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Mohammadi S, Hejazi SR. Presentation of the model and optimal control of non-linear fractional-order chaotic system of glucose-insulin. Comput Methods Biomech Biomed Engin 2024; 27:836-848. [PMID: 37145154 DOI: 10.1080/10255842.2023.2205979] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2022] [Accepted: 04/17/2023] [Indexed: 05/06/2023]
Abstract
Recent advances in optimal diabetes control have made it possible for diabetic patients to live longer, healthier, and happier lives. In this research, particle swarm optimization and genetic algorithm are applied in order to control the non-linear fractional order chaotic system of glucose-insulin optimally. A fractional system of differential equations discussed the chaotic behavior of the growth of the blood glucose system. Particle swarm optimization and genetic algorithm were used to solve the presented optimal control problem. The results showed that when the controller is applied from the beginning, the results of the genetic algorithm method are excellent. All the results obtained for the particle swarm optimization method show that this method is also very successful and the results are very close to the genetic algorithm method.
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Affiliation(s)
- Shaban Mohammadi
- Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran
| | - S Reza Hejazi
- Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Semnan, Iran
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2
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Abubakar IN, Essabbar M, Saikouk H. Analysis of the performances of various controllers adopted in the biomedical field for blood glucose regulation: a case study of the type-1 diabetes. J Med Eng Technol 2023; 47:376-388. [PMID: 38757394 DOI: 10.1080/03091902.2024.2353036] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2023] [Accepted: 05/01/2024] [Indexed: 05/18/2024]
Abstract
Diabetes remains a critical global health concern that necessitates urgent attention. The contemporary clinical approach to closed-loop care, specifically tailored for insulin-dependent patients, aims to precisely monitor blood glucose levels while mitigating the risks of hyperglycaemia and hypoglycaemia due to erroneous insulin dosing. This study seeks to address this life-threatening issue by assessing and comparing the performance of different controllers to achieve quicker settling and convergence rates with reduced steady-state errors, particularly in scenarios involving meal interruptions. The methodology involves the detection of plasma blood glucose levels, delivery of precise insulin doses to the actuator through a control architecture, and subsequent administration of the calculated insulin dosage to patients based on the control signal. Glucose-insulin dynamics were modelled using kinetics and mass balance equations from the Bergman minimal model. The simulation results revealed that the PID controller exhibited superior performance, maintaining blood glucose concentration around the preferred threshold ∼98.8% of the time, with a standard deviation of 2.50. This was followed by RST with a success rate of 98.5% and standard deviation of 5.00, SPC with a success rate of 58% and standard deviation of 2.99, SFC with a success rate of 55% and standard deviation of 10.08, and finally LCFB with a rate of 10% and significantly higher standard deviation of 64.55.
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Affiliation(s)
| | - Moad Essabbar
- Euromed Research Center, Euromed University of Fes, Fez, Morocco
| | - Hajar Saikouk
- Euromed Research Center, Euromed University of Fes, Fez, Morocco
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3
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Zahedifar R, Keymasi Khalaji A. Control of blood glucose induced by meals for type-1 diabetics using an adaptive backstepping algorithm. Sci Rep 2022; 12:12228. [PMID: 35851835 PMCID: PMC9293929 DOI: 10.1038/s41598-022-16535-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2022] [Accepted: 07/12/2022] [Indexed: 11/24/2022] Open
Abstract
In this study, an adaptive backstepping method is proposed to regulate the blood glucose induced by meals for type-1 diabetic patients. The backstepping controller is used to control the blood glucose level and an adaptive algorithm is utilized to compensate for the blood glucose induced by meals. Moreover, the effectiveness of the proposed method is evaluated by comparing results in two different case studies: in the presence of actuator faults and the loss of control input for a short while during treatment. Effects of unannounced meals three times a day are investigated for a nominal patient in every case. It is argued that adaptive backstepping is the preferred control method in either case. The Lyapunov theory is used to prove the stability of the proposed method. Obtained results, indicated that the adaptive backstepping controller is stable, and the desired level of glucose concentration is being tracked efficiently.
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Affiliation(s)
- Rasoul Zahedifar
- Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University, Tehran, P.O.B. 15719-14911, Iran
| | - Ali Keymasi Khalaji
- Department of Mechanical Engineering, Faculty of Engineering, Kharazmi University, Tehran, P.O.B. 15719-14911, Iran.
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4
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Acharya D, Das DK. 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 2022; 60:1347-1361. [DOI: 10.1007/s11517-022-02511-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2021] [Accepted: 01/18/2022] [Indexed: 10/18/2022]
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5
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Batmani Y, Khodakaramzadeh S, Moradi P. Automatic Artificial Pancreas Systems Using an Intelligent Multiple-Model PID Strategy. IEEE J Biomed Health Inform 2021; 26:1708-1717. [PMID: 34587104 DOI: 10.1109/jbhi.2021.3116376] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Abstract
In this paper, an individualized intelligent multiple-model technique is proposed to design automatic artificial pancreas (AP) systems for the glycemic regulation of type 1 diabetic patients. At first, using the multiple-model concept, the insulin-glucose regulatory system is mathematically identified by constructing some local models. In this step, trade-offs between the number of local models and the complexity of the overall closed-loop system are made by defining and solving a bi-objective optimization problem. Then, optimal AP systems are designed by tuning a bank of proportionalintegralderivative (PID) controllers via the genetic algorithm (GA). A fuzzy gain scheduling strategy is employed to determine the participation percentages of the PID controllers in the control action. Finally, two safety mechanisms, called insulin on board (IOB) constraint and pump shut-off, are installed in the AP systems to enhance their performance. To assess the proposed AP systems, in silico experiments are performed on virtual patients of the UVA/Padova metabolic simulator. The obtained results reveal that the proposed intelligent multiple-model methodology leads to AP systems with limited hyperglycemia and no severe hypoglycemia.
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6
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Alam W, Khan Q, Riaz RA, Akmeliawati R. Arbitrary-order sliding mode-based robust control algorithm for the developing artificial pancreas mechanism. IET Syst Biol 2020; 14:307-313. [PMID: 33399094 PMCID: PMC8687268 DOI: 10.1049/iet-syb.2018.5075] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2018] [Revised: 04/15/2020] [Accepted: 05/27/2020] [Indexed: 11/20/2022] Open
Abstract
In Diabetes Mellitus, the pancreas remains incapable of insulin administration that leads to hyperglycaemia, an escalated glycaemic concentration, which may stimulate many complications. To circumvent this situation, a closed-loop control strategy is much needed for the exogenous insulin infusion in diabetic patients. This closed-loop structure is often termed as an artificial pancreas that is generally established by the employment of different feedback control strategies. In this work, the authors have proposed an arbitrary-order sliding mode control approach for development of the said mechanism. The term, arbitrary, is exercised in the sense of its applicability to any n-order controllable canonical system. The proposed control algorithm affirms the finite-time effective stabilisation of the glucose-insulin regulatory system, at the desired level, with the alleviation of sharp fluctuations. The novelty of this work lies in the sliding manifold that incorporates indirect non-linear terms. In addition, the necessary discontinuous terms are filtered-out once before its employment to the plant, i.e. diabetic patient. The robustness, in the presence of external disturbances, i.e. meal intake is confirmed via rigorous mathematical stability analysis. In addition, the effectiveness of the proposed control strategy is ascertained by comparing the results with the standard literature.
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Affiliation(s)
- Waqar Alam
- Department of Electrical and Computer Engineering, COMSATS University Islamabad, Islamabad, Pakistan
| | - Qudrat Khan
- Center for Advanced Studies in Telecommunications (CAST), COMSATS University Islamabad, Islamabad, Pakistan.
| | - Raja Ali Riaz
- Department of Electrical and Computer Engineering, COMSATS University Islamabad, Islamabad, Pakistan
| | - Rini Akmeliawati
- School of Mechanical Engineering, The University of Adelaide, Adelaide, South Australia 5005, Australia
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7
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Batmani Y, Khodakaramzadeh S. Blood glucose concentration control for type 1 diabetic patients: a multiple-model strategy. IET Syst Biol 2020; 14:24-30. [PMID: 31931478 DOI: 10.1049/iet-syb.2018.5049] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022] Open
Abstract
In this study, a multiple-model strategy is evaluated as an alternative closed-loop method for subcutaneous insulin delivery in type 1 diabetes. Non-linearities of the glucose-insulin regulatory system are considered by modelling the system around five different operating points. After conducting some identification experiments in the UVA/Padova metabolic simulator (accepted simulator by the US Food and Drug Administration (FDA)), five transfer functions are obtained for these operating points. Paying attention to some physiological facts, the control objectives such as the required settling time and permissible bounds of overshoots and undershoots are determined for any transfer functions. Then, five PID controllers are tuned to achieve these objectives and a bank of controllers is constructed. To cope with difficulties of the presence of delays in subcutaneous blood glucose (BG) measuring and in administration of insulin, a glucose-dependent setpoint is considered as the desired trajectory for the BG concentration. The performance of the obtained closed-loop glucose-insulin regulatory system is investigated on the in silico adult cohort of the UVA/Padova metabolic simulator. The obtained results show that the proposed multiple-model strategy leads to a closed-loop mechanism with limited hyperglycemia and no severe hypoglycemia.
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Affiliation(s)
- Yazdan Batmani
- Department of Electrical Engineering, University of Kurdistan, Sanandaj, Iran.
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Khan MW, Abid M, Khan AQ, Mustafa G, Ali M, Khan A. Sliding mode control for a fractional-order non-linear glucose-insulin system. IET Syst Biol 2020; 14:223-229. [PMID: 33095743 PMCID: PMC8687314 DOI: 10.1049/iet-syb.2020.0030] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/26/2020] [Revised: 05/21/2020] [Accepted: 08/03/2020] [Indexed: 07/25/2024] Open
Abstract
By providing the generalisation of integration and differentiation, and incorporating the memory and hereditary effects, fractional-order modelling has gotten significant attention in the past few years. One of the extensively studied and utilised models to describe the glucose-insulin system of a human body is Bergman's minimal model. This non-linear model comprises of integer-order differential equations. However, comparison with the experimental data shows that the fractional-order version of Bergman's minimal model is a better representative of the glucose-insulin system than its original integer-order model. To design a control law for an artificial pancreas for a diabetic patient using a fractional-order model, different techniques, including feedback linearisation, have been applied in the literature. The authors' previous work shows that the fractional-order version of Bergman's model describes the glucose-insulin system in a better way than the integer-order model. This study applies the sliding mode control technique and then compares the obtained simulation results with the ones obtained using feedback linearisation.
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Affiliation(s)
| | - Muhammad Abid
- Department of Electrical Engineering, Pakistan Institute of Engineering and Applied Sciences, Islamabad, Pakistan
| | - Abdul Qayyum Khan
- Department of Electrical Engineering, Pakistan Institute of Engineering and Applied Sciences, Islamabad, Pakistan
| | - Ghulam Mustafa
- Department of Electrical Engineering, Pakistan Institute of Engineering and Applied Sciences, Islamabad, Pakistan
| | - Muzamil Ali
- Department of Mechanical Engineering, Pakistan Institute of Engineering and Applied Sciences, Islamabad, Pakistan
| | - Asifullah Khan
- PIEAS Artificial Intelligence Center (PAIC), Islamabad, Pakistan
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9
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Artificial Pancreas Control Strategies Used for Type 1 Diabetes Control and Treatment: A Comprehensive Analysis. APPLIED SYSTEM INNOVATION 2020. [DOI: 10.3390/asi3030031] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
This paper presents a comprehensive survey about the fundamental components of the artificial pancreas (AP) system including insulin administration and delivery, glucose measurement (GM), and control strategies/algorithms used for type 1 diabetes mellitus (T1DM) treatment and control. Our main focus is on the T1DM that emerges due to pancreas’s failure to produce sufficient insulin due to the loss of beta cells (β-cells). We discuss various insulin administration and delivery methods including physiological methods, open-loop, and closed-loop schemes. Furthermore, we report several factors such as hyperglycemia, hypoglycemia, and many other physical factors that need to be considered while infusing insulin in human body via AP systems. We discuss three prominent control algorithms including proportional-integral- derivative (PID), fuzzy logic, and model predictive, which have been clinically evaluated and have all shown promising results. In addition, linear and non-linear insulin infusion control schemes have been formally discussed. To the best of our knowledge, this is the first work which systematically covers recent developments in the AP components with a solid foundation for future studies in the T1DM field.
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Kalamian N, Khaloozadeh H, Ayati SM. Adaptive state-dependent impulsive observer design for nonlinear deterministic and stochastic dynamics with time-delays. ISA TRANSACTIONS 2020; 98:87-100. [PMID: 31492473 DOI: 10.1016/j.isatra.2019.08.034] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2018] [Revised: 08/17/2019] [Accepted: 08/20/2019] [Indexed: 06/10/2023]
Abstract
The present research has introduced a novel adaptive state-dependent impulsive observer (ASDIO) used to control diverse nonlinear systems with time-varying delay. This designed ASDIO is in conformity with the approach of extended pseudo-linearization for the purpose of parametrizing a nonlinear system with time-delay to a pseudo-linear time-delay structure having state-dependent coefficients. This technique makes the ASDIO applicable to nonlinear systems with distributed, multiple, and time-varying delays. The time-varying and delay-independent Lyapunov functional approach, coupled with the comparison method for impulsive systems, was used to confirm the stability of ASDIO. This new theorem affirmed the state and parameter estimation error to approach zero asymptotically through distinct and less-conservative adequate conditions with respect to practical linear matrix inequalities. Furthermore, the maximum impulse time was specified via the presented stability theorem. The ASDIO has also been offered for a special set of stochastic nonlinear systems with time-delay. An investigation of the asymptotic stability for the intended ASDIO was performed via a new theorem employing the comparison principle for stochastic impulsive systems. Accordingly, this observer was simulated on an epidemic system with time-delay nonlinear features to affirm its performance.
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Affiliation(s)
- Nasrin Kalamian
- Department of Systems and Control Engineering, K.N. Toosi University of Technology, Tehran, Iran.
| | - Hamid Khaloozadeh
- Department of Systems and Control Engineering, K.N. Toosi University of Technology, Tehran, Iran.
| | - S Moosa Ayati
- School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran.
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11
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Karsaz A. Chattering -free hybrid adaptive neuro-fuzzy inference system-particle swarm optimisation data fusion-based BG-level control. IET Syst Biol 2020; 14:31-38. [PMID: 31931479 DOI: 10.1049/iet-syb.2018.5019] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022] Open
Abstract
In this study, a closed-loop control scheme is proposed for the glucose-insulin regulatory system in type-1 diabetic mellitus (T1DM) patients. Some innovative hybrid glucose-insulin regulators have combined artificial intelligence such as fuzzy logic and genetic algorithm with well known Palumbo model to regulate the blood glucose (BG) level in T1DM patients. However, most of these approaches have focused on the glucose reference tracking, and the qualitative of this tracking such as chattering reduction of insulin injection has not been well-studied. Higher-order sliding mode (HoSM) controllers have been employed to attenuate the effect of chattering. Owing to the delayed nature and non-linear property of glucose-insulin mechanism as well as various unmeasurable disturbances, even the HoSM methods are partly successful. In this study, data fusion of adaptive neuro-fuzzy inference systems optimised by particle swarm optimisation has been presented. The excellent performance of the proposed hybrid controller, i.e. desired BG-level tracking and chattering reduction in the presence of daily glucose-level disturbances is verified.
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Affiliation(s)
- Ali Karsaz
- Department of Electrical and Electronic Engineering, Khorasan Institute of Higher Education, Mashhad, Iran.
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12
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Automatic blood glucose control for type 1 diabetes: A trade-off between postprandial hyperglycemia and hypoglycemia. Biomed Signal Process Control 2019. [DOI: 10.1016/j.bspc.2019.101603] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
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Nath A, Deb D, Dey R, Das S. Blood glucose regulation in type 1 diabetic patients: an adaptive parametric compensation control-based approach. IET Syst Biol 2019; 12:219-225. [PMID: 30259867 PMCID: PMC8687408 DOI: 10.1049/iet-syb.2017.0093] [Citation(s) in RCA: 35] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022] Open
Abstract
Here, a direct adaptive control strategy with parametric compensation is adopted for an uncertain non‐linear model representing blood glucose regulation in type 1 diabetes mellitus patients. The uncertain parameters of the model are updated by appropriate design of adaptation laws using the Lyapunov method. The closed‐loop response of the plasma glucose concentration as well as external insulin infusion rate is analysed for a wide range of variation of the model parameters through extensive simulation studies. The result indicates that the proposed adaptive control scheme avoids severe hypoglycaemia and gives satisfactory performance under parametric uncertainty highlighting its ability to address the issue of inter‐patient variability.
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Affiliation(s)
- Anirudh Nath
- Electrical Engineering Department, National Institute of Technology, Silchar 788010, Assam, India.
| | - Dipankar Deb
- Electrical Engineering Department, Institute of Infrastructure Technology Research and Management, Ahmedabad 380026, Gujarat, India
| | - Rajeeb Dey
- Electrical Engineering Department, National Institute of Technology, Silchar 788010, Assam, India
| | - Sipon Das
- Electrical Engineering Department, National Institute of Technology, Silchar 788010, Assam, India
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Delavari H, Heydarinejad H, Baleanu D. Adaptive fractional-order blood glucose regulator based on high-order sliding mode observer. IET Syst Biol 2019; 13:43-54. [DOI: 10.1049/iet-syb.2018.5016] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/10/2018] [Revised: 04/24/2018] [Accepted: 06/11/2018] [Indexed: 12/24/2022] Open
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15
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Nath A, Dey R. Robust observer based control for plasma glucose regulation in type 1 diabetes patient using attractive ellipsoid method. IET Syst Biol 2019; 13:84-91. [PMID: 33444475 PMCID: PMC8687389 DOI: 10.1049/iet-syb.2018.5054] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/25/2018] [Revised: 08/21/2018] [Accepted: 11/27/2018] [Indexed: 02/01/2023] Open
Abstract
This paper deals with the design of robust observer based output feedback control law for the stabilisation of an uncertain nonlinear system and subsequently apply the developed method for the regulation of plasma glucose concentration in Type 1 diabetes (T1D) patients. The principal objective behind the proposed design is to deal with the issues of intra‐patient parametric variation and non‐availability of all state variables for measurement. The proposed control technique for the T1D patient model is based on the attractive ellipsoid method (AEM). The observer and controller conditions are obtained in terms of linear matrix inequality (LMI), thus allowing to compute easily both the observer and controller gains. The closed‐loop response obtained using the designed controller avoids adverse situations of hypoglycemia and post‐prandial hyperglycemia under uncertain conditions. Further to validate the robustness of the design, closed‐loop simulations of random 200 virtual T1D patients considering parameters within the considered ranges are presented. The results indicate that hypoglycemia and post‐prandial hyperglycemia are significantly reduced in the presence of bounded (±30% ) parametric variability and uncertain exogenous meal disturbance.
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Affiliation(s)
- Anirudh Nath
- Electrical Engineering Department, National Institute of TechnologySilcharAssam788010India
| | - Rajeeb Dey
- Electrical Engineering Department, National Institute of TechnologySilcharAssam788010India
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Biswas P, Sutradhar A, Datta P. Estimation of parameters for plasma glucose regulation in type-2 diabetics in presence of meal. IET Syst Biol 2019; 12:18-25. [PMID: 29337286 PMCID: PMC8687173 DOI: 10.1049/iet-syb.2017.0036] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022] Open
Abstract
In this study, the authors propose a methodology for the estimation of glucose masses in stomach (both in solid and liquid forms), intestine, plasma and tissue; insulin masses in portal vein, liver, plasma and interstitial fluid using only plasma glucose measurement. The proposed methodology fuses glucose–insulin homoeostasis model (in the presence of meal intake) and plasma glucose measurement with a Bayesian non‐linear filter. Uncertainty of the model over individual variations has been incorporated by adding process noise to the homoeostasis model. The estimation is carried out over 24 h for the healthy people as well as a type II diabetes mellitus patients. In simulation, the estimator follows the truth accurately for both the cases. Moreover, the performances of two non‐linear filters, namely the unscented Kalman filter (KF) and cubature quadrature KF are compared in terms of root mean square error. The proposed methodology will be helpful in future to: (i) observe a patient's insulin–glucose profile, (ii) calculate drug dose for any hyperglycaemic patients and (iii) develop a closed‐loop controller for automated insulin delivery system.
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Affiliation(s)
- Prova Biswas
- Department of Health and Family Welfare, Institute of Pharmacy Jalpaiguri, Swasthya Bhawan, Jalpaiguri PIN 735 101, West Bengal, India
| | - Ashoke Sutradhar
- Department of Electrical Engineering, Indian Institute of Engineering Science and Technology Shibpur, Howrah PIN 711 103, West Bengal, India
| | - Pallab Datta
- Centre for Healthcare Science and Technology, Indian Institute of Engineering Science and Technology Shibpur, Howrah PIN 711 103, West Bengal, India.
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