose level in patients with type 1 diabetes: In silico studies, Department of Electrical Engineering, Shahid Rajaee Teacher Training University of Iran, Mathematical Biosciences 305 (2018) 122–132.
[21] H. Heydarinejad, H. Delavari, and D. Baleanu, Fuzzy type-2 fractional Backstepping blood glucose control based on sliding mode observer, Int. J. Dyn. Control, pp. 1–14, 2018.
[22] S. M. Abtahi, Chaos control in attitude dynamics of a gyrostat satellite based on linearised Poincare'map estimation by support vector machine”. Journal of Multi-body Dynamics, Vol. 227(3) 302–312.
[23] S. M. Abtahi, 2017, Chaotic study and chaos control in a half-vehicle model with semi-active suspension using discrete optimal Ott–Grebogi–Yorke method. Journal of Multi-body Dynamics, Vol. 231(1) 148–155.