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196 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 13, NO. 2, MARCH 2005

Experimental Results on Adaptive Output FeedbackControl Using a Laboratory Model Helicopter

Ali T. Kutay, Anthony J. Calise, Senior Member, IEEE, Moshe Idan, and Naira Hovakimyan, Senior Member, IEEE

AbstractExperimental results are presented that illustrate arecently developed method for adaptive output feedback control.The method permits adaptation to both parametric uncertaintyand unmodeled dynamics, and incorporates a novel approachthat permits adaptation under known actuator characteristicsincluding actuator dynamics and saturation. Only knowledge ofthe relative degree of the controlled system within the bandwidthof the control design is required. The controller design was testedby controlling the pitch axis of a three degrees-of-freedom (DOF)helicopter model, using attitude feedback through a low-resolutionoptical sensor.

Index TermsAdaptive control, neural networks (NNs), output

feedback, uncertain systems.

I. INTRODUCTION

RESEARCH in adaptive control is motivated by many

applications, modeling for which may vary from having

accurate low-frequency models in the case of rigid bodies, to

having no reasonable set of model equations in the case of

active control of flows and combustion processes. Moreover,

growing interest in the use of novel actuation devices intro-

duces additional uncertainty into the problem. Regardless of the

extent of the model accuracy that may be present, an important

aspect in any control design is the effect of parametric un-

certainty and unmodeled dynamics. Intensive research effortshave been devoted to adaptive control of uncertain nonlinear

systems. Universal approximation capabilities of neural net-

works (NNs) have been widely employed to model complex

nonlinear physical phenomena. The majority of papers on this

subject conclude with numerical simulations that illustrate the

advantages inherent in adaptive approaches. Very few of such

papers include experimental results.

Successful experimental evaluations of NN-based adaptive

control methods reported in the literature, several of which are

detailed below, date back to the early 1990s. A NN-based adap-

tive state feedback controller has been tested on a unicycle robot

in [1], with stability guaranteed based on Lyapunov analysis. Anoutput feedback direct NN-based adaptive controller was tested

Manuscript received August 15, 2003; revised April 19, 2004. Manuscriptreceived in final form June 9, 2004. Recommended by Associate Editor S. Kim.

A. T. Kutay and A. J. Calise are with the School of Aerospace Engi-neering, Georgia Institute of Technology, Atlanta, GA 30332 USA (e-mail:[email protected]; [email protected]).

M. Idan is with the Faculty of Aerospace Engineering, Technion-Israel Insti-tute of Technology, Haifa 32000, Israel (e-mail: [email protected]).

N. Hovakimyan was withGeorgiaInstituteof Technology, Atlanta, GA 30332USA. She is now with the Department of Aerospace and Ocean Engineering,Virginia Polytechnic Institute and State University, Blacksburg, VA 24061 USA(e-mail: [email protected]).

Digital Object Identifier 10.1109/TCST.2004.839563

on a force control servomechanism in [2], with stability shown

for a linear positive real plant. A full state feedback neural iden-

tifier and controller has been tested on a four-bar linkage load

system in [3], where the structure of the nonlinearity is assumed

known. A disk with a high-friction load mounted to a motor

has been used as a test bed for evaluation of a full state feed-

back direct adaptive control method in [4], in which the struc-

ture of the nonlinearity is assumed known. A full state feedback

neural dynamic adaptive controller with no stability guarantee

has been tested on a selective compliant assembly robot arm

(SCARA) robot in [5]. The method in [6] uses a NN trained on-

line with a recursive least squares training algorithm without anystability analysis to approximate the inverse model of the plant.

An output feedback method that uses a high-gain observer to

estimate states and integrates NNs into an adaptive robust con-

trol method has been tested on a linear motor drive system in

[7]. Stability and transient performance are guaranteed in this

paper, and asymptotic tracking is shown for the case where only

parametric uncertainty exists in the system. A NN-based output

feedback variable structure control method with guaranteed sta-

bility evaluated on a four-bar linkage system is presented in

[8]. Most of the earlier experimental works either lack a sta-

bility analysis, or assume that the structure of the nonlinearity

is known. Also, to our knowledge, no experimental results of anadaptive output feedback control method that can be applied to

systems with unmodeled dynamics and actuator nonlinearities

such as saturation have been reported.

In this paper, we evaluate experimentally the theoretical

results of a recently developed adaptive output feedback

method [9] in conjunction with a method for protecting the

adaptive element from nonlinear actuator characteristics such

as saturation and possibly neglected dynamics [10]. The model

used in the experiments is a laboratory-scale bench-top three

degrees-of-freedom (DOF) helicopter produced by Quanser

Consulting Inc. We consider control of the 1-DOF pitch motion

of the helicopter to evaluate the single-inputsingle-output

(SISO) design approach of [9]. There are significant nonlinear-

ities in the system due to friction and the aerodynamics of the

propellers. Only the angular position of the helicopter is used

for feedback.

The paper is organized as follows. In Section II, we describe

the experiment setup. Section III formulates the problem and

briefly describes the controller design. Experimental results are

presented in Section IV. Section V summarizes the paper.

II. EXPERIMENT SETUP

The laboratory model helicopter used to evaluate the adaptive

output feedback control method is shown in Fig. 1. It consists

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KUTAY et al.: EXPERIMENTAL RESULTS ON ADAPTIVE OUTPUT FEEDBACK CONTROL 197

Fig. 1. Three-DOF model helicopter.

of a rectangular frame and two propellers mounted at its two

ends with axes normal to the frame. The helicopter frame is

free to roll about its center where it is connected to the end

of a long arm, which is free to rotate in pitch and yaw. The

system has a total of three DOF with two control inputs as the

voltages applied to the electric motors driving the propellers.

Control voltage is applied equally to both motors, keeping the

helicopter frame horizontal. Regulated output is the pitch angleof the arm, denoted by , measured by a 12-b encoder.

Design of the adaptive controller requires the relative degree

of the regulated output , and the sign and upper bound on the

magnitude of the control effectiveness , where is the

control. Open-loop experimental analysis presented in [11] re-

veals that the relative degree of the regulated output is for

frequencies up to 3 rad/s and the control effectiveness is approx-

imately . Open-loop frequency analysis also

shows that the system has nonlinear characteristics, mainly due

to friction, nonlinear actuation system, and nonuniform mass

distribution.

III. DESCRIPTION OF THE ADAPTIVE OUTPUT FEEDBACK

METHOD

The adaptive output feedback method employs feedback lin-

earization, coupled with an online NN-based adaptive element

to compensate for modeling errors, and a linear compensator

for the ideally linearized dynamics. The compensator also gen-

erates an auxiliary signal for training the linearly parameterized

NN by filtering the tracking error. For this, a stable low-pass

filter is used to meet a strictly positive real (SPR) condition of a

transfer function associated with the error dynamics. This con-

dition is utilized in the Lyapunov stability analysis to construct

the NN adaptation law using only available measurements [9].

Pseudocontrol hedging (PCH) is incorporated within the

above adaptive control setting to address unmodeled actuator

dynamics and saturation. PCH was first introduced for the state

feedback case [10], and later applied in an output feedback

setting [12]. The main idea behind the PCH approach is to

limit or hedge the reference model (RM) of a model reference

adaptive control architecture to prevent the adaptive element

from attempting to adapt to the actuation anomalies, while

not affecting adaptation to other sources of inversion error, for

which compensation is possible. Conceptually, PCH moves

the RM backward by an estimate of the amount the controlled

system did not move due to selected actuator characteristics.PCH has been successfully tested on various simulation and

Fig. 2. Controller architecture with PCH loop (shown with dashed lines).

experimental applications in both full state and output feedback

settings [13].

The overall control architecture, including the PCH loop, is

depicted in Fig. 2. To briefly summarize the controller design

process, let the actual dynamics of the model helicopter be given

by

(1)

where is the system state, , are the

system input (achieved control) and output (measurement) sig-

nals, respectively, and , are unknown func-

tions. We assume that the dynamic model in (1) satisfies the

inputoutput feedback linearization condition with relative de-

gree , i.e.,

(2)

Here, , such that for

and . Our aim is to design an output feedback con-

trol law that utilizes the available measurement , to achieve

output tracking of a bounded trajectory .

A. Feedback Linearization and Model Inversion Error

Feedback linearization is performed by introducing the trans-

formation

(3)

where is the commanded control, is commonly referred

to as a pseudocontrol signal and is an approxima-tion of in which only is used in the approximation.

Consequently, the approximation may be very crude. Using (3),

the output dynamics (2) can be expressed as

(4)

where

(5)

The control input to be commanded is obtained from (3) as

(6)

The pseudocontrol is chosen to have the form(7)

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Fig. 3. Computation of the PCH signal.

where is the output of a RM that definesthe desired response

of the closed-loop system, is the output of a linear dynamic

compensator designed to stabilize the ideally linearized system,

and is the adaptive control signal designed to approximately

cancel . In the case of perfect actuation ( ), the RM

is designed as resulting in the following error dy-

namics:

(8)

where is the tracking error.

B. PCH

When the applied control is different from the commanded

control due to, e.g., actuator saturation, PCH modifies the

RM by introducing a signal . To compute the PCH signal

, a measurement or an estimate of the actuator position is

required. If actuator position measurements are not available, a

model that includes the characteristics we want to protect the

adaptive system from can be used to generate actuator position

estimates. The process is illustrated in Fig. 3 for an actuator

model that has position limit, rate limit, actuator dynamics, and

time delay. Any of these characteristics can significantly change

the system dynamics and even render the system unstable.

The PCH signal is defined as the difference between the

commanded pseudocontrol and the estimated achievable pseu-

docontrol

(9)

Next, is introduced as an additional input into the RM,

forcing it to move back. If the RM update without PCH was

of the form

(10)

where is the external command signal, then the RM update

with PCH is

(11)

The instantaneous pseudocontrol output of the RM that is used

as an input to the linearized plant model is not changed by the

use of PCH and remains

(12)

Fig. 4. th-order RM with PCH signal.

The effect of the PCH signal on a linear th-order RM is shown

schematically in Fig. 4. With the modified RM (11), the error

dynamics become

(13)

where

(14)

Equation (13) is in the same form as (8), the error dynamics

without PCH, with a very important difference that appears in

the place of in the expression for the modeling error. This

in effect prevents the adaptive process from seeing the portion

of the modeling error that is due to difference between and

. Without PCH, the modeling error that the NN is designed to

cancel contains all the effects of the actuation anomalies. Since

the other sources of nonlinearities and modeling error still ap-

pear in the error signal, the NN continues to compensate for

them. An extreme case can exist during periods of full saturation

in which the adaptive process is no longer in control, but is still

capable of tracking the modeling error. Thus, PCH also permits

the introduction of limited authority adaptive control in prac-

tical applications. Such limited authority control might extend

to the limit of having no authority, in which case the adaptive

process is simply monitoring the model error, and can be en-

gaged only when it is determined that the modeling error is suf-

ficiently large (for example, in the event of an actuator failure).

More general methods for accommodating saturation in adap-

tive systems have recently been reported in [14]. In the experi-mental results reported in the next section, we use PCH to shield

the adaptive system from the dc motor dynamics and the voltage

limit that is enforced to protect the motor windings.

C. Linear Compensator and Adaptive Signal Design

A single-inputtwo-output dynamic compensator denoted by

(15)

is used to generate the linear control signal together withan auxiliary error signal that is required to ensure an imple-

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Fig. 5. Block diagram of the error dynamics.

mentable adaptive law. The stability analysis requires that thetransfer function from to given by

(16)

be SPR. This transfer function is depicted in Fig. 5. For ,

it is not possible to make SPR, so a stable low-pass filter

is introduced in (16) so that can

be made SPR

(17)

The adaptive signal is the output of a linearly parameterized NN,

represented by

(18)

where is the NNweight vector, isa suitably chosenvector

of radial basis functions filtered through , and is the

input vector composed of current and past inputoutput data.

NN weights are initialized as zero and updated using

(19)

where the positivedefinite matrix and are the

adaptation gains.

IV. EXPERIMENT RESULTS

In this section, we present experimental results obtained using

the laboratory helicopter model depicted in Fig. 1. The arm car-

rying the helicopter is balanced so that it remains horizontal

when the propellers are not actuated, and this position is de-

fined as zero pitch angle. Positive and negative commands in

the following results correspond to positions above and belowthe horizontal, respectively.

The PCH loop contains an actuator model that includes the

characteristics that are desired to be hedged from the adaptive

system. The most important characteristic that can destabilize

the system is saturation of the control voltage introduced

to protect the control hardware. In addition to saturation, a

first-order dynamic model of the dc motors that was identi-

fied in [11] is also included in the PCH loop, reducing the

relative degree of the plant as seen by the adaptive system to

two. Motivation for removing the actuator dynamics from the

adaptive system is to simplify the design of the linear com-

pensator, and to demonstrate the effectiveness of PCH against

actuator dynamics. Hence, the controller design is performedusing , implying that the ideally inverted plant transfer

Fig. 6. Output tracking of the model helicopter with sinusoidal inputs.

function is approximated by the linear model .

The approximate model inversion function introduced in (3)

is selected as where the constant

is chosen in accordance with the assumption stated in [9] that

guarantees existence and uniqueness of a solution for .

Consequently, the adaptive element of the controller must com-

pensate for nonlinearities of the system, parameter uncertainty,

and unmodeled actuator dynamics.

The linear compensator (15) that stabilizes the linear system

is designed as

(20)The above compensator places the poles of the closed-loop

system at , . The SPR filter is chosen as

(21)

A linearly parameterized NN with ten neurons is used with the

adaptation gains and . Pitch angle of

the arm is commanded to follow the output of a linear third-

order RM, designed with a pair of complex conjugate poles with

natural frequency rad s and damping , and a

real pole at s . A second-order RM would be sufficientto generate for the design. A third-order RM is

used to ensure that is continuous in case input to the RM is

not.

Results for two cases are presented. In the first case, the RM

is driven by a sum of three sinusoids with frequencies 1.5, 3,

and 4.5 rad/s, and in the second one it is driven by a series of

positive and negative step commands. Fig. 6 shows the results

for the first case. The upper two plots show the tracking perfor-

mance without PCH; the first plot depicts experimental results

performed without NN compensation and the second with NN

compensation. The dotted curves show the output of the RM and

the solid curves show the actual pitch angle. The lower two plots

show the responses with PCH turned on. As explained earlier,PCH modifies the output of the RM. The desired pitch attitude is

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Fig. 7. Commanded and applied control voltages for the sinusoidal inputs.

the unmodified RM command, shown with dashed lines. If this

command is not achievable with the supplied actuator and in-

verted plant models (just a double integrator for this example),

PCH modifies it and generates an estimate of the best achiev-

able command, shown with dash-dotted lines. This would be the

best achievable command if the actuator and the plant models

were exact. Since they are not, the dash-dotted lines shown in

the bottom two plots are estimates. Note that the dash dotted

lines are nearly indistinguishable from the actual response.

The top two plots show that the helicopter cannot track the

command without PCH, even when the NN is incorporated: the

system is unstable both with and without NN. The sharp cor-ners in the response curves correspond to instants when the heli-

copter arm hits the table. Experiments were stopped around

s to protect the helicopter. The instability encountered here is

not unexpected. The adaptive method requires knowledge of the

relative degree. The assumed relative degree of ignores

the dynamics of the actuators. When PCH is off, the actual rela-

tive degree as seen by the adaptive controller is , which vi-

olated a basic assumption in the overall approach. Nonetheless,

the most significant factor causing the instability is probably

control saturation observed in the following figure. The bottom

two plots in Fig. 6 with PCH show that modified RM commands

are tracked almost perfectly both with and without NN adapta-

tion. However, there is a significant improvement with NN adap-

tation since the RM commands, both with and without PCH, and

the helicopter response are all nearly identical.

Fig. 7 shows the commanded and applied controls cor-

responding to the results in Fig. 6. Vertical axis limits are

adjusted to focus on the applied voltage variations rather than

the commanded voltage variations. Without PCH, voltage ap-

plied to the motors is almost always saturated. It is not apparent

in the figure, but the amplitudes of the commanded voltages

without PCH gradually increase, a further indication that the

closed-loop system is unstable. The value of the voltage limit

( V) is treated as a known quantity, and used to model the

actuator limits in the PCH loop. In general, if it is not known,then it is preferable to use a conservative value for the limit.

Fig. 8. Output tracking and control activity of the model helicopter with step

inputs.

With PCH, the durations of periods of saturation are reduced,

and when adaptation is on, the saturation is almost completely

eliminated. One striking feature in Fig. 7 is the excessive noise

in the control activity when both NN and PCH are on. The

reason for the noisy control activity will be discussed at the end

of this section.

Results for the second case of step inputs are presented in

Fig. 8. Adaptation is on at the beginning, then it is turned off at

s and turned on again at s. PCH is on throughout

the experiment. The upper plot shows tracking performance, and

the lower plot shows the commanded and applied voltages. Thedashed and dotted curves show the RM outputs with and without

hedging. The response tracks the hedged RM output closely,

except when adaptation is turned off. When adaptation is off,

the response is very oscillatory, and the helicopter strikes the

table when commanded in the downward direction. The over-

shoot and oscillations are completely eliminated when adapta-

tion is on. After s disturbances are applied (by manu-

ally pushing on the helicopter frame) to demonstrate disturbance

rejection. Note that the second disturbance causes the control

signal to saturate for a while. The large error that occurs when

a disturbance is applied is due to the control voltage limit.

Both Figs. 6 and 7 exhibit a noisy control activity when adap-tation is on. This is due to the fact that a 12-b resolver (4096

counts per revolution) was used to measure the pitch angle of

the arm, which corresponds to approximately 0.1 deg. resolu-

tion. The staircase form of the feedback signal causes the NN

to generate sudden peaks to compensate the sudden changes in

the error signal, and leads to a noisy control signal as observed

in Figs. 6 and 7. In effect, the adaptive process views quanti-

zation error as modeling error, and attempts to adapt to it. The

development of a method for hedging that can be applied at the

sensor level remains a topic for future research. A higher res-

olution sensor would eliminate the noise in the control signal.

This fact has been verified in simulation. Fig. 9 shows simulated

control activity in which we employed models of a 12 b and24 b (16 777 216 counts per revolution) angular resolver, which

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Fig. 9. Control activity in simulation with 12-b and 24-b resolvers.

corresponds to approximately 2 resolution. Control

activity with a 12-b resolver is very noisy, similar to the exper-

imental results. Increasing the resolution of the sensor to 24 b

without changing any other parameter in the design eliminates

the noise-like activity in the control response.

V. SUMMARY

This paper presents experimental evaluation of a NN-basedadaptive output feedback control method applied to a labora-

tory model helicopter. The method is based on model inversion

with feedback linearization and uses a linearly parameterized

NN to cancel modeling errors. Also, a method for protecting

the adaptive element from the effects of unmodeled actuator dy-

namics and saturation has been employed. Experiments revealed

robustness of the method to parameter uncertainty, unmodeled

dynamics, and disturbances, and effectiveness of PCH in pro-

tecting the adaptive process during periods of control saturation.

REFERENCES

[1] D. W. Vos, L. Valavani, and A. H. von Flotow, Intelligent model ref-erence nonlinear friction compensation using neural networks and Lya-punov based adaptive control, in Proc. IEEE Int. Symp. Intelligent Con-trol, 1991, pp. 417422.

[2] T. Yabuta and T. Yamada, Neural network controller characteristicswith regard to adaptive control, IEEE Trans. Syst., Man, Cybern., vol.22, no. 1, pp. 170177, Jan.-Feb. 1992.

[3] S. I. Mistry, S. Chang, and S. S. Nair, Indirect control of a class ofnonlinear dynamic systems, IEEE Trans. Neural Netw., vol. 7, no. 4,pp. 10151023, Jul. 1996.

[4] D. Shukla, D. M. Dawson, and F. W. Paul, Real time adaptive controlexperiments with a multiple neural network based DCAL controller, inProc. IEEE Conf. Control Applications, 1997, pp. 371376.

[5] B. Bouzouia, M. Kadri, and N. Louam, Experimental neural decom-poseddynamic adaptive control of robot manipulator, inIEEE Int. Conf.Intelligent Robots and Systems, vol. 1, 1999, pp. 488493.

[6] C. Pereira, J. Henriques, andA. Dourado, Adaptive RBFNNversus con-ventional self-tuning: Comparison of two parametric model approachesfor nonlinear control, Control Eng. Practice, vol. 8, no. 1, pp. 312,Jan. 2000.

[7] J. Q. Gong and B. Yao, Neural network adaptive robust control withapplication to precision motion control of linearmotors,Int. J. AdaptiveControl Signal Process., vol. 15, no. 8, pp. 837864, Dec. 2001.

[8] C.-L. Hwang and C.-Y. Hsieh, A neuro-adaptive variable structure con-

trol for partially unknown nonlinear dynamic systems and its applica-tion, IEEE Trans. Contr. Syst. Technol., vol. 10, no. 2, pp. 263271,Mar. 2002.

[9] A. J. Calise, N. Hovakimyan, and M. Idan, Adaptive output feedbackcontrol of nonlinear systems using neural networks, Automatica, vol.37, no. 8, pp. 12011211, 2001.

[10] E. N.Johnson and A.J. Calise, Limited authority adaptive flight controlfor reusable launch vehicles, J. Guid. Control Dyn., vol. 26, no. 6, pp.906913, Nov.-Dec. 2003.

[11] A. T. Kutay, A. J. Calise, M. Idan, and N. Hovakimyan, Experimentalresults on adaptive output feedback control using a laboratory modelhelicopter, in Proc. AIAA Guidance, Navigation, and Control Conf.,2002, pp. 20024921.

[12] N. W. Kim, Improved methods in neural network based adaptive outputfeedback control, with applications to flight control, Ph.D. dissertation,Georgia Tech., Atlanta, GA, 2003.

[13] A. J. Calise, E. N. Johnson, M. D. Johnson, and J. E. Corban, Applica-

tions of adaptive neural-network control to unmanned aerial vehicles,in Proc. AIAA/ICAS Int. Air and Space Symp. and Exposition: Next 100Years, Dayton, OH, Jul. 2003.

[14] E. Lavretsky and N. Hovakimyan, Positive mu-modification for stableadaptation in a class of nonlinear systems with actuator constraints, inProc. ACC04.

Ali T. Kutay received the B.Sc. and M.Sc. degreesfrom the Aerospace Engineering Department,Middle East Technical University, Ankara, Turkey,in 1996 and 1999, respectively. He is currently

working toward the Ph.D. degree at the GeorgiaInstitute of Technology, Atlanta.

Anthony J. Calise (S63M74SM04) was a Pro-fessor of Mechanical Engineering at Drexel Univer-sity, Philadelphia, PA, for eight years prior to joiningthe faculty at theGeorgia Institute of Technology, At-

lanta. He also worked for ten years in industry for theRaytheon Missile Systems Division and DynamicsResearch Corporation, where he was involved withanalysis and design of inertial navigation systems,optimalmissileguidance, and aircraft flight path opti-mization. Since leaving industry, he has worked con-

tinuously as a consultant for19 years.He is theauthorof over 150 technical reports and papers. The subject areas that he has publishedin include optimal control theory, aircraft flight control, optimal guidance ofaerospace vehicles, adaptive control using neural networks, robust linear con-trol, and control of flexible structures. In the area of adaptive control, he hasdeveloped a novel combination for employing neural-network-based control incombination with feedback linearization. Applications include flight control offighter aircraft, helicopters, and missile autopilot design. He is a former Asso-ciate Editor for the Journal of Guidance, Control, and Dynamics.

Dr. Calise was the recipient of the USAF Systems Command Technical

Achievement Award, and the AIAA Mechanics and Control of Flight Award.He is a Fellow of the AIAA and an Associate Editor for the IEEE C ONTROLSYSTEMS MAGAZINE.

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Moshe Idan received the B.Sc. and M.Sc. degreesfrom the Aerospace Engineering Department atthe Technion-Israel Institute of Technology, Haifa,Israel, in 1983 and 1986, respectively, and thePh.D. degree from the Department of AerospaceEngineering, Stanford University, Stanford, CA, in1990.

Since 1991, he has been with the Department of

Aerospace Engineering, TechnionIsrael Institute ofTechnology. From 2000to 2001, he spent a sabbaticalin the School of Aerospace Engineering, Georgia In-

stitute of Technology, Atlanta. His research concentrates on robust and adaptiveflight control system design techniques and applications.

Naira Hovakimyan (M01SM02) received thePh.D. degree in physics and mathematics from theInstitute of Applied Mathematics, Russian Academyof Sciences, Moscow, in 1992.

After receiving the Ph.D. degree, she joinedthe Institute of Mechanics, Armenian Academy ofSciences, as a Research Scientist, where she workeduntil 1997. In 1997, she was awarded a governmental

postdoctoral scholarship to work at INRIA, France.The subject areas in which she has published includedifferential pursuit-evasion games, optimal control

of robotic manipulators, robust control, adaptive estimation, and control. In1998, she wasinvited to the School of AerospaceEngineering, Georgia Instituteof Technology, Atlanta, where she worked as a Research Faculty Memberuntil 2003. In 2003, she joined the Department of Aerospace and OceanEngineering, Virginia Polytechnic Institute and State University, Blacksburg,an Associate Professor. She has authored over 90 refereed publications. Hercurrent interests are in the theory of adaptive control and estimation, neuralnetworks, and stability theory.

Dr. Hovakimyan received the SICE International Scholarship for the bestpaper of a young investigator in the VII ISDG Symposium, Japan, 1996. She isalso the receipient of the 2004 Pride @ Boeing Award. She is a Senior Memberof AIAA, a Member of AMS and ISDG, and is an Associate Editor for the IEEEControlSystems Society, theIEEE TRANSACTIONS ON NEURAL NETWORKS, andthe International Journal of Control Systems and Automation.

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