Robust Glycemic Regulation via Takagi–Sugeno Explicit Model Predictive Control for Type 1 Diabetes Management

SAYDTAHIRI Assia; ELMAJIDI Azzedine; HATIM Anas; ELLOUAD Hicham

Robust Glycemic Regulation via Takagi–Sugeno Explicit Model Predictive Control for Type 1 Diabetes Management

SAYDTAHIRI Assia, ELMAJIDI Azzedine, HATIM Anas, ELLOUAD Hicham

1 LARTID, National School of Applied Sciences of Marrakech, Cadi Ayyad University, Marrakech, Morocco
2 LAREFERENCE, Faculty of Legal Economic and Social Sciences of Marrakech, Cadi Ayyad University, Marrakech, Morocco
3 LEBPBAI, Faculty of medicine and pharmacy of Marrakech, Cadi Ayyad University, Marrakech, Morocco
a.saydtahiri.ced@uca.ac.ma, elmajidi@gmail.com, hatim.anas@gmail.com, h.ellouad.ced@uca.ac.ma

How to cite: SAYDTAHIRI Assia, ELMAJIDI Azzedine, HATIM Anas, ELLOUAD Hicham, Robust Glycemic Regulation via Takagi-Sugeno Explicit Model Predictive Control for Type 1 Diabetes Management, Sciences Methods and Technologies International Journal (SciMeTech), (2026) Vol 2, Issue 2, p 32-39

Abstract

In this paper, we propose a TS-eMPC control strategy for blood glucose regulation in patients with type 1 diabetes using artificial pancreas technology. In the proposed methodology, the optimal control policy associated with MPC is computed offline using the exact fuzzy state feedback controller framework of Takagi-Sugeno form; this reduces the online complexity to O(n) without having to solve an online optimization problem. Our physiological model will be the Bergman minimal model whose only nonlinearity can be represented exactly using sector nonlinearity theory, hence obtaining a two-rule T-S system. The local gains are calculated by solving a constrained quadratic regression problem on a database generated by optimal MPC policies, with actuator saturation constraints enforced automatically. Formal closed-loop stability is demonstrated using the spectral radius of the product-norm operator on an invariant set containing initial states. Simulation results show trajectory tracking with less than \(6\%\) error compared to the optimal MPC control under meal disturbances; this corresponds to a time in range of \(99\%\) with no hypoglycemia events occurring; the performance beats all other compared MPC approaches.

Keywords: Type 1 diabetes, Artificial pancreas, Model Predictive Control, Takagi-Sugeno fuzzy systems, Stability analysis

References

American Diabetes Association. (2023). Standards of medical care in diabetes-2023. Diabetes Care, 46(Suppl 1), S1.
Keith-Hynes, P., Mize, B., Robert, A., & Place, J. (2014). The diabetes assistant: a smartphone-based system for real-time control of blood glucose. electronics, 3(4), 609-623.
Sherr, J. L., Cengiz, E., Palerm, C. C., Clark, B., Kurtz, N., Roy, A., & Weinzimer, S. A. (2013). Reduced hypoglycemia and increased time in target using closed-loop insulin delivery during nights with or without antecedent afternoon exercise in type 1 diabetes. Diabetes care, 36(10), 2909-2914.
Baucom, K. J., Queen, T. L., Wiebe, D. J., Turner, S. L., Wolfe, K. L., Godbey, E. I., & Berg, C. A. (2015). Depressive symptoms, daily stress, and adherence in late adolescents with type 1 diabetes. Health Psychology, 34(5), 522.
Mauseth, R., Lord, S. M., Hirsch, I. B., Kircher, R. C., Matheson, D. P., & Greenbaum, C. J. (2015). Stress testing of an artificial pancreas system with pizza and exercise leads to improvements in the system's fuzzy logic controller. Journal of diabetes science and technology, 9(6), 1253-1259.
Magni, L., Raimondo, D. M., Bossi, L., Dalla Man, C., De Nicolao, G., Kovatchev, B., & Cobelli, C. (2007). Model predictive control of type 1 diabetes: an in silico trial.
Acharya, D., & Das, D. K. (2022). An efficient nonlinear explicit model predictive control to regulate blood glucose in type-1 diabetic patient under parametric uncertainties. Biomedical Signal Processing and Control, 71, 103166.
Aiello, E. M., Jaloli, M., & Cescon, M. (2024). Model predictive control (MPC) of an artificial pancreas with data-driven learning of multi-step-ahead blood glucose predictors. Control Engineering Practice, 144, 105810.
Chakrabarty, A., Zavitsanou, S., Doyle, F. J., & Dassau, E. (2017). Event-triggered model predictive control for embedded artificial pancreas systems. IEEE Transactions on Biomedical Engineering, 65(3), 575-586.
Kovatchev, B., Castillo, A., Pryor, E., Kollar, L. L., Barnett, C. L., DeBoer, M. D., & NAP Study Team. (2024). Neural-net artificial pancreas: a randomized crossover trial of a first-in-class automated insulin delivery algorithm. Diabetes technology & therapeutics, 26(6), 375-382.
Tanaka, K., & Wang, H. O. (2004). Fuzzy control systems design and analysis: a linear matrix inequality approach. John Wiley & Sons.
Ganji, M., & Pourgholi, M. (2024, May). An LMI-based robust fuzzy controller for blood glucose regulation in type 1 diabetes. In 2024 32nd International Conference on Electrical Engineering (ICEE) (pp. 1-7). IEEE.
Yan, S., Chu, L. L., & Cai, Y. (2023). Robust H∞ control of T-S fuzzy blood glucose regulation system via adaptive event-triggered scheme. Biomedical Signal Processing and Control, 83, 104643.
Giaccalgi, M., Andrieu, V., Tarbouriech, S., & Astolfi, D. (2023). LMI conditions for contraction, integral action, and output feedback stabilization for a class of nonlinear systems. Automatica, 154, 111106.
Nath, A., Dey, R., & Balas, V. E. (2016, August). Closed loop blood glucose regulation of type 1 diabetic patient using Takagi-Sugeno fuzzy logic control. In International Workshop Soft Computing Applications (pp. 286-296). Cham: Springer International Publishing.
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, 101627.
Khalesi, Z., Dehghani, M., & Vafamand, N. (2021). Insulin dosage control of time-delayed type-1 diabetes. In Control Strategy for Time-Delay Systems (pp. 95-110). Academic Press.
Belarbi, K. (2019). On matrix norms, stability and stabilization of a class of discrete Takagi-Sugeno fuzzy systems. IEEE Transactions on Fuzzy Systems, 27(10), 1999-2008.
Mansell, E. J., Docherty, P. D., Fisk, L. M., & Chase, J. G. (2015). Estimation of secondary effect parameters in glycaemic dynamics using accumulating data from a virtual type 1 diabetic patient. Mathematical biosciences, 266, 108-117.
Beck, R. W., Bergenstal, R. M., Cheng, P., Kollman, C., Carlson, A. L., Johnson, M. L., & Rodbard, D. (2019). The relationships between time in range, hyperglycemia metrics, and HbA1c. Journal of diabetes science and technology, 13(4), 614-626.

[1] American Diabetes Association. (2023). Standards of medical care in diabetes-2023. Diabetes Care, 46(Suppl 1), S1.

[2] Keith-Hynes, P., Mize, B., Robert, A., & Place, J. (2014). The diabetes assistant: a smartphone-based system for real-time control of blood glucose. electronics, 3(4), 609-623.

[3] Sherr, J. L., Cengiz, E., Palerm, C. C., Clark, B., Kurtz, N., Roy, A., & Weinzimer, S. A. (2013). Reduced hypoglycemia and increased time in target using closed-loop insulin delivery during nights with or without antecedent afternoon exercise in type 1 diabetes. Diabetes care, 36(10), 2909-2914.

[4] Baucom, K. J., Queen, T. L., Wiebe, D. J., Turner, S. L., Wolfe, K. L., Godbey, E. I., & Berg, C. A. (2015). Depressive symptoms, daily stress, and adherence in late adolescents with type 1 diabetes. Health Psychology, 34(5), 522.

[5] Mauseth, R., Lord, S. M., Hirsch, I. B., Kircher, R. C., Matheson, D. P., & Greenbaum, C. J. (2015). Stress testing of an artificial pancreas system with pizza and exercise leads to improvements in the system's fuzzy logic controller. Journal of diabetes science and technology, 9(6), 1253-1259.

[6] Magni, L., Raimondo, D. M., Bossi, L., Dalla Man, C., De Nicolao, G., Kovatchev, B., & Cobelli, C. (2007). Model predictive control of type 1 diabetes: an in silico trial.

[7] Acharya, D., & Das, D. K. (2022). An efficient nonlinear explicit model predictive control to regulate blood glucose in type-1 diabetic patient under parametric uncertainties. Biomedical Signal Processing and Control, 71, 103166.

[8] Aiello, E. M., Jaloli, M., & Cescon, M. (2024). Model predictive control (MPC) of an artificial pancreas with data-driven learning of multi-step-ahead blood glucose predictors. Control Engineering Practice, 144, 105810.

[9] Chakrabarty, A., Zavitsanou, S., Doyle, F. J., & Dassau, E. (2017). Event-triggered model predictive control for embedded artificial pancreas systems. IEEE Transactions on Biomedical Engineering, 65(3), 575-586.

[10] Kovatchev, B., Castillo, A., Pryor, E., Kollar, L. L., Barnett, C. L., DeBoer, M. D., & NAP Study Team. (2024). Neural-net artificial pancreas: a randomized crossover trial of a first-in-class automated insulin delivery algorithm. Diabetes technology & therapeutics, 26(6), 375-382.

[11] Tanaka, K., & Wang, H. O. (2004). Fuzzy control systems design and analysis: a linear matrix inequality approach. John Wiley & Sons.

[12] Ganji, M., & Pourgholi, M. (2024, May). An LMI-based robust fuzzy controller for blood glucose regulation in type 1 diabetes. In 2024 32nd International Conference on Electrical Engineering (ICEE) (pp. 1-7). IEEE.

[13] Yan, S., Chu, L. L., & Cai, Y. (2023). Robust H∞ control of T-S fuzzy blood glucose regulation system via adaptive event-triggered scheme. Biomedical Signal Processing and Control, 83, 104643.

[14] Giaccalgi, M., Andrieu, V., Tarbouriech, S., & Astolfi, D. (2023). LMI conditions for contraction, integral action, and output feedback stabilization for a class of nonlinear systems. Automatica, 154, 111106.

[15] Nath, A., Dey, R., & Balas, V. E. (2016, August). Closed loop blood glucose regulation of type 1 diabetic patient using Takagi-Sugeno fuzzy logic control. In International Workshop Soft Computing Applications (pp. 286-296). Cham: Springer International Publishing.

[16] 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, 101627.

[17] Khalesi, Z., Dehghani, M., & Vafamand, N. (2021). Insulin dosage control of time-delayed type-1 diabetes. In Control Strategy for Time-Delay Systems (pp. 95-110). Academic Press.

[18] Belarbi, K. (2019). On matrix norms, stability and stabilization of a class of discrete Takagi-Sugeno fuzzy systems. IEEE Transactions on Fuzzy Systems, 27(10), 1999-2008.

[19] Mansell, E. J., Docherty, P. D., Fisk, L. M., & Chase, J. G. (2015). Estimation of secondary effect parameters in glycaemic dynamics using accumulating data from a virtual type 1 diabetic patient. Mathematical biosciences, 266, 108-117.

[20] Beck, R. W., Bergenstal, R. M., Cheng, P., Kollman, C., Carlson, A. L., Johnson, M. L., & Rodbard, D. (2019). The relationships between time in range, hyperglycemia metrics, and HbA1c. Journal of diabetes science and technology, 13(4), 614-626.