Control Engineering Methods for Blood Glucose Levels Regulation

Abstract

In this article, we review recently proposed, advanced methods, for the control of blood glucose levels, in patients with type 1 diabetes. The proposed methods are based on various techniques, such as predictive control, filters, and machine learning. Results have shown that the artificial pancreas may control blood glucose levels better than conservative insulin administration while avoiding the risk of hypoglycemia or hyperglycemia. The most commonly used methods for controlling blood glucose levels are giving good results, while methods based on machine learning algorithms also offer promising performance. Nevertheless, there are numerous challenges in designing algorithms for the artificial pancreas, which need to be considered. The aim of this research is to provide an overview of the latest achievements in this research field, find the best solutions, and, ultimately, improve them in the future.

Full text

Acta Polytechnica Hungarica Vol. 19, No. 7, 2022
– 127 –
Control Engineering Methods for Blood Glucose
Levels Regulation
Jelena Tašić1, Márta Takács2 and Levente Kovács1
1Physiological Controls Research Center, Óbuda University, 1034 Budapest, Bcsi
t 96/b, Hungary
2John von Neumann Faculty of Informatics, Óbuda University, 1034 Budapest,
Bcsi t 96/b, Hungary
Email: tasic.jelena@uni-obuda.hu, takacs.marta@nik.uni-obuda.hu, kovacs@uni-
obuda.hu
Abstract: In this article, we review recently proposed, advanced methods, for the control of
blood glucose levels, in patients with type 1 diabetes. The proposed methods are based on
various techniques, such as predictive control, filters, and machine learning. Results have
shown that the artificial pancreas may control blood glucose levels better than conservative
insulin administration, while avoiding the risk of hypoglycemia or hyperglycemia. The most
commonly used methods for controlling blood glucose levels are giving good results, while
methods based on machine learning algorithms also offer promising performance.
Nevertheless, there are numerous challenges in designing algorithms for the artificial
pancreas, which need to be considered. The aim of this research is to provide an overview
of the latest achievements in this research field, find the best solutions and, ultimately,
improve them in the future.
Keywords: Artificial pancreas; continuous glucose monitoring; model predictive control;
sliding mode control; Kalman filters; machine learning; neural networks; type 1 diabetes
1 Introduction
In the last few decades, the number of people suffering from diabetes has
constantly increased. According to the latest information, about 422 million
people worldwide have diabetes, while 1.5 million deaths are directly attributed to
diabetes each year [1]. Diabetes is a chronic autoimmune disease that occurs when
the pancreas produces little or no insulin, as in type 1 diabetes (T1D), or when the
body produces insulin but cannot use it effectively, as in type 2 diabetes (T2D).
This disease destroys pancreatic β-cells, which are responsible for the production
of the insulin peptide hormone, which regulates blood glucose (BG) levels.

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Although T2D makes up 90-95% of cases, our focus will be on T1D, which is also
known as juvenile diabetes or insulin-dependent diabetes.
Due to the lack of internal insulin production, patients with T1D need treatment
with exogenous insulin, which is necessary for their survival. However, it should
be taken into account that external administration of insulin also has its risks. In
case of hypoglycemia, the patient’s BG level is below 3.9 mmol/l (70 mg/dl),
which can lead to a potential loss of consciousness, seizures, coma, or death. On
the other hand, we have elevated BG levels or hyperglycemia, where the patient’s
BG level is greater than 11.1 mmol/l (200 mg/dl). This can lead to serious damage
to the patient's body system and long-term complications such as neuropathies,
nephropathy, or cardiovascular disease [2].
The artificial pancreas (AP) is a closed-loop glucose controller that provides
automatic delivery of insulin. It consists of a continuous subcutaneous insulin
infusion (CSII) pump which communicates with the continuous glucose
monitoring (CGM) system that measures the BG levels, to automatically deliver
insulin when needed [3]. After calculating the required amount of insulin, the
pump releases and delivers an appropriate dose to the patient’s body using a
specific control algorithm.
The results showed that the AP may control the BG levels and reduce the risk of
hypoglycemia better than the conservative insulin administration compared with
conventional insulin therapy (open-loop control) [4]. Even though the recently
proposed methods give good results, there are many challenges in designing
algorithms that need to be considered. Glucose metabolic disorders can occur
under the influence of various factors such as changes in diet, circadian rhythm,
stress, alcohol consumption, unannounced physical exercise, menstrual cycle,
chronic metabolic variations, or insulin sensitivity [5]. Also, there are additional
factors such as urgent time requirements, unknown analytical relationships
between custom parameters and measured values, and security issues, which
present additional challenges for the development of the algorithms [6].
After a brief introduction of T1D and AP, in Section II we present a review of
control methods based on model predictive control, Bayesian optimization, sliding
mode control, proportional integral derivative control, linear parameter varying,
iterative learning control, active disturbance rejection control, robust fixed point
transformations, disturbance observer, terminal synergetic, state feedback
linearization, and bioinspired AP. In Section III is given a brief review of a
method for the identification of parameters, while in Section IV we review
methods based on kernel and Kalman filters. In Section V we present a review of
novel approaches based on machine learning such as unsupervised and supervised
learning, clustering, artificial neural networks, and bioinspired reinforcement
learning. Finally, we conclude with Section VI.

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2 Approaches Based on Control Methods
In this Section, we present recently proposed methods for controlling and
regulating BG levels, but also for preventing large delays in insulin absorption.
One of the most commonly used methods is model predictive control, which is
used to handle meal announcements [7], control BG levels, limit insulin infusion
rates, and improve its delivery through the prediction horizon. The sliding mode
control approach is a common method used for handling insulin stabilization,
regulating glycaemia, and improving glucose regulation. A proportional integral
derivative model-based approach that relies on physiological models that consider
the operation of metabolism is also commonly used. Other approaches include
Bayesian optimization, linear parameter varying, iterative learning control, robust
fixed point transformations, active disturbance control, disturbance observer,
terminal synergetic, state feedback linearization, and bioinspired AP.
2.1 Model Predictive Control Approach
Most of the proposed methods, which have been tested in clinical studies, are
based on the linear model predictive control (MPC). MPC has shown that it is able
to stabilize BG levels, but also to improve the bolus calculator for more efficient
meal management [8-10]. Currently, used calculators depend on the correction
between BG levels and insulin intakes. The reason is that a linear relationship
between the size of the announced meal and the insulin bolus should be assumed
[11].
While Chakrabarty et al. [12] used an observer-based MPC algorithm with the
novel event-triggered communication (ETC) method for reducing sensor-
controller transmissions, Cairoli et al. [3] improved MPC with a signal temporal
logic (STL) method using the Hovorka compartment ordinary differential equation
(ODE) model (Fig. 1). The STL was able to provide safe BG pathways allowing
soft constraints, even during meal disturbances, while avoiding hypoglycemia and
hyperglycemia.
Figure 1
Scheme of the applied Hovorka compartment ODE model [3]

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A recursive subspace-based empirical modeling algorithm based on the predictor-
based subspace identification (PBSID) method was presented by Rashid et al. [13]
to determine the linear dynamic model, while CGM measurements were used to
determine the appropriate values for the plasma insulin concentration (PIC)
bounds and risk indexes. The proposed method provided a stable, time-varying,
and individualized state-space model for predicting CGM measurements, while
keeping BG levels within the safe range, without meal announcement.
Boiroux et al. [14] presented the identified physiological model for describing the
glucose-insulin dynamics for the nonlinear MPC (NMPC), where virtual patients
were generated using the Hovorka model, as well as its parameter distributions, to
test the identification procedure (Fig. 2). The results showed that the proposed
method has the potential to be used in NMPC algorithms.
Figure 2
The proposed MPV model [14]
On the other hand, Embaby et al. [15] proposed a novel adaptive NMPC (AMPC)
approach, consisting of a Cobelli model, a fuzzy logic controller (FLC), a
feedforward neural network (FFNN), and an adaptation method, for BG levels
regulation. The FLC was used to compute the amount of insulin infusion and
maintain BG levels in a normal range, while the genetic algorithm was used to
solve FLC optimization problems and improve search performance. The FFNN
was used as the NMPC to manage the insulin delay between the time of injection
and its interaction, while the adaptation method was used to adjust the
compensation of the proposed system for physiological differences between
patients. The results indicated that the time of increase in BG levels was in the
normal range, causing less hyperglycemia.
To update the real-time control penalty parameters for a zone MPC (ZMPC)
method, Shi et al. [16] applied a dynamic cost function. The proposed method
gave a good performance for announced moderate meal-bolus, unannounced
meals, and physical exercises, and improved BG levels, while the rate of insulin
delivery was within a safe range, without the risks of hypoglycemia.
Chakrabarty et al. [17] implemented an embedded ZMPC method, using the fast
adaptive memetic algorithm (FAMA) and the fast alternating direction method of
multipliers (FADMM) algorithm to solve convex constraints of the linear MPC
method. The generated closed-loop data were used to select the optimization

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algorithm and the appropriate setting parameters. The proposed method was able
to maintain BG regulation and it was compatible with other embedded systems.
Abuin et al. [18] improved the robustness of a time-varying pulsatile ZMPC
(pZMPC) with the linear time-invariant (LTI) method, by adding a circadian
insulin sensitivity (SI) scheme. The performance of the time-varying pZMPC was
compared with respect to the linear time-invariant pZMPC-LTI, with the models
configured with low and high SI. The pZMPC-h achieved better performance
during high SI intervals by improving the analyzed metrics, while during the
period of low SI it produced hyperglycemic events.
Hajizadeh et al. [19] integrated a multivariable AP (mAP) method with a
controller performance monitoring, assessment, and modification (CPMAM)
system to analyze closed-loop behavior, modify MPC parameters, and automate
insulin delivery systems during different meal amounts and exercise times (Fig. 3).
The CPMAM system was proposed for the adaptive learning MPC (AL-MPC) and
then applied in the mAP system for real-time estimation using various key
performance indexes (KPIs). The control of BG levels was improved without the
risk of hypoglycemia.
Figure 3
The proposed mAP method with integrated CPMAM system [19]

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Reenberg et al. [20] presented a linear MPC-based algorithm for critically ill
patients in an intensive care unit (ICU). The proposed algorithm is based on a
stochastic continuous-discrete state-space model and represents a model of multi-
input single-output (MISO) transfer function. To demonstrate the performance of
the closed-loop algorithm, the Bergman minimal model (BMM), the Hovorka ICU
Model, and the Chase ICU Model were used. Additional measurement delays,
which are associated with glucose-sensing or enteral nutrition, have made it
difficult to achieve strict glycemic control, which increases the risk of
hypoglycemia.
Sun et al. [21] proposed a novel event-triggered MPC (ET-MPC) algorithm for
personal insulin dosing to regulate BG levels and reduce computational
requirements during unannounced meals and physical activity, performed
according to pre-established criteria. The proposed method proved to be robust to
a CGM data deficiency and signal loss, providing personalized assessment, while
maintaining BG levels in a safe range without risk of hypoglycemia.
2.2 Bayesian Optimization Approach
A method based on the multivariate Bayesian optimization (BO) approach and the
dynamic parameter selection module for solving the parameter adaptation problem
was presented by Shi et al. [6]. The dynamic parameter selection module was used
to determine the parameters, while the BO-based optimization module was used to
automatically adjust the selected parameter and to optimize an unknown cost
function, as is shown in Fig. 4. The efficiency and robustness of the proposed
algorithm was verified in two scenarios. In the first case, the rate of insulin
delivery was improved, while BG levels were reduced to the euglycemic range. In
the second case, the algorithm was able to improve the duration of insulin
delivery. Therefore, the proposed method may properly adjust the parameters to
achieve their regulation, without the risk of hypoglycemia.
Figure 4
The proposed method based on the dynamic parameter selection module (blue) and the optimization
module (green) [6]

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2.3 Sliding Mode Control Approach
Beneyto et al. [22] applied an insulin-only controller using fast-acting
carbohydrates (CHO) for the recommender system to improve the regulation of
BG levels caused by unannounced physical activity. The proposed method
consists of a proportional–derivative (PD) controller with insulin feedback (IFB)
and a safety auxiliary feedback element (SAFE) layer, as shown in Fig. 5.
The SAFE layer consists of insulin on board (IOB) constraints, a sliding mode
reference conditioning (SMRC) block, and a low-pass first-order filter, while the
CHO controller is based on a predictive quantified PD controller. Comparison of
the original insulin-only controller and the combined insulin CHO recommender
system showed that the novel combined system may reduce daily episodes of
hypoglycemia and increase the rate of insulin delivery within acceptable limits.
Figure 5
The proposed insulin-only controller (blue) with the CHO controller (orange) [22]
Moscardö et al. [23] used the SMRC method to improve the coordinated
configuration (CC) control structure with IOB limitation for coordinated BG
control levels (Fig. 6). A comparison of CC and CC-SMRC control structures was
made based on meals, snacks, and exercise scenarios. Although the results of the
proposed method were better during the exercise periods, than during the meals, in
the most demanding exercise scenario, insulin delivery levels were not sufficient
to prevent hypoglycemia.

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Figure 6
The proposed method based on the CC-SMRC controller [23]
Leyva et al. [24] presented methods based on the positive sliding mode control
(SMC) and the control Lyapunov function (CLF), where the cascade structure of
the physiological model was used to improve the rate and stabilize BG levels,
while the compartmental mathematical model was used to reproduce glucose
metabolism, and insulin and glucagon dynamics. Although both methods managed
to solve the problem of stabilization, the CLF gave better results by improving the
convergence rate and generating a continuous signal that prevented the
accumulation of insulin.
A finite-time synergistic control approach based on a gain-scheduled Luenberger
observer (GSLO) was presented by Alam et al. [25] to establish a closed-loop
insulin delivery system (Fig. 7). A finite-time back-stepping SMC strategy was
used to regulate glycemia, while the CLF law was systematically achieved in a
recursive procedure. The intravenous glucose tolerance test (IVGTT) model
(BMM), was considered to design a nonlinear control algorithm. The robustness of
the system was achieved despite external disturbances, while postprandial
hyperglycemia and hypoglycemia were suspended.
Figure 7
The proposed closed-loop control system based on the GSLO [25]

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2.4 Proportional Integral Derivative Control Approach
Kushner et al. [26] presented a novel non-deterministic data-driven model with a
proportional integral derivative (PID) based closed-loop system to predict patient
reaction to the proposed system while maintaining BG levels control.
The proposed model was able to efficiently adjust key controller parameters and
improve BG levels control. To reduce insulin absorption delay, Barnes and Jones
[27] applied the continuous intraperitoneal insulin infusion (CIPII) method based
on the PID controller. The IMC-PID controller based on the internal model control
(IMC) tuning method was introduced, which employs an inverter to realize the
PID controller feedback. The time delay was adjusted using a first-order with time
delay (FOPTD) model, along with a Pade approximation. The proposed controller
was able to successfully control the oscillations of BG levels.
A novel PID control-based method, consisting of an adaptive weighted PID
(AWPID) controller and a look-ahead PID with retrospective estimation error
correction (LAPID-REC), was presented by Alshalalfah et al. [28] to prevent large
delays incurred in insulin action and glucose sensitivity. In the AWPID approach,
the proportional gain of the PID controller was rated based on the short-term CGM
history, while in the LAPID-REC approach prospective estimates of future
measurements were used to calculate the control action with retrospective
estimation error correction. The safety and performance of standard PID control
were improved, while the LAPID-REC approach showed high performance over
existing techniques, especially under sensor noise, counteracting the long delays
that occur in CGM and insulin action.
2.5 Linear Parameter Systems Approach
Eigner et al. [29] presented an advanced controller design method for a
physiological model, using a theorem based on the linear parameter varying (LPV)
and linear matrix inequality (LMI), which was applied on a modified version of
the minimal model. The resulting controller used a state feedback type control rule
due to the applicable LPV-LMI conditions.
Conversely, Colmegna et al. [30] extended the IOB safety loop method with an
inner switched LPV (SLPV) controller and an outer sliding-mode safety layer
(SAFE), to limit the controller’s action, during multiple meals and exercises.
A mode selection algorithm was added to combine the hyperglycemia detection
module with heart rate (HR) data for automatically adjusted controller settings
(Fig. 8). The proposed method was able to effectively reduce the risk of
hypoglycemia during the moderate exercise scenario.

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Figure 8
The extended method based on the SLPV and SAFE [30]
2.6 Iterative Learning Control Approach
Modifications of the Dalla Man metabolic model were proposed by Cescon et al.
[31] by adding a long-acting insulin absorption model to facilitate validation of the
control strategy for the multiple daily injections (MDI) therapy. A once-a-day
iterative learning control (ILC) based dosing method was proposed to provide
basal insulin delivery. Fig. 9 presents the proposed model of subcutaneous insulin
absorption, with the amount of injected rapid-acting and long-acting. In the case of
fasting, meal and meal with induced insulin resistance, the ILC performed better
than the open-loop dose, by providing an appropriate amount of basal insulin.
Figure 9
The proposed model of subcutaneous insulin absorption [31]
Cescon et al. [32] also proposed the ILC algorithm for the delivery of long-acting
(basal) and rapid-acting (bolus) insulin, for patients following the MDI therapy
(Fig. 10). The ILC updates basal therapy consisting of one long-acting insulin
injection per day, while by updating the mealtime-specific insulin-to-carbohydrate
ratio, the run-to-run (R2R) controller adjust meal bolus therapy. The results
showed that the proposed method can provide robustness against random
variations, resistance to protocol deviations while improving glycemic regulation
over time.

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Figure 10
The proposed compartment model of insulin subsystem [32]
2.7 Robust Fixed Point Transformations Approach
To create a robust and adaptive control approach for BG levels control, Kovács et
al. [33] presented a novel robust fixed point transformation (RFPT) based
controller approach which consists of the two delay blocks corresponding to the
cycle time of the digital controller (Fig. 11). Although the proposed method
constantly absorbed external glucose concentration, it was able to interfere with
the negative effect of inherent model uncertainties and measurement disturbances,
while reducing the risk of hyperglycemia and hypoglycemia.
Figure 11
Scheme of the proposed RFPT method [33]

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2.8 Active Disturbance Rejection Control Approach
Cai et al. [34] proposed an active disturbance rejection control (ADRC) method by
adding IOB and insulin delivery constraints to ensure the safety of the control
algorithm. The controller consists of the ADRC module (composed of tracking
differentiator, extended state observer (ESO) and nonlinear feedback) and the
constraints module (composed of the IOB, non-negative and maximum input
constraints). The proposed method was able to achieve satisfactory performance of
BG regulation and insulin delivery rate without the risk of hypoglycemia.
2.9 Disturbance Observer Approach
Sanz et al. [35] used disturbance observer (DOB) to estimate the effect of
unannounced meals, and feedforward compensator for the insulin
pharmacokinetics, to control postprandial BG levels of patients. The results
showed that the DOB may successfully estimate and counteract the effect of meals
and the sudden drops in BG levels while avoiding hypoglycemia.
For unannounced meals with high CHO content, a median time-in-range was 80%
with large intra-subject variability, while for announced meals the median time-in-
range was increased up to 88%, even considering severe bolus mismatch and CHO
counting errors.
2.10 Terminal Synergetic and Feedback Linearization
Controller Approaches
Babar et al. [36] extended BMM (EBMM) with the nonlinear terminal synergetic
controller (TSC) and the state feedback linearization based controller (SFC), while
the Lyapunov theory was used to provide asymptotic stability of the proposed
controllers. White noise was added to the EBMM, and then the performance of
each controller was evaluated to check their ability to withstand disturbance.
Compared to other controllers, the TSC gave the best results with about zero
steady-state error, lesser settling, convergence time, with acceptable overdrafts.
2.11 Bioinspired AP Approach
A bi-hormonal bioinspired AP (BiAP) controller was extended with a novel hybrid
hormonal-insulin sensitivity glucose (InSiG) by Güemes et al. [37], to determine
insulin and glucagon doses with the coordinated bi-hormonal BiAP controller, and
to determine the desired SI from CGM with a standard PD (sPD) controller. After
comparing the InSiG controller and the coordinated bi-hormonal BiAP controller,
the results showed that the InSiG controller was able to improve BG levels control
while maintaining within the target range without the risk of hypoglycemia.

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Although, the proposed controller was able to reduce the delivered dose of insulin
and significantly reduce the glucagon dose, the relationship between the
magnitude of nervous system stimulation and the SI dynamics remained unknown.
3 Approaches Based on Sensitivity Analysis
Staal et al. [38] investigated methods to improve recognition and estimation of the
most appropriate model parameters to reduce the parameters of critical models.
The identification of nonlinear state-space model parameters was also
investigated. The nonlinear observability rank condition (NORC) was used for
structural, while sensitivity analysis and the Fisher information matrix (FIM) were
used for practical identifications. A simplified model, derived from CGM, scarce
self-monitoring of BG (SMBG), meal and insulin data, showed to be useful for the
AP applications.
4 Approaches Based on Filters
In this Section, we review recently proposed methods based on extended Kalman
and kernel filtering algorithms for detecting unannounced meals or missed meal
announcements, real-time insulin pump faults detection, insulin infusion rate
regulation, and BG levels control.
4.1 Extended Kernel Filter
To improve computational efficiency in online glucose prediction, Yu et al. [39]
extended an adaptive kernel filter (KRLS) algorithm with the sparsification
criteria. The KRLS algorithm was combined with the approximate linear
dependency (ALD) and the surprise criterion (SC) to design an online sparse
ALD-KRLS and SC-KRLS algorithms. The proposed online adaptive method
proved to be insensitive to abnormal or inaccurate CGM measurements and it was
adaptable to prediction models. Thus, it could effectively reduce the
computational load and regulate the time delay in the nonlinear dynamics of
glucose.
4.2 Extended Kalman Filter
Fushimi et al. [40] proposed the integration of the automatic switching signal
generator (SSG) into the automatic regulation of glucose (ARG) algorithm and an
advanced version of the switched linear quadratic Gaussian (SLQG) controller, to
regulate the basal insulin infusion rate. The SSG module, based on the KF, was

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used to generate a filtered version of BG levels. Despite the large delay in
selecting the post-meal controller mode, the proposed algorithm had efficiency of
83.3% in terms of meal detection, it was able to regulate the basal insulin infusion
rate and generate insulin feedback during unannounced meals, without
significantly increasing the risk of hypoglycemia or hyperglycemia.
A novel kernel function for the Gaussian process was proposed by Ortmann et al.
[2] by improving the existing MPC controller and solving the problem of noise in
measurements during unannounced meals. The unscented KF was used to assess
the condition, extract data, and change SI. The extracted data were processed using
a Gaussian filter to predict future effects, while the MPC optimized the received
data to calculate the volume of insulin injections, as shown in Fig. 12.
The collected training data became insensitive to noise after the application of the
Gaussian process, making the controller insensitive to unannounced meals.
Figure 12
The proposed method based on the unscented KF, Gaussian process, and MPC [2]
To present a novel adaptive model-based algorithm for detecting unannounced
meals, Fathi et al. [41] used a linear KF to compute the evaluation of BG
measurements, applying the statistical generalized likelihood ratio test under the
null hypothesis, to estimate the impact of an unannounced meal on BG levels.
The proposed algorithm managed to successfully detect unannounced moderate
meals 96.29% of the time, without false positives.
Boiroux et al. [42] presented a model for nonlinear estimation of the maximum
probability of estimated parameters, where the state covariance matrix and its
gradient were calculated using explicit Runge-Kutta schemes, while the method
implementation was verified by using a numerical example for nonlinear
parameter estimation.
On the other hand, Kovács et al. [43] applied advanced LPV, linear matrix
inequality (LMI), tensor product (TP) model transformation, and extended KF
(EKF) control methods, to guarantee strong safety control of BG levels.
An extension of the minimal model was applied to simulate the glucose-insulin
dynamics and glucose and insulin absorption. The control structure of the TP
model was combined with LMI based optimization and LPV control (TP-LMI-
LPV controller), EKF, and D/A converter (Fig. 13). The proposed controller was
able to intervene effectively during the process and provide appropriate control
actions, thus satisfy predefined requirements while avoiding hypoglycemia.

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Figure 13
Scheme of the proposed method with the TP-LMI-LPV controller and mixed EKF [43]
Kovács et al. [44] also introduced the dual EKF (DEKF) framework to estimate
the state variables and model parameters at the same time by utilizing the discrete
LPV methodology. A nonlinear model was applied to the quasi-LPV (qLPV)
model (derived from the nonlinear Cambridge T1DM model) to map the noise
effects that occurred during the application of the CGM system. The results
showed that the proposed method was able to estimate state variables with good
accuracy.
Meneghetti et al. [45] proposed a method for real-time insulin pump fault
detection and missed meal announcements to improve the safety of the AP system
architecture. The proposed method consists of an offline model and a predictor
module, and an online prediction and alert module, as shown in Fig. 14.
The confounding factor introduced by meals was tested to detect insulin pump
faults ability. The proposed method was able to improve patient feedback,
providing various alarms and effectively preventing pump malfunctioning due to
user errors, without causing hyperglycemic events.
Figure 14
The proposed fault detection method [45]
Sala-Mira et al. [46] compared the LPV dual KF, the LPV joint KF, and the
nonlinear sliding mode observer (NSMO), to evaluate the effect of observer
structure on estimation performance. Observers were composed of the Hovorka
and Identifiable Virtual Patient (IVP) models, which represents a compromise
between the Bergman and Hovorka model in terms of structural complexity and

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accuracy. Analysis of variance (ANOVA) and multiple comparisons were used to
assess the individual factors. Based on PIC and rate of appearance, the results
showed that proportions of variance were low for each factor, indicating a small
difference between observer structures.
5 Machine Learning Algorithms
In this Section, we review recently proposed Machine Learning methods [47] for
automatic insulin infusion, insulin pump failure detection, physical activity
prediction, overnight glycemic control quality prediction, online prediction of BG
levels and its stability, gradient problems, but also to improve prediction accuracy
and robustness of previous methods. The proposed methods are based on
unsupervised and supervised learning, clustering, artificial neural networks, and
bioinspired reinforcement learning.
5.1 Algorithms Based on Unsupervised Learning
An unsupervised model-free approach based on data-driven techniques for
anomaly detection was presented by Meneghetti et al. [48] to detect insulin pump
malfunction. Machine learning (ML) methods for detecting anomalies, using local
outlier factor (LOF), connectivity-based outlier factor (COF), and isolation forest
(iF/iForest), were applied to the extracted set of features. To overcome
correlations between time-closed samples, the for time series data (4TSD)
procedure was applied to LOF and COF. The optimal parameter configuration for
LOF and iForest was able to provide satisfactory detection performance while
maintaining high accuracy. After comparison with the traditional multivariate
control chart (MCC) method, the results showed that COF outperformed other
methods, while LOF and iForest offered comparable performance. Despite the
good performance, iForest has been shown to be prone to errors and instabilities.
5.2 Algorithms Based on Supervised Learning
Güemes et al. [49] proposed a novel data-driven method for predicting the
overnight quality of glycemic control, by analyzing a small data set from CGM
measurements, meal intake, and insulin bolus. To classify the overnight quality of
glycemic control, binary classification algorithms such as random forest classifier
(RFC), artificial neural networks (ANN), support vector machine (SVM), linear
logistic regression (LLR), and extended tree classifier (ETC) were used.
The proposed method was able to predict overnight BG levels within the target
range with reasonable accuracy of 0.7. However, a larger data set is needed to
fully validate the proposed method.

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The solution based on supervised ML, to predict future BG levels, was proposed
by Eigner et al. [50]. To prove the concept, TensorFlow and Keras frameworks
were used with the AIDA diabetes simulator for data generation. The results
showed that the proposed method gives an accurate prediction of BG levels within
acceptable limits, with overall accuracy of 0.879, taking into account that the
accuracy of predicting normal BG levels should be improved.
Dénes-Fazakas et al. [51] applied synthetic data generated by an extended open-
source version of the Jacobs T1DM simulator, which employs the Cambridge
model and contains an embedded physical activity sub-model. To predict the
presence of physical activity, a logistic regression, AdaBoost classifier, decision
tree classifier, Gaussian naive Bayes, the k-nearest neighbor classifier (k-NN),
SVM, RFC, and multilayer perceptron networks (MLP) were used, and then
trained classifiers were applied to all feature vectors of the test data set. Decision
tree, k-NN, and RFC gave the best results, with overall accuracy of 0.91, 0.95 and
0.98. Other models may be also suitable, but they need additional mechanisms to
avoid false positives.
5.3 Algorithms Based on Clustering
Montaser et al. [52] proposed a seasonal autoregressive integrated moving average
(SARIMAX) model, an extended version of the non-seasonal ARIMAX model,
and examined the possibility of preprocessing original CGM measurements to
obtain sets of similar glycemic profiles (clusters) to identify a seasonal model of
postprandial periods. Using the fuzzy c-means (FCM) clustering method, the
number of sets and corresponding features of the BG profile was obtained in the
modeling step, while the Box-Jenkins methodology was used to identify the
seasonal model for each cluster set. The results showed that using online BG
predictions through a global seasonal model may reduce the risk of hypoglycemia
or hyperglycemia.
A data-driven approach for determining the final set of daily CGM profiles
(motifs) was presented by Lobo et al. [53] so that almost every generated daily
profile could be matched with one of the motifs from the final set. A training data
set was used to identify candidate motif sets, while a validation data set was used
to select the final set. The results showed that robustness was successfully
established while matching with representative daily CGM profiles in the test data
set was 99.0%.
5.4 Algorithms Based on Artificial Neural Networks
Aliberti et al. [54] applied a nonlinear autoregressive (NAR) neural network and
long short-term memory (LSTM) on BG signals, to improve prediction accuracy
and robustness of previous methods (Fig. 15). NAR was used to solve BG stability
problems, while LSTM was used to explode and disappear the gradient, as well as
to maintain long-term information over time.

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.
Figure 15
The proposed solution with applied NAR and LSTM methods [54]
Compared to the recurrent neural networks (RNNs), the LSTM was more resistant
to the exploding and vanishing gradient problems. The NAR model gave good
prediction accuracy only for a short-term period (30-minute prediction horizon),
while the LSTM exhibited very good performance for predicting both short-term
and long-term BG levels (60 minute prediction horizon).
Li et al. [55] proposed a convolutional RNN (CRNN) method that consists of a
multilayer convolutional neural network (CNN), a RNN layer with LSTM cells,
and fully connected layers, to predict BG levels. The CNN was used to extract
features or patterns of the multidimensional time series, while a modified RNN
was used to analyze the previous sequential data and predict BG levels.
The results showed that the proposed method was able to predict BG levels with
high accuracy.
To predict BG levels, Zhu et al. [56] proposed a novel deep learning framework
with the edge inference on a microcontroller unit (MCU) embedded in a low-
power system, by using CGM measurements and the RNN that builds on LSTM
(Fig. 16). Collected data from wearable devices were uploaded to the server. Then,
a well-trained deep neural network (DNN) was embedded in the MCU and further
implemented in wearable devices to help in decision making. The proposed
framework was agnostic to the types of neural networks employed and learning
targets, and it showed a good BG prediction performance. Therefore, it could be
applied for the realization of various tasks on wearable devices, such as event
detection (e.g. meals, exercise, illness, errors) and glucose regulation.
A novel deep reinforcement learning (RL) model for optimizing single-hormone
(insulin) and dual-hormone (insulin and glucagon) delivery was presented by Zhu
et al. [57].

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Figure 16
The system architecture of the proposed DNN-based method [56]
Dilated RNNs were applied to the structure of double deep Q-network (DQNs), to
develop personalized models through a two-step framework that involves transfer
learning (Fig. 17). Proposed methods gave good control of BG levels with a
significant reduction in hypoglycemia making the use of deep RL a sustainable
approach to closed-loop BG control, with the best TIR score of 93%.
Figure 17
Scheme of the proposed double DQN method [57]

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5.5 Bioinspired Reinforcement Learning
A novel AI-based bioinspired RL approach for automated insulin infusion was
proposed by Lee et al. [58], to maintain BG levels and robustness of the CGM
sensor. The layer-wise relevance propagation (LRP) method was used to analyze
input-output relevance and define the rate of insulin infusion. The proposed LRP
method was able to provide information about insulin distribution, making the
decision step by step, without distinguishing between basal and bolus insulin,
which is similar to the principle of human β-cells. A trained policy could
automatically maintain fasting BG levels after unannounced meal intake without a
prediction model, automatically respond and regulate postprandial glucose,
provide robustness with respect to CGM sensor noise, achieve a mean BG level in
the normal range of 89.56%, and without the risks of hypoglycemia.
Conclusions
In this work, we reviewed various recently proposed methods, based on predictive
control, sensitivity analysis, filters and machine learning algorithms, intended for
regulating insulin delivery and controlling BG levels in patients with T1D.
The control approaches included control methods based on model predictive
control, Bayesian optimization, sliding mode control, proportional integral
derivative control, linear parameter varying, iterative learning control, active
disturbance rejection control, robust fixed point transformation, disturbance
observer, terminal synergetic controller, state feedback linearization based
controller and bi-hormonal bioinspired AP. Combining common control methods
has shown good results in controlling BG levels while maintaining a safe range.
The proposed methods based on the Kalman filter, combined with different
control methods, gave good results in state variables and model parameters
estimation.
Other successful approaches included methods that are based on machine learning
techniques, such as, unsupervised and supervised learning, clustering, artificial
neural networks and bioinspired reinforcement learning. The Long Short-term
Memory has shown very good performance for predicting short-term and long-
term BG levels, while combining with recurrent neural networks could predict BG
levels with high accuracy. Novel, deep reinforcement machine learning
algorithms, promise improved performance for larger experimental datasets, with
the support of powerful hardware platforms. Clustering methods gave good results
in predictive modeling, decision support, and automated systems, while
bioinspired reinforcement learning was able to provide insulin distribution
information, automated postprandial regulation, sensor robustness, and fully
automate BG levels control for unannounced meals. For the case of insulin
infusion, bioinspired reinforcement learning made the decisions step by step,
without distinguishing between basal and bolus insulin, similar to the principle of
the human β-cells.

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Acknowledgment
This project has received funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 Research and Innovation Program
(grant agreement No. 679681). Project No. 2019-1.3.1-KK-2019-00007 has been
implemented with the support provided from the National Research, Development,
and Innovation Fund of Hungary, financed under the 2019-1.3.1-KK funding
scheme.
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