1238 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 7, JULY 2007

Identification and Control for Heart Rate RegulationDuring Treadmill Exercise

Steven W. Su*, Member, IEEE, Lu Wang, Branko G. Celler, Member, IEEE, Andrey V. Savkin, Senior Member, IEEE,and Ying Guo, Member, IEEE

Abstract—This paper proposes a novel integrated approach forthe identification and control of Hammerstein systems to achievedesired heart rate profile tracking performance for an automatedtreadmill system. For the identification of Hammerstein systems,the pseudorandom binary sequence input is employed to decouplethe identification of dynamic linear part from input nonlinearity.The powerful -insensitivity support vector regression method isadopted to obtain sparse representations of the inverse of staticnonlinearity in order to obtain an approximate linear model ofthe Hammerstein system. An controller is designed for theapproximated linear model to achieve robust tracking perfor-mance. This new approach is successfully applied to the design ofa computer-controlled treadmill system for the regulation of heartrate during treadmill exercise. Minimizing deviations of heartrate from a preset profile is achieved by controlling the speed ofthe treadmill. Both conventional proportional-integral-derivative(PID) control and the proposed approaches have been employedfor the controller design. The proposed algorithm achieves muchbetter heart rate tracking performance.

Index Terms— control, hammerstein model identification,heart rate control, robust control, support vector regression.

I. INTRODUCTION

AUTOMATED exercise testing systems have become in-creasingly important in sport training, medical diagnosis,

rehabilitation and analysis of cardio respiratory kinetics [1]–[3].These systems can fully implement programmed exercise andtraining protocols to achieve desired exercising and testingresults. The major aim of this paper is to develop a computer con-trolled treadmill system, which can control the heart rate of thesubject according to a preset heart rate profile. Some commercialtreadmills are already available which offer heart rate control.However, these normally use very simple control strategies, theircontrol performance is poor and they have no mechanism for set-tingadesiredheart rateprofile. In thispaper,wedesigna treadmillexercise system which can automatically control the treadmillspeed to accurately track a desired preset heart rate profile.

Manuscript received June 30, 2006; revised October 29, 2006. This work wassupported in part by the Australian Research Council under Grant DP0452186.Asterisk indicates corresponding author.

*S. W. Su is with the Human Performance Group, Biomedical Systems Labo-ratory, School of Electrical Engineering and Telecommunications University ofNew South Wales, Sydney, N.S.W. 2052, Australia, and also with the Facultyof Engineering, University of Technology, Sydney, Australia (e-mail: Steven.Su@uts.edu.au).

L. Wang, B. G. Celler, and A. V. Savkin are with the Human PerformanceGroup, Biomedical Systems Laboratory, School of Electrical Engineering andTelecommunications University of New South Wales, Sydney, N.S.W. 2052,Australia.

Y. Guo is with the Autonoumous Systems Lab, CSIRO ICT Center, Australia.Color versions of one or more of the figures in this paper are available online

at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TBME.2007.890738

Fig. 1. A Hammerstein system.

Proportional-integral-derivative (PID) control is the mostpopular control algorithms in industry due to its simplicity instructure and ease of tuning. However, this paper shows theacceptable heart rate tracking performance cannot be achievedby PID controller because of highly nonlinear behavior of thecontrolled system. To achieve better tracking performance anew model-based robust control strategy is developed, whichsuccessfully compensates the nonlinearity by using a Hammer-stein model.

The Hammerstein model can be described as a static non-linear block (input nonlinearity) followed by a dynamic linearsystem (see Fig. 1). Hammerstein models may account for non-linear effects encountered not only in industrial processes [4],[5], but also in physiological processes [6], [7]. For example,electrically stimulated muscle [8], the upper limb [6], the muscleforce [9], and the skeletal joints movements [10] can be ef-fectively modelled by a nonlinear static element cascaded bya linear dynamic element.

To obtain the desired heart rate tracking result, this paperpresents an integrated modelling and control approach basedon Hammerstein models. This approach includes two integratedparts: the identification of Hammerstein model and model-basedrobust control.

The identification of Hammerstein model is a very activeresearch topic [11]–[13]. As suggested by Bai [14], there aremainly four kinds of approaches: 1) overparameterizationmethod (two-stage procedures) [12], [15], [16]; 2) stochasticmethod (gray box procedure) [11], [17], [18]; 3) iterativemethod [13], [19]; or 4) separable least squares method [20].As discussed in [14], these approaches all have their ownadvantages and disadvantages. Recently, Goethals et al. [12]presented a novel overparametrization (two-stage procedures[21]) identification approach for Hammerstein systems. Themost distinguishing part of that approach is the utility of apowerful machine learning method, least square support vectormachine (LSSVM) [22]. This novel machine learning methodsets that paper apart from existing papers.

Support Vector Regression (SVR)-based regression [23]SVR is a new technique, which has been successfully appliedto nonlinear function estimation [12], [22], [24]. Vapnik et al.established and developed the foundation of SVM [25], [26].The formulation of SVM embodies the structure of the riskminimization principle, which has been shown to be superior

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SU et al.: IDENTIFICATION AND CONTROL FOR HEART RATE REGULATION DURING TREADMILL EXERCISE 1239

to other traditional empirical risk minimization principles [27].SVM-based regression applies the kernel methods implicitlyto transform data into a feature space (this is known as akernel trick [28]), and uses linear regression to get a nonlinearfunction approximation in the feature space. SVR is veryefficient in terms of speed and complexity, and successfullysolves the over-fitting problem [29] by introducing regulariza-tion techniques.

This paper applies the SVM approach combined with thestochastic method [11] to identify physiological processes.There are at least two aspects which are different with respectto paper [12].

First, the stochastic method [16] is employed in preference tothe over parameterization method [11]. As discussed in [11] and[30], the error of the identification of Hammerstein model is notonly from linear and nonlinear parts themselves but also fromthe coupling between them. Pseudorandom binary sequences(PRBS) are applied to decouple the identification of the twoparts as suggested in [11].

Another main difference is the usage of -insensitivity SVM[31], [32] instead of LS-SVM [22], [33], [34]. Both LS-SVMand -insensitivity SVM have the merits of SVM approaches.However, the loss function used by -insensitivity SVM, onlypenalizes errors greater than a threshold [see (3)]. This leadsto a sparse representation of the decision rule giving significantalgorithmic and representation advantages [31]. On the otherhand, the ridge regression used by LS-SVM typicallyoften causes the loss of sparseness representation.

Most existing control methods for Hammerstein systems arebased on direct inversion of the static nonlinearity combinedwith existing linear control approaches [5], [35]. These methodsconsider control and identification separately. They identify theHammerstein model first and then invert the static nonlinearitypart to obtain an approximated linear model. There are mainlytwo disadvantages of these approaches. First, if the identifiednonlinearity has input multiplicity then the inversion is un-achievable. Second, even when the inversion exists uniquely itis often hard to achieve an explicit analytic expression.

Based on -insensitivity SVR, the inverse of the static non-linearity rather than the nonlinearity is identified directly. Then,the control is designed for the approximated linear modelto achieve robust tracking performance [36]. It should be notedthe inverse of the static nonlinearity cannot be achieved directlyby using the method proposed in [12].

In recent years, control has proved to be a very effi-cient tool for robust control design [37]–[40]. control tech-niques have already been successfully applied in some biomed-ical problems (e.g., in automatic insulin injection for blood glu-cose regulation in diabetic patients [41].)

The proposed identification and -based control approachwas applied for the automated heart rate regulation system de-sign, and excellent tracking results are achieved. This is also thefirst report of an SVM application in the area of cardiovascularsystem identification and control practice.

The paper is organized as follows. The details of SVM-basedidentification and control approach are given in Section II.Section III presents the application of the proposed approachfor the regulation of heart rate of treadmill exerciser.

Fig. 2. The precompensated Hammerstein system.

II. SVM-BASED IDENTIFICATION AND CONTROL APPROACH

In this paper, we use a Hammerstein model to dynamicallydescribe the relationship between walking speed and heart ratevariation. We do this for the following reasons. The steady-staterelationship between walking speed and work load is nonlinear.The dynamic linearity between work load (in the range from50 to 125 W) and heart rate variation was established by, for ex-ample, Hajek et al. [42]. It is, therefore, reasonable to use a non-linear static element cascaded by a linear dynamic element toapproximately describe the relationship during moderate tread-mill exercises.

In this paper, as assumed in most gray box procedure (or sto-chastic method) [11], the steady-state gain of the linear dynamicmodel is constrained to be unity, and the steady-state charac-teristic of the overall model is determined by the static non-linearity. As mentioned in the introduction, the linear dynamicidentification of Hammerstein models can be decoupled fromthat of nonlinear parts by using pseudorandom binary sequences[11]. However, the PRBS inputs often cannot excite the nonlin-earity sufficiently. To identify the nonlinear part or its inverse,steady-state experiments should be performed. In this section,the identification of the inverse of nonlinear part is introducedfirst.

A. Modelling the Inverse of the Nonlinear Function By UsingSVR

To transfer a Hammerstein system to a linear system, a prec-ompensator as shown in Fig. 2 can be applied as in [35].

For the identification of the inverse of nonlinearity, the socalled -insensitivity SVR regression will be employed, whichis convex and very efficient in terms of speed and complexity.

Now we briefly introduce the SVR approach [43].Let be a set of inputs and outputs data points (

, , is the number of points). The goalof the support vector regression is to find a function whichhas the following form:

(1)

where represents the high-dimensional feature spaceswhich are nonlinearly transformed from . The coefficientsand are estimated by minimizing the regularized risk function

(2)

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1240 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 7, JULY 2007

The first term is called the regularized term. The second termis the empirical error measured by -insensitivity loss functionwhich is defined as

(3)

This defines an tube. The radius of the tube and the regular-ization constant are both determined by user.

The selection of parameter depends on application knowl-edge of the domain. Theoretically, a small value of willunder-fit the training data because the weight placed on thetraining data is too small, thus resulting in large values ofmean square error on the test sets. However, when is toolarge, SVR will over-fit the training set so that willlose its meaning and the objective goes back to minimizingthe empirical risk only. Parameter controls the width of the-insensitive zone. Generally, the larger the the fewer number

of support vectors and, thus, the sparser the representation ofthe solution. However, if the is too large, it can deteriorate theaccuracy on the training data.

By solving the above constrained optimization problem, wehave

(4)

As mentioned before, by the use of kernels, all necessarycomputations can be performed directly in the input space,without having to compute the map explicitly. Afterintroducing the kernel function , the above equationcan be rewritten as follows.

(5)

Where the coefficients corresponding to each . Thesupport vectors are the input vectors whose correspondingcoefficients .

For linear support regression, the kernel function is, thus, theinner product in the input space

(6)

For nonlinear SVR, there are a number of kernel functionswhich have been found to provide good generalization ca-pabilities, such as polynomials, radial basis function (RBF),or sigmoid. Here, we give the polynomials and RBF kernelfunctions as follows:

RBF kernel:

Polynomial kernel:

Details about SVR, such as the selection of radius of thetube, kernel function, and the regularization constant , can befound in [28], [43].

It should be emphasized that, as we need to model the inverseof the nonlinear function (see Fig. 2), the measured steady-state output (heart rate) will be used as the input data, and theinput (treadmill speed) as the output data.

Fig. 3. A mixed sensitivity H control problem.

B. Identification of Linear Dynamic Part

In [11], Bai showed that the identification of linear part of aHammerstein model can be decoupled from nonlinear part withthe help of the PRBS input. The reason is that any static non-linearity can be exactly characterized by a linear function, whendriven by PRBS inputs which have a binary nature.

When a PRBS input is employed for the identification of theHammerstein system, as shown in [11, equation (2.3)], the iden-tification of a Hammerstein model can be simplified as a linearidentification problem. Any linear identification approach canbe applied. Here, the parametric approach as suggested in [11]is adopted.

C. -Based Tracking Controller Design

After the precompensator is employed, the Hammersteinsystem can be treated as a linear dynamic system. However, thisapproximated linear system often has modelling errors. In thispaper, the input disturbances and additive model uncertaintyare considered as modelling errors. In order to achieve desiredtracking performance under input disturbance and additivemodel uncertainty, an controller is employed for theprecompensated Hammerstein system. This controller designproblem can be formulated as a mixed sensitivity problem[36], [37], [44]–[46] as shown in Fig. 3. is the process tobe controlled, and is the robust controller. is the exoge-nous input (disturbance or reference input). and are thecontrolled variables. and are the complementary sen-sitivity weighting function and sensitivity weighting function,respectively. The formulated mixed sensitivity problem is thedesign of the robust controller to ensure that the weightedsensitivity function and complementary sensitivity functionare bounded so that both robust performance and the desiredstability margin can be obtained [37], [47], [48].

General guidelines for weighting function selection can befound in, for example [44], [49]. In order to obtain offset freetracking, a commonly used method is to include an integratorin the sensitivity weighting function . If model uncertainty

is known, we normally need to select the complemen-tary sensitivity weighting function such that

for all to obtain robust stability. However, derivingthe model uncertainty is very challenging especially fornonlinear systems. In this paper, we first select such that

is big enough to ensure robust stability. Then, grad-ually decrease to diminish the conservativeness.

III. HEART RATE REGULATION APPLICATION

The major aim of this section is to apply the proposed identi-fication and control approach to develop a computer controlled

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SU et al.: IDENTIFICATION AND CONTROL FOR HEART RATE REGULATION DURING TREADMILL EXERCISE 1241

Fig. 4. The computer controlled treadmill system.

treadmill system, which can automatically control the treadmillspeed to accurately track a desired preset heart rate profile.

A. Experimental Equipment

The computer controlled treadmill and its related data collec-tion and processing system are shown in Figs. 4 and 5.

The treadmill used in the system is the Powerjog “G” Se-ries fully motorized medical grade treadmill manufactured bySport Engineering Limited, U.K.. Control of the treadmill canbe achieved through an RS232 serial port. The treadmill canreceive commands from the computer controller via this link,and obeys such commands without supervision. The measure-ment of heart rate in the designed system is implemented usinga wireless Polar system. However, even in the absence of ex-ternal interference the heart rate can vary substantially over timeunder the influence of various internal or external factors. There-fore, an improved exponential weighted moving average filtertogether with a simple outlier detection algorithm [3], [50], [51]is adopted for the estimation of the heart rate. Specifically, thecontrol computer collects heart rate signal from a Polar receiverthrough an analog input port every 2 s, and calculates heart rateby using an edge detection algorithm. Only measured heart ratewithin a reasonable range [for example, between 50 and 150beats per minute (bpm)] was counted in the measured sequencein order to remove outliers.

Assume is the sequence of the measured heart rate. Weapply the exponentially weighted moving average filter to thesequence

where is the filter coefficient. In this paper, the value of wasselected as 0.35, to achieve optimal filtering effects.

B. Nonlinearity Modelling By Using Support VectorRegression

In order to identify the nonlinear relationship, steady-state ex-periments are performed and recorded. Six young healthy malesubjects volunteered to participate in the study. Their physicalcharacteristics are presented in Table I.

All experiments were conducted in the afternoon, and thesubjects were permitted to have a light meal 1 h before exper-iments. Initially, the subjects were asked to walk for about 10min on the treadmill to familiarize themselves with the exper-iment. The subjects were then requested to walk at five levelsof different speeds (3–6 km/h and a subject specific maximumwalking speed, typically 7 km/h). Each level took a total periodof 5 min, and was followed by a 10-min resting period. Finally,in order to identify the linear dynamic part of the Hammersteinsystem, subjects were also requested to walk on the treadmillunder a PRBS input as shown in Fig. 6. The detailed descrip-tions of this PRBS signal is given in Section III-C. Throughoutthe experiments heart rates were recorded.

In this paper, both linear and -insensitivity SVR regressionmethods are applied to model the inverse of the nonlinear func-tion . We randomly select 22 data points (73% of the totaldata points) to train the model, and 8 data points (27% of totaldata points) to test the regression results. Comparing SVR re-gression with linear regression, the former obtains the better re-sults. SVR regression decreases the training error (Mean SquareError) from 0.294 to 0.259 , while testing error de-creases from 0.382 to 0.265 . This partially proves thatthe steady-state relationship between walking speed and heartrate is nonlinear. After such comparisons, we utilize all exper-imental data to perform SVR regression in order to include asmuch as experimental information in the model as possible. Thedetailed regression results, such as the selected design parame-ters (including insensitivity region , kernel function, and theregularization constant ) and the support vector number, aresummarized in Table II and Fig. 7. In Fig. 7, the continuouscurve stands for the estimated input output steady-state rela-tionship. The dotted lines indicate the -insensitivity tube. Theplus markers are the points of input and output data. The circledplus markers are the support points. The quality of control (seeSection III-E) also demonstrates that this nonlinear SVR modelis a good representation of the inverse of the nonlinear func-tion. It should be emphasized that -insensitive SVR just uses 5points (16.7% of the total points) to sparsely describe the non-linear relationship efficiently.

C. Linear Dynamic Modelling

From a physiological analysis of cardiovascular systems [52],two transitory components are known to contribute to the heartrate response: at the beginning of exercise the rapid componentof vagal inhibition and then a much slower acting complex ofsympathetic effects. For the dynamic modelling of heart ratevariation during exercise, some complicated model structures[42], [53] have been proposed based on physiological analysis.However, from a control application point of view, these modelsare too complicated and often lead to poor determinability ofparameters and, thus, poor control performance. Hajek et al.proposed a simpler version of the model presented in [42] asfollows:

(7)

In (7), is the Laplace form of the heart rate variation, and input ( is its Laplace form) is the work-

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1242 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 7, JULY 2007

Fig. 5. Block diagram for computer controlled treadmill system.

TABLE ISUBJECT CHARACTERISTICS (N = 6)

Fig. 6. Two periods of 31 bits PRBS inputs (treadmill speed) and its corre-sponding outputs (averaged heart rate of six subjects).

TABLE IIDETAILS ABOUT THE ESTIMATION OF THE INVERSE OF THE NONLINEAR

FUNCTION BY SVR

load. Workload is the amount of power being demanded of anexercising subject, manifesting itself to the subject as exerciseintensity. Input ( is its Laplace form) is constant 1when , zero when . As input is de-

Fig. 7. Modelling of the inverse of the nonlinear function by using �-insensi-tivity SVR.

pendent on it is, therefore, not an independent input. Fur-thermore, the fast component (which is associated with )cannot be observed distinctly in our experimental data. Thus,the effects of is neglected but treated as model uncertaintyin order to reduce design complexity. Therefore, a first ordermodel (with input disturbances) to model the heart variationduring exercise is a good choice from physiological analysis.Later, we will show that this model structure is also confirmedby two popular model selection criteria.

In this paper, a PRBS [54], [55] input is employed to de-couple the identification of linear dynamic from nonlinearity ofthe Hammerstein system. A PRBS input (see Fig. 6) has twolevels ( or ) and may switch from one level to theother only at constant time intervals . A PRBS is periodicwith period , where N is an integer. In this paper,

, , , and .An important issue for the PRBS-based experiment implemen-tation is the synchronization of the input PRBS signal and theoutput measurement. In this paper, a triaxial accelerometers aremounted on the lower back of treadmill exerciser to synchronizebody movements with measured ECG signal, which ensures re-liable estimation of time delay (see Fig. 8).

Based on experimental data (see Fig. 6), the structure is de-termined by using the Matlab Identification Toolbox. Two pop-

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SU et al.: IDENTIFICATION AND CONTROL FOR HEART RATE REGULATION DURING TREADMILL EXERCISE 1243

Fig. 8. The triaxial accelerometer monitored two periods of 31 bits PRBSsignal.

ular model selection criteria, Akaike information criterion andminimum description length were used to select the first orderARX (Auto Regressive eXternal) model with time delay as thebest model structure for linear dynamics. The identified linearmodel is given as follows:

(8)

with sampling period s. Note the time delay containedin (8) includes the delay of the response of human cardiovas-cular system as well as the lag time of the automated treadmillsystem.

D. Robust Tracking Controller Design

The identified model inevitably has modelling errors. In thispaper, the modelling errors are considered in two forms: inputdisturbance and model uncertainty. To achieve robust trackingunder input disturbances and model uncertainty, a mixed sen-sitivity controller [37], [45], [46] is designed for the iden-tified model. As the design of discrete time mixed sensitivity

controllers is not as mature as for continuous time sys-tems, the design of the weighting function of the mixed sen-sitivity problem is implemented by using its continuouscounterpart. Specifically, we convert the discrete time model,(8) (with sampling period s) into a continuous timemodel by using the matched pole-zero method of [56]. Theweighting function in this paper is recursively selected basedon general guidelines of [44], [49]. In order to obtain offsetfree tracking, we select the sensitivity weighting function inthe form of (with sufficiently small).We select the complementary sensitivity weighting function as

to acquire desired stability margin as well as tosatisfy rank condition (full rank requirement of matrix ofthe augmented process) of standard problem. After sev-eral recursive design steps, we obtained the following set of

Fig. 9. Typical step response comparison between proposed approach and con-ventional PID control.

Fig. 10. Step responses for all subjects.

parameters for the weighting functions to obtain an augmentedmodel for the weighted process: , , and

.The augmented continuous model is then converted to its dis-

crete time form. Finally, a mixed sensitivity controller canbe designed for this discrete time model

(9)

E. Heart Rate Regulation Results

The step responses of heart rate control by using PID and theproposed control approach are compared in Fig. 9. The step re-sponses for all subjects are shown in Fig. 10. It can be seen thatthe proposed controller achieved much better performance thanconventional PID control. The main reason is the compensa-tion of the system nonlinearity by using a Hammerstein modelfor the heart rate. Specifically, the heart rate variation due to achange of walking speed from a slow speed (for example, from

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1244 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 7, JULY 2007

Fig. 11. A typical heart rate tracking for an exercising heart rate profile.

Fig. 12. Heart rate tracking results for all subjects.

3 to 3.5 km/h) is much smaller than that for the same alterna-tion from a fast speed (for example, from 6 km/h to 6.5 km/h).The proposed approach copes with such difference by using theidentified inverse of the nonlinear function as a precompen-sator (see Fig. 2) to systematically compensate for the nonlin-earity, whereas linear controllers (such as conventional PID con-trollers) cannot.

Finally, the proposed controller was used to track a presetdesired heart rate profile. The profile includes three stages: 5min increasing (from resting heart rate to 110 beats/min), 15min holding (110 beats/min), and 5 min decreasing (from 110beats/min to normal.). This is comparable to heart rate profilesrecommended for optimal low level aerobic training at about60% of maximum effort. Figs. 11 and 12 demonstrate thatquite satisfactory tracking of the desired heart rate profile wasachieved. From the shape of treadmill speed shown in Figs. 11and 12, it is also observed that the treadmill speed is decreasedin a slightly different rate for different subjects whilst the heartrate is maintained at around 110 bpm. These data suggest the

hypothesis that fit subjects will have a low rate of decreaseof treadmill speed. This hypothesis is being further tested inour laboratory, using the newly designed computer controlledtreadmill.

IV. CONCLUSION

In this paper, an integrated modelling and control approachis developed for Hammerstein systems as applied to the regu-lation of cardiovascular system response to exercise. The sto-chastic method is adopted to decouple the identification of linearand nonlinear parts. Powerful -insensitivity SVR is employed toidentify the inverse of input nonlinearity in order to transfer Ham-merstein systems to linear systems. A robust tracking con-troller is then designed for the converted Hammerstein system.The approach is successfully applied to a heart rate regulationsystem for exercise on a motorized treadmill. This is the first re-port of an SVM application in cardiovascular system identifica-tion and control practice, and achieves excellent results. It shouldbe mentioned that because of the sparse representation [31], [57]of the static nonlinearity obtained by using -insensitivity SVR,the implementation complexity is greatly reduced. We believethat the ability to track a predetermined heart rate profile maybe useful in cardiac rehabilitation programs or for safer exercisefor individuals at risk.

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Steven W. Su (M’99) received the B.S. and M.S.degrees from Harbin Institute of Technology (HIT),Harbin, China, in 1990 and 1993, respectively. He re-ceived the Ph.D. degree from the Research Schoolof Information Sciences and Engineering (RSISE),the Australian National University (ANU), Canberra,Australia, in 2002.

He was a postdoctoral research fellow in School ofChemical Engineering and Industrial Chemistry, theUniversity of New South Wales (UNSW) from 2002to 2004. He was also served as a Research Fellow in

School of Electrical Engineering and Telecommunications, the University ofNew South Wales, Sydney, Australia, from 2004 to 2006. He is currently a Lec-turer with the Group of Mechatronics and Intelligent Systems, the Faculty ofEngineering, University of Technology, Sydney (UTS). He is also a VisitingLecturer with the Biomedical System Laboratory, the School of Electrical En-gineering, UNSW. His main research interests include biomedical system mod-eling and control, robust and adaptive control, fault tolerant control, nonlinearprocess control, and navigation system design.

Lu Wang received the M.E. degree in computer en-gineering from the University of New South Wales(UNSW), Sydney, Australia, in 2002. She finishedthe Ph.D. degree study in electrical engineering atUNSW in 2006.

She is currently a Research Associate in theschool of electrical engineering at UNSW. Her mainresearch interests include mathematical modelling ofthe human cardiovascular and respiratory systems,exercise physiology, and analysis of cardiovascularand respiratory variability signals.

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1246 IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 54, NO. 7, JULY 2007

Branko G. Celler (M’87) graduated from the Uni-versity of New South Wales (UNSW), Sydney, Aus-tralia, with the B.Sc. degree in 1969 and the B.E.E.degree (Hons) in 1971. He received the Ph.D. degreein 1978 at the same university.

He undertook a Postdoctoral Fellowship at JohnsHopkins Baltimore, MD. He returned to the UNSWin 1981 and was Foundation Director of the Biomed-ical Systems Laboratory, the Human PerformanceLaboratory, and the Centre for Health Informatics.He was Head of the School of Electrical Engineering

and Telecommunications for almost nine years. His research interests includebiomedical instrumentation and systems, noninvasive modelling of cardio-vascular performance, home telecare and remote monitoring, and medicalinformatics.

Andrey V. Savkin (SM’00) was born in 1965 in No-rilsk, USSR. He received the M.S. (1987) and thePh.D. degrees (1991) from The Leningrad University,Leningrad, USSR, in 1987 and 1991, respectively.

From 1987 to 1992, he worked in the All-UnionTelevision Research Institute, Leningrad. From 1992to 1994, he held a postdoctoral position in the Depart-ment of Electrical Engineering, Australian DefenceForce Academy, Canberra, Australia. From 1994 to1996, he was a Research Fellow with the Departmentof Electrical and Electronic Engineering and the Co-

operative Research Center for Sensor Signal and Information Processing, the

University of Melbourne, Melbourne, Australia. Since 1996, he has been a Se-nior Lecturer, and then an Associate Professor with the Department of Elec-trical and Electronic Engineering at the University of Western Australia, Perth,Australia. Since 2000, he has been a Professor with the School of ElectricalEngineering and Telecommunications, The University of New South Wales,Sydney, Australia. His current research interests include robust control and fil-tering, hybrid dynamical systems, missile guidance, networked control systems,computer-integrated manufacturing, control of mobile robots, computer vision,and application of control and signal processing to biomedical engineering andmedicine. He has published four books and numerous journal and conferencepapers on these topics and served as an Associate Editor for several internationaljournals and conferences.

Ying Guo (M’99) received the B.E. and the M.E.degrees in electrical engineering from the North-western Polytechnic University, Xi’an, China, in1994 and 1996, respectively. She received the Ph.D.degree in machine learning from the Australian Na-tional University, Canberra, Australia, in November2001.

She is currently a Senior Research Scientistwith the Commonwealth Scientific and IndustrialResearch Organisation (CSIRO), Sydney, Australia.Her current research interests include statistical

machine learning theory, data mining, analysis of machine learning algorithms,and application of machine learning algorithms in multiagent system.

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