research article an improved pid algorithm based on...

Research ArticleAn Improved PID Algorithm Based on Insulin-on-BoardEstimate for Blood Glucose Control with Type 1 Diabetes

Ruiqiang Hu and Chengwei Li

School of Electrical Engineering and Automation, Harbin Institute of Technology, Harbin 150001, China

Correspondence should be addressed to Ruiqiang Hu; [email protected]

Received 16 April 2015; Revised 27 May 2015; Accepted 2 June 2015

Academic Editor: Tao Huang

Copyright © 2015 R. Hu and C. Li. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Automated closed-loop insulin infusion therapy has been studied for many years. In closed-loop system, the control algorithmis the key technique of precise insulin infusion. The control algorithm needs to be designed and validated. In this paper, animproved PID algorithmbased on insulin-on-board estimate is proposed and computer simulations are done using a combinationalmathematical model of the dynamics of blood glucose-insulin regulation in the blood system. The simulation results demonstratethat the improved PID algorithm can perform well in different carbohydrate ingestion and different insulin sensitivity situations.Compared with the traditional PID algorithm, the control performance is improved obviously and hypoglycemia can be avoided.To verify the effectiveness of the proposed control algorithm, in silico testing is done using the UVa/Padova virtual patient software.

1. Introduction

Diabetes, a disorder of endocrinemetabolism, is an incurabledisease. Diabetes affects millions of people in the world,and it is a disease with considerable complications includ-ing retinopathy, nephropathy, peripheral neuropathy, andblindness [1]. According to a prediction produced by theInternational Diabetes Federation in 2014, approximately 387million people suffered from diabetes worldwide by 2014 andabout 592million patients by 2035 [2].Thus, themaintenanceof blood glucose concentration in a normal range is of criticalimportance for diabetic.

Type 1 diabetes is mainly due to the reason that the 𝛽-cell of pancreas cannot secrete insulin. They must rely onexogenous insulin to regulate blood glucose concentration.Currently, patients with type 1 diabetes are treated with eithermultiple daily injections (MDI) or continuous subcutaneousinsulin infusion (CSII) delivering via an insulin pump [3].The CSII has shown more advantages than MDI methodbecause of the increasing flexibility of diet, exercise, conve-nience, and precision [4]. Various open-loop insulin pumpsthat are available in the market are programmable to deliverthe required amount of insulin. However, a fully automated

closed-loop insulin infusion system that can deliver appropri-ate amounts of insulin to patients without any manual inter-ference is developing [5]. The closed-loop system containsthree main components, which are (1) continuous glucosemonitoring (CGM), (2) intelligent controller, and (3) insulinpump.

For open-loop insulin pump, a bolus calculator is used tocalculate bolus insulin doses that can help diabetic regulatethe postprandial blood glucose concentration. The boluscalculator takes into account many factors, such as currentblood glucose, target blood glucose, amount of carbohy-drate ingested, insulin sensitivity, correction factor (CF),and insulin : carbohydrate ratio (I : C) as well as duration ofinsulin action (“insulin on board (IOB)”) [4].

For closed-loop insulin pump, the real-time CGM systemis already commercially available and the control algorithmis the key technique of precise insulin infusion. The controlalgorithm requires high robustness and reliability. There arevarious control algorithms including PID control [6], modelpredictive control (MPC) [7, 8], optimal control [9], adaptivecontrol [10], and sliding mode control [11]. Among thosecontrol algorithms, the PID controller is widely used inindustrial control systems. The PID controller is attractive

Hindawi Publishing CorporationComputational and Mathematical Methods in MedicineVolume 2015, Article ID 281589, 8 pageshttp://dx.doi.org/10.1155/2015/281589

2 Computational and Mathematical Methods in Medicine

for blood glucose control based on the features of simplestructure with few parameters, easy implementation, goodadaptation, and robustness.

Many closed-loop control algorithms had not consideredthe IOB factor. A limitation of IOB can optimize the outputof control algorithm and decrease the risk of hypoglycemia.As the open-loop insulin pump, the previous insulin admin-istration may lead to hypoglycemia. So the IOB estimate isconsidered to limit the insulin infusion dose. In this paper,the improved PID control algorithm based on IOB estimateis introduced. Controller performance is evaluated in asimulation study under a physiologicalmodel and consideredthe carbohydrate ingestion and insulin sensitivity changed.Also, theUVa/Padova virtual patient software is used to verifythe effectiveness of PID controller with IOB estimate.

The paper is organized as follows. In Section 2, a combi-national complicated and detailed model of glucose-insulinkinetic is introduced, which is based on theHovorka et al. andDallaMan et al. model.The PID controller with IOB estimateis designed, and the performance is evaluated by simulationin Section 3. The in silico testing using ten virtual patientsis discussed in Section 4. The final conclusion is located inSection 5.

2. Glucose-Insulin Mathematical Model

Mathematical models of glucose-insulin interactions havebeen studied for over the past 50 years. Simple linear modelswere proposed by Ackerman et al. [12]. More complicatednonlinear models were proposed in later studies. In many ofthese models, compartmental modeling approach has beenused. In this approach, the body is divided into compartmentsrepresenting different organs or parts of the body andmass balance equations are derived for each compartment.The compartmental minimal model of Bergman et al. [13]has been widely used in many studies. More complicatedcompartmental models proposed by Cobelli and Mari [14],Hovorka et al. [15], and Dalla Man et al. [16] have consideredmore compartments for better understanding the behaviorof different parts of the body. These models for glucose-insulin interactions have been widely used in studying thephysiological behavior of diabetic patients.

In this paper, the glucose and insulin metabolic modelrefers to the model developed by Hovorka et al. [15] andDalla Man et al. [16, 17]. The Hovorka model is a nonlinearcompartmental model with three subsystems for glucose,insulin, and insulin action. The carbohydrate digestion andabsorption model refers to Dalla Man’s model in this paper.The combinational model is close to a realistic patient model.

2.1. Glucose Subsystem. The glucose subsystem is dividedinto two compartments: masses of glucose in the accessiblecompartment and masses of glucose in the nonaccessiblecompartment. The core model is a two-compartment repre-sentation of glucose kinetics. Consider

𝑄1 (𝑡) = − [𝐹𝑐01

𝑉𝐺𝐺 (𝑡)

+ 𝑥1 (𝑡)]𝑄1 (𝑡) + 𝑘12𝑄2 (𝑡) − 𝐹𝑅

+𝑈𝐺(𝑡) +EGP0 [1−𝑥3 (𝑡)] ,

𝑄2 (𝑡) = 𝑥1 (𝑡) 𝑄1 (𝑡) − [𝑘12 +𝑥2 (𝑡)] 𝑄2 (𝑡) ,

𝐺 (𝑡) =𝑄1 (𝑡)

𝑉𝐺

,

𝐹𝑐01 ={{{{{

𝐹𝑐01 if 𝐺 ≥ 81mg/dL,𝐹01𝐺

4.5otherwise,

𝐹𝑅={{{

0.003 (𝐺 − 9) 𝑉𝐺

if 𝐺 ≥ 162mg/dL,

0 otherwise,

(1)

where 𝑄1 and 𝑄2 are the masses of glucose in the accessibleand nonaccessible compartments, respectively. 𝑘12 is thetransfer rate constant from the nonaccessible to the accessiblecompartment. 𝑉

𝐺is the distribution volume of the accessible

compartment. 𝐺 is the glucose concentration. EGP0 is theendogenous glucose production extrapolated to the zeroinsulin concentration. 𝐹𝑐01 is the total insulin-independentglucose flux, corrected for the ambient glucose concentration.𝐹𝑅is the renal glucose clearance above the glucose threshold

of 162mg/dL. The gut absorption rate 𝑈𝐺is introduced in

Section 2.4 of carbohydrate digestion and absorption model.

2.2. Insulin Subsystem. The insulin subsystem describes theinsulin absorption and insulin action on glucose kinetics.Theplasma insulin concentration 𝐼(𝑡) is described by

𝐼 (𝑡) =𝑈 (𝑡)

𝑉𝐼

− 𝑘𝑒𝐼 (𝑡) , (2)

where 𝑘𝑒is the fractional elimination rate and 𝑉

𝐼is the

distribution volume.

2.3. Insulin Action Subsystem. The three insulin actions onglucose kinetics are represented by

𝑥1 = − 𝑘𝑎1𝑥1 (𝑡) + 𝑘𝑏1𝐼 (𝑡) ,

𝑥2 = − 𝑘𝑎2𝑥2 (𝑡) + 𝑘𝑏2𝐼 (𝑡) ,

𝑥3 = − 𝑘𝑎3𝑥3 (𝑡) + 𝑘𝑏3𝐼 (𝑡) ,

(3)

where 𝑥1, 𝑥2, and 𝑥3 are the effects of insulin on glucosedistribution/transport, glucose disposal, and endogenousglucose production, respectively; 𝑘

𝑎1, 𝑘𝑎2, and 𝑘𝑎3 are thedeactivation rate constants; 𝑘

𝑏1, 𝑘𝑏2, and 𝑘𝑏3 are the activationrate constants.

The insulin sensitivities of glucose distribution/transportand glucose intracellular disposal are represented individu-ally as follows:

𝑆𝑓

IT =𝑘𝑏1𝑘𝑎1,

𝑆𝑓

ID =𝑘𝑏2𝑘𝑎2,

𝑆𝑓

IE =𝑘𝑏3𝑘𝑎3.

(4)

Computational and Mathematical Methods in Medicine 3

Table 1: IOBmodel parameter 𝑘DIA for different durations of insulinaction.

DIA (h) 2 3 4 5 6 7 8𝑘DIA × 10−3 39 26 19.5 16.3 13 11.3 9.9

2.4. Carbohydrate Digestion and Absorption. The carbohy-drate digestion and absorption model consists of three-compartment nonlinear model, two for the glucose in thestomach solid 𝑄sto1 and liquid 𝑄sto2 and one for the glucosein the intestinal tract 𝑄gut. Consider

𝑄sto1 (𝑡) = − 𝑘gri ∗ 𝑄sto1 (𝑡) +𝐷 ∗ 𝛿 (𝑡) ,

𝑄sto2 (𝑡) = − 𝑘empt ∗ 𝑄sto2 (𝑡) + 𝑘gri ∗ 𝑄sto1 (𝑡) ,

𝑄gut (𝑡) = − 𝑘abs ∗ 𝑄gut (𝑡) + 𝑘empt ∗ 𝑄sto2 (𝑡) ,

𝑄sto (𝑡) = 𝑄sto1 (𝑡) +𝑄sto2 (𝑡) ,

(5)

where 𝐷 is the amount of carbohydrate to be ingested, 𝛿(𝑡)is the impulse function, 𝑘gri is the rate of grinding coefficientin the stomach, 𝑘empt is the rate of fractional coefficient withwhich the chyme enters the intestine, and 𝑘abs is the rateconstant of intestinal absorption.

3. PID Controller with IOB Estimate

3.1. Insulin-on-Board Estimate. The insulin on board isdefined as the amount of administered insulin that is stillactive in the body. Some insulin pump estimates the IOBto correct the boluses in order to avoid hyper- or hypo-glycemia [4]. The IOB estimate is based on the insulin actioncurves. Here the IOB estimation is represented by a two-compartment dynamical model:

𝐶1 (𝑡) = 𝑢 (𝑡) − 𝑘DIA𝐶1 (𝑡) ,

𝐶2 (𝑡) = 𝑘DIA (𝐶1 (𝑡) −𝐶2 (𝑡)) ,

IOB (𝑡) = 𝐶1 (𝑡) +𝐶2 (𝑡) ,

(6)

where 𝐶1 and 𝐶2 are the two compartments and 𝑢(𝑡) is theinsulin dose. The constant 𝑘DIA is tuned for each patient somodel replicates the corresponding DIA. Figure 1 shows theinsulin activity curves obtained with model for typical DIAvalue, while Table 1 shows the corresponding values 𝑘DIA fortypical DIA values [18]. The insulin action is different amongeach individual; there are many factors, such as exercise,stress, illness, and heat.The different insulin action curves areprovided by insulin pump to calculate insulin bolus.

The insulin duration ranges from 2 h to 8 h; diabetespatient should choose a reasonable duration time. If patientsets the duration of insulin action time less than the actualtime, it will increase the risk of hypoglycemia. The insulinpump indicates that there has been no longer active IOB andwill infuse more insulin dose to consume blood glucose. Onthe other hand, if patient sets the duration of insulin actiontime longer than the actual time, it will increase the risk ofhyperglycemia. The patient will take a smaller insulin dose

0 1 2 3 4 5 6 7 80

10

20

30

40

50

60

70

80

90

100

Time (h)

Insu

lin o

n bo

ard

(%)

2h3h4h5h

6h7h8h

Figure 1: Estimated time profiles of insulin activity parameterizedby DIA.

than is necessary to regulate the blood glucose back to the setvalue.

3.2. Design of PID Controller with IOB Estimate. The struc-ture of the PID controller with IOB estimate is demonstratedin Figure 2, where 𝐺

𝑜is the real blood glucose concentration

of diabetes patient, 𝐺𝑚

is the measured blood glucose byglucose sensor, 𝐺

𝑡is the target blood glucose concentration,

and 𝑈𝐼is the final insulin infusion rate.

The 𝑈PID control law is as follows:

𝑈PID = 𝑈0 + 𝑘𝑐 [(𝐺𝑚 −𝐺𝑡) +1𝜏𝐼

∫𝑡

0(𝐺𝑚−𝐺𝑡) 𝑑𝑡

+ 𝜏𝐷

𝑑 (𝐺𝑚− 𝐺𝑡)

𝑑𝑡] ,

(7)

where 𝑈PID is the closed-loop control output. 𝐺𝑚− 𝐺𝑡is the

error of the target blood glucose and the measured bloodglucose. 𝑈0 is the basal insulin infusion rate. There are threeadjustable parameters: proportional gain (𝑘

𝑐), integral time

(𝜏𝐼), and derivative (𝜏

𝐷).

The control output of insulin infusion rate 𝑈𝐼is based on

the IOB estimate and the constraint output of insulin infu-sion. Figure 3 shows the inner structure of control algorithm.The output of controller is

𝑈𝐼= 𝑘𝑈PID, (8)

where the gain 𝑘 is obtained as the average value of 𝜔 and thevalue is set as 0 ≤ 𝑘 ≤ 1.


PatientPumpPIDcontroller

Blood glucose sensor

IOB estimate

Constraint ofinsulin infusion

Meal

−UIUPID

Gm

GoGt

Figure 2: Structure of the improved PID controller with IOB estimate.

IOB model

Constraint ofinsulin infusion

IOBotherwise

UIUPID

IOB

𝜔 = {10

ekUPID

if e ≥ 0

Figure 3: Structure of the IOB estimate.

The IOB estimate is based on the error of the IOB(𝑡)(6) and IOB limit. In [19], the author proposed a method tocalculate the IOB limit. The IOB value is obtained at time:(CHO+80 g)/(60 g/h), where CHO is the amount of carbohy-drate intake. Although eachmeal is different for a patient, thecorresponding limits are practically equal. For different dura-tion of insulin action, the value of IOB is different.The error is

𝑒 = IOB− IOB. (9)

Based on (6) and (9), the time evolution of 𝑒 is governedby

𝑑𝑒

𝑑𝑡= 𝑘DIA𝐶2 −𝜔𝑈𝐼, (10)

that is,

𝑑𝑒

𝑑𝑡= 𝑘DIA𝐶2 −𝑈𝐼 if 𝑒 ≥ 0,

𝑑𝑒

𝑑𝑡= 𝑘DIA𝐶2 if 𝑒 < 0,

(11)

from (11), after infusing the insulin, the IOB increases quicklysurpassing the IOB; hence 𝑒 < 0. The switching 𝜔 turns to 0.When IOB falls under the IOB, 𝑒 becomes a positive value and𝜔 switches to 1. Under the controlmode,𝜔 switches between 0and 1.We calculate the𝜔 value during each 10min period, andthe gain 𝑘 is the average value of 𝜔. So the proposed control

algorithm can decrease the insulin infusion rate and avoid thehypoglycemia event.

In this paper, the upper constraint output of PID con-troller is considered.Theupper constraint is based on the IOBestimate, correction factor, and I : C ratio. The significanceof upper constraint is to avoid overinfusion of insulin. It iscalculated by the following condition:

If 𝐼CHO + 𝐼𝐺 > IOB,

𝑈max = 𝐼CHO + 𝐼𝐺 − IOB,

Else 𝑈max = 𝐼CHO,

(12)

where 𝑈max is the maximum constraint output of insulininfusion rate and 𝐼CHO is the amount of insulin needed tocompensate for a given meal and is calculated by

𝐼CHO = 𝐷 ⋅ (I : C) , (13)

where 𝐷 is the mass of a given meal and I : C ratio is that 1unit of insulin can consume the amount of CHO. 𝐼

𝐺is the

amount of insulin needed to correct for a positive deviationfrom the target glucose concentration and is calculated by thefollowing condition:

If 𝐺𝑚−𝐺𝑡> 0,

𝐼𝐺= (𝐺𝑚−𝐺𝑡) ⋅CF,

Else 𝐼𝐺= 0,

(14)


0 200 400 600 800 1000 1200 1400 16000

50

100

150

200

250

Glu

cose

(mg/

dL)

Time (min)

Without IOB limitationWith IOB limitation

(a)

0 200 400 600 800 1000 1200 1400 16000

5

10

15

20

25

Time (min)

IOB

(IU

)

Without IOB limitationWith IOB limitation

(b)

Figure 4: (a) Glucose responses profiles with IOB limitation {DIA(h) = 2 h, IOB = 13} and without IOB limitation; (b) IOB dose responsesprofiles with and without IOB limitation.

Table 2: Simulation conditions of glucose-insulin mathematicalmodel.

Weight 75 kgDIA (h) 2 h∼8 hIOB 13∼36Meal time 0min 500min 1000minCHO 40 g 60 g 50 gI : C 1U : 20 gCF 1U : 80mg/dL

where 𝐺𝑚and 𝐺

𝑡are the current measured and target blood

glucose concentrations, respectively. CF is the correctionfactor.

3.3. Simulation Results. The proposed control algorithm isevaluated under the glucose-insulin mathematical modelmentioned in Section 2. Table 2 shows the simulation condi-tions.

Figure 4(a) shows the glucose responses using the pro-posed PID controller with and without IOB limitation underthe {DIA(h) = 2 h, IOB = 13} conditions. It can avoidthe hypoglycemia event after three different meals ingested.When the estimated IOB reaches the limitation constraint,the switching law begins to take effect. The IOB dosefalls below its limitation. Figure 4(b) shows the IOB doseresponses with and without IOB limitation.

Figure 5 shows the glucose responses under the{DIA(h) = 2 h, IOB = 13} and {DIA(h) = 8 h, IOB = 36}conditions. Under different duration of insulin action, thevalue of IOB limitation needs to be calculated again.The sim-ulation results indicate that the PID controlwith IOB estimateis effective and stabile for blood glucose control.

We all know that the insulin sensitivity (IS) is variedduring a 24-hour period. The IS is employed for eachof the three insulin sensitivity parameters in the Hovorkamodel. There are three IS values: ISnom, ISmin, and ISmax.The maximum and minimum values of IS varied randomlyon a daily basis following uniform distributions. ISmax is

equal to 1.5ISnom. ISmin is equal to 0.5ISnom [3]. In oursimulations, IS increases 1.5ISnom during 0–1000min, and ISdecreases 0.5ISnom after 1000min. To an extent, it can testthe performance of controller. Figure 6 compares the glucoseresponses for insulin sensitivity changes under the proposedcontroller. It can avoid the hyperglycemia or hypoglycemia.

In order to evaluate the performance of control algorithm,the blood glucose index (BGI) and standard deviation (SD)are adopted. The BGI is a metric proposed by Kovatchev etal. [20], to evaluate the risk for hypoglycemia and hyper-glycemia. BGI is equal to LBGI + HBGI, where LBGI andHBGI are low and high BG readings, respectively. SD is thestandard deviation of glucose concentration. The statisticalresults are given in Table 3. Both PID controller and PIDcontroller with IOB estimate are analyzed under the differentinsulin sensitivity. In all situations, the proposed controllerhas smaller BGI and SD values comparedwith PID controller.It demonstrates that the improved controller performs well.

4. In Silico Test on Virtual Patient

In order to evaluate the performance of the proposed PIDcontroller, the test is performed on ten virtual subjects usingthe UVa/Padova virtual patient software. The patients areassumed to have three meals in a day. The multiple meals are30 g CHO at 7 a.m., 50 g at 12 p.m., and 40 g at 6 p.m.

In the simulation, the control-variability grid analysis(CVGA) provides a summary of the quality of glucose regula-tion for a virtual subject [21]. CVGA plays an important rolein the tuning of closed-loop glucose control algorithms andalso in the comparison of their performance. Each subjectpresents by one data point for any given observation period.There are nine rectangular zones that are defined as follows:A-zone means accurate control, Lower B-zone means benigndeviations into hypoglycemia, Upper B-zone means benigndeviations into hyperglycemia, B-zone means benign controldeviations, Lower C means overcorrection of hyperglycemia,Upper C means overcorrection of hypoglycemia, Lower Dmeans failure to deal with hypoglycemia, Upper D meansfailure to deal with hyperglycemia, and E means erroneouscontrol. Considering the sensor noise, the 𝑋-𝑌 coordinates


0 200 400 600 800 1000 1200 1400 160050

100

150

200

250

Glu

cose

(mg/

dL)

Time (min)

DIA = 2h, IOB = 13

DIA = 8h, IOB = 36

(a)

0 200 400 600 800 1000 1200 1400 16000

5

10

15

20

25

Time (min)

IOB

(IU

)

DIA = 2h, IOB = 13

DIA = 8h, IOB = 36

(b)

Figure 5: Glucose and IOB dose responses profiles under {DIA(h) = 2 h, IOB = 13} and {DIA(h) = 8 h, IOB = 36}, respectively.

IS increase IS decrease

IS increase

0 200 400 600 800 1000 1200 1400 16000

50

100

150

200

250

Glu

cose

(mg/

dL)

Time (min)

IS changed without IOB limitationIS changed with IOB limitation

Figure 6: Glucose responses profiles under IS changed with and without IOB limitation.

110 90 70 50

400

300

180

110

Lower 95% confidence bound (mg/dL)

Upp

er95

% co

nfide

nce b

ound

(mg/

dL)

Upper C Upper D E-zone

Upper B-zone

zone

B-zone Lower D

A-zoneLower B-

Lower C

A-zone 30%, B-zone 70%, C-zone 0%, D-zone 0%, and E-zone 0%

(a)

110 90 70 50

400

300

180

110

A-zone 80%, B-zone 20%, C-zone 0%, D-zone 0%, and E-zone 0%

Lower 95% confidence bound (mg/dL)

Upp

er95

% co

nfide

nce b

ound

(mg/

dL)

Upper C Upper D E-zone

Upper B-zone

zone

B-zone Lower D

A-zoneLower B-

Lower C

(b)

Figure 7: The control-variability grid analysis (CVGA) plot for the PID controller with (a) and without (b) IOB estimate.


Table 3: Results for blood glucose control under DIA (h) = 2 h, where insulin sensitivities are normal and changed.

Insulin sensitivity Control algorithm 𝐺max (mg/dL) 𝐺min (mg/dL) BGI SD (mg/dL)

IS normal With IOB limitation 214.8 72.6 4.2 42.2Without IOB limitation 210.7 41.8 9.8 48.7

IS changed With IOB limitation 213.2 70.2 4.6 44.6Without IOB limitation 225.9 35.6 10.4 51.8

of CVGA would be the 95% confidence bound of a virtualpatient’s data.

The results indicate that 30% of virtual subjects are withinA-zone and 70% of virtual subjects are within B-zone underthe traditional PID controller as shown in Figure 7(a) and80% of virtual subjects are within A-zone and 20% of virtualsubjects are within B-zone under the PID controller with IOBestimate as shown in Figure 7(b). The results indicate thatthe PID controller with IOB estimate is effective and robust.The blood glucose can be regulated more accurately than thetraditional PID controller. It is excellent performance in tightblood glucose control and avoiding the hypoglycemic.

5. Conclusions

An improved PID algorithm for blood glucose control ispresented.The features of the proposed control algorithm arethat the PID controller is based on the IOB estimate and theupper constraint. The control algorithm is evaluated usinga combinational glucose-insulin mathematical model. Thesimulation results have demonstrated that the hypoglycemicevents can be avoided and the glucose responses in a reason-able range under multimeal ingested and insulin sensitivitychanged. The statistical results also indicate that the BGIand SD values are smaller compared with the traditionalPID control. Based on the in silico test, the CVGA indicatesthat the proposed PID controller can regulate glucose in anaccurate control range and reduce the risk of hypoglycemic.It is demonstrated to be very robust and effective. Thesimulations of this paper will provide useful theoretical basisfor blood glucose control.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

Acknowledgments

This work was supported by the Fundamental ResearchFunds for the Central Universities, (Grant no. HIT. IBRSEM.201307) and the program for Harbin City Science and Tech-nology Innovation Talents of Special Fund Project (Grant no.2014RFXXJ065).

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