14 IEEE CONTROL SYSTEMS MAGAZINE » JUNE 2007

» P E O P L E I N C O N T R O L

DOMITILLA DEL VECCHIO

Q. Thank you for speaking with IEEECSM.

Domitilla: You’re welcome!

Q. There is increasing interest inhybrid systems. What, exactly, is ahybrid system?

Domitilla: A hybrid system is onewith continuous dynamics and discretedecisions. In the most general form,these systems are represented by contin-uous variables that evolve according todifferential equations as well as by dis-crete variables that evolve according tologic rules. A typical example is a multi-robot system, in which continuous vari-ables represent the position and velocityof a robot, while discrete variables regu-late the internal communication andcoordination protocol among the robots.Traffic systems are also intrinsicallyhybrid since the drivers can decide toswitch the dynamics of their vehiclefrom the “stop” mode to the “go” mode,and from the “go straight” mode to the“turn left” mode. In each one of thesemodes, however, the vehicle dynamicsare continuous.

Q. One of your papers involves whathappens at a traffic intersection. I’veoften thought that there is a “regionaltraffic culture” in the sense that driversin some areas abide by certain, unwrit-ten rules of behavior and etiquette. Isthat possible? More to the point, whathave you learned by observing andmodeling traffic?

Domitilla: In our 2004 ICRA papercoauthored with Richard Murray andClaire Walton, the objective was tounderstand to what extent human deci-

sions are predictable in a structuredenvironment such as a traffic intersec-tion. For example, given the configura-tion of vehicles at a traffic intersection,when does a driver consider it safe tocross the intersection? When is a left turnperformed? To answer these questions,we constructed a traffic intersectionemulation in our lab, in which human

drivers were remotely driving smallvehicles through the intersection. Yield-ing rules were established a priori, andthe drivers were asked to respect themwhile crossing the intersection. The vehi-cles’ trajectories were recorded by anoverhead camera system and fed to alearning algorithm. The learning algo-rithm had to (without a priori knowl-edge of the yielding rules) learn from thedriver trajectories the most likely yield-ing rules used by the drivers. Further-more, the algorithm had to predict,based on the learned yielding rules, thetime trajectories of each driver at theintersection in new experiment sessions.By these experiments, we found that thedecisions drivers make at a traffic inter-section can be predicted with about an80% success rate.

Q. In your work on gene networks,you refer to implementing a circuit inE. coli. How does one go about doingthat? What do you expect to learn?

Domitilla: By circuit, I abstractlyrefer to a network of activation andrepression interactions among species.In a living system, such as the bacteria

In this issue of IEEE Control Systems Magazine, we speak with Domitilla Del Vec-

chio, assistant professor in the Electrical Engineering and Computer Science

Department of the University of Michigan in Ann Arbor. Prof. Del Vecchio’s research

interests include modeling, estimation, and control of systems with hybrid dynamics.

She has worked on a wide range of applications, including multirobot systems, gene

regulatory networks, and human motion recognition.

We also speak with Athanasios (Thanos) Antoulas of the Department of Electrical

and Computer Engineering at Rice University. Prof. Antoulas was born in Athens,

Greece, and studied at ETH Zurich. His research interests focus on dynamical sys-

tems and computation, especially model reduction. He is the author of the recent

book Approximation of Large-Scale Systems published by SIAM and is an editor-in-

chief of Systems and Control Letters.

Traffic and Weather

Domitilla Del Vecchio, assistant professor inthe Electrical Engineering and ComputerScience Department of the University ofMichigan in Ann Arbor. Professor Del Vec-chio’s interests involve systems with contin-uous and discrete dynamics withapplications to traffic systems, multirobotsystems, and gene regulatory networks.

JUNE 2007 « IEEE CONTROL SYSTEMS MAGAZINE 15

E. coli, the species under considerationare typically proteins, which regulatethe most fundamental functions in liv-ing creatures. Activation and repres-sion interactions among proteins areobtained in various ways, in particularthrough protein-DNA binding with themechanism of gene transcriptional reg-ulation. Implementing a circuit designin bacteria involves designing the geneDNA sequences that create networks ofactivation and repression interaction.The implementation in bacteria of a cir-cuit with a theoretically predictedbehavior can teach researchers funda-mental facts. In particular, we (as con-trol systems engineers) hope tounderstand to what extent modularityassumptions and input/output charac-terization of blocks, which are com-monly used in control systems and inelectronics, are in fact legitimate in abiomolecular network. What input/out-put characterizations of blocks (ifany) are appropriate for networks ofgene activations and repressions? Howshould blocks be interconnected? Theanswer to these questions may lead tonew systems principles and to the needfor developing more fundamental sys-tems theory.

Q. How did you become interested inthese problems?

Domitilla: I have been fascinated bythe idea of doing engineering with bio-logical hardware since I was in highschool and people were talking about

genetic engineering. The first opportuni-ty I had to work on the topic was towardthe end of my Ph.D. at Caltech.

Q. You’ve been involved in a lot ofdiverse research projects. Do you feelyou’ve benefited from this broadexposure?

Domitilla: I have definitely benefitedfrom a broad exposure, and for this Ihave to thank my Ph.D. adviser, RichardMurray. Before my Ph.D. I focused on avery narrow set of topics and techniques.This focus was useful for teaching me tolook at the same problem from differentperspectives and for applying multipledisciplines to a problem at hand. As amatter of fact, part of my Ph.D. disserta-tion is based on using computer sciencetools to solve a control problem in acomputationally efficient way. This typeof solution is a result of being exposed tocomputer science techniques.

Q. Can you describe the laboratoryyou’re developing for your researchprojects?

Domitilla: I am currently developinga multi-agent decision and control test-bed. The test-bed is composed of 30-cmlong scaled vehicles (three at themoment, 12 in the final configuration)with onboard computer and wirelesscommunication in an arena of about 6 ×6 m equipped with a positioning systememulating GPS. A distinctive feature ofthese vehicles is that a motion controlleremulates the scaled driveline and steer-

ing dynamics of a Hummer vehicle,including transmission dynamics andmotor maps provided by my colleagueHosam Fathy in the Mechanical Engi-neering Department. The onboard com-puter provides steering, braking, andthrottle inputs, and, by virtue of the scal-ing, will be able to run the same low-level control algorithms developed for afull-scale vehicle. This scaling makes thetestbed suitable for testing distributedcontrol algorithms of multi-agent sys-tems arising in intelligent transportation.

Q. Although you’ve been teaching fulltime for less than a year, do you haveany advice you wish to share withfuture new instructors?

Domitilla: Actually, I have beenteaching full time for exactly one yearnow. I do not have any specific adviceother than the one that I keep giving tomyself: “Be focused!”

Q. What are some of your interestsoutside of teaching and education?

Domitilla: My main interests are run-ning long distances, backpacking andhiking in the mountains, and skiing.When I was in Italy I regularly hiked forweek-long periods in the Alps. Sincebeing in the United States, I have goneon several multiple-days hikes in theSierras.

Q. Thank you for speaking with IEEECSM.

Domitilla: You’re most welcome!

ATHANASIOS C. ANTOULAS

Q. I’d like to start by asking aboutyour educational background. Howdid your education lead you to thesystems and control field?

Thanos: I studied at ETH inZurich, where I received degrees inboth electrical engineering and math-ematics. At first I planned to studymathematical physics in graduateschool. While I was finishing mydiploma thesis in mathematics, how-ever, I heard that someone named

Rudy Kalman was coming to ETH. Irecognized the name from the Kalmanfilter, which we had learned about inone of my undergraduate classes.After consulting Eduard Stiefel (oneof the key people in applied mathe-matics at ETH at the time) ProfessorKalman offered to become my Ph.D.advisor provided that I already hadone publication, which was the case.Hence began my journey in the sys-tems and control field.

I should also add that during myfirst semester of graduate studies,

Kalman was on leave and had invitedJan Willems to replace him. Thus, myfirst mentor was Jan, whose influenceon my research direction and tastewas significant and with whom I stillhave a close relationship.

Q. One of the key themes in yourresearch has been “rational interpo-lation.” What is rational interpola-tion, and why is it a fundamentalproblem in systems theory?

Thanos: The rational interpolationproblem is concerned wi th the

16 IEEE CONTROL SYSTEMS MAGAZINE » JUNE 2007

construction of rational matrix func-tions from (usually finitely many) sam-ples of their values. In particular onemay wish to construct solutions com-patible with the data that satisfydegree constraints and norm con-straints or are positive real. Rationalinterpolation is fundamental in systemtheory because for linear systems theproblem is related to the constructionof the state from input/output mea-surements. For instance, if we aregiven impulse response data, then wehave the realization problem. For arbi-trary (not necessarily impulseresponse) measurements, which maybe inaccurate (corrupted with noise),then we have the system identificationproblem. Furthermore, the interpolationproblem comes up prominently inmodel reduction, where the goal is toreplace a high-order model with a modelof significantly reduced complexity.

Q. Congratulations on your recentbook, Approximation of Large-ScaleDynamical Systems! What did you setout to accomplish with this volume?

Thanos: Physical as well as artifi-cial processes are described mainly bymathematical models, which can beused for simulation, control, or designoptimization. The weather and verylarge scale integration (VLSI) chipsare examples of such processes. In thisframework of mathematical models,there is an ever-increasing need forimproved accuracy, which leads tomodels of high complexity.

The basic motivation for systemapproximation is the need for simpli-fied models that capture the main fea-tures of the original complex model.This need arises from limited compu-tation, accuracy, and storage capabili-ties. The simplified model is thenused in place of the original complexmodel to accomplish the tasks men-tioned above, namely, simulation,control, or design optimization.

The aim of my book is to provide acomprehensive picture of modelreduction, that is, system approxima-tion. The book’s distinctive feature isthe combination of system theory on

the one hand with numerical linearalgebra and computational considera-tions on the other. My goal was toprovide insight into the issue ofmodel reduction and the ensuingtradeoffs between accuracy andcomplexity.

More precisely, the book addressesthe approximation of dynamical sys-tems that are described by a finite setof differential or difference equations,together with a finite set of algebraicequations. First, approximation meth-

ods are presented that are related tothe singular value decomposition(SVD), such as balanced truncation.Then, approximation methods relatedto Krylov or moment matching con-cepts are discussed. Roughly speak-ing, the SVD algorithms preserveimportant properties of the originalsystem, such as stability, and in addi-tion provide an explicit quantizationof the approximation error. AlthoughKrylov concepts lack these properties,they lead to methods that can beimplemented in a numerically moreefficient way. Thus, while SVD meth-ods can be applied to relatively low-dimensional systems, Krylov methodsare applicable to problems whosecomplexity can be several orders ofmagnitude higher. Combining thesetwo approximation methods leads toa third one, namely, SVD-Krylov-based approximation, which aims at

merging their salient features and isiterative in nature.

Q. How do your current researchinterests impact model reductionproblems?

Thanos: The challenge in modelreduction is to combine system-theo-retic considerations with those arisingin large-scale computation. I willmention two examples in this regard,one from linear algebra and the otherfrom system theory.

The first is the eigenvalue problem,which in principle can be solved intwo steps. The first step is the deter-mination of the eigenvalues as rootsof the characteristic polynomial, andthe second is the determination of theeigenvectors as solutions of sets of lin-ear equations. In many cases thisapproach works well in practice whenthe dimension of the matrix is small.Even then, however, it can fail; thisfailure prompted the development ofthe QR algorithm in numerical linearalgebra. (The QR algorithm factors agiven matrix as a product of anorthogonal matrix and an upper trian-gular matrix.) But for large matrices(with dimension in the thousands ormillions) this procedure has nochance of being carried out success-fully due to numerical problems. Insuch cases a different approach is nec-essary. Such an approach is offered byiterative methods. In other words, forlarge matrices one can hope to com-pute only a few “significant” eigen-values and their correspondingeigenvectors by means of a smallnumber of iterations, where “signifi-cant” is context dependent. Forinstance the Google algorithm fordetermining page rank is based on thecomputation of the eigenvector corre-sponding to the dominant eigenvalueof a matrix of size a few billion (thenumber of internet nodes) andinvolves one or two iterations eachtime that the page rank is updated.

The second example is concernedwith the physical verification of VLSIchips, which are complex devices. ThePentium IV chip for instance, contains

Athanasios (Thanos) Antoulas, Departmentof Electrical and Computer Engineering, RiceUniversity. Prof. Antoulas’s interests includedynamical systems and computation with anemphasis on model reduction.

JUNE 2007 « IEEE CONTROL SYSTEMS MAGAZINE 17

over 40 million components, andoperates at a speed of 2 GHz. Onemeasure of the complexity of this chipis that it consists of seven layers, andanother is the fact that the length ofthe interconnections among the vari-ous components (the interconnect) is ofthe order of 2 km. The lowest of theseven is the semiconductor layer,which contains all of the transistors.Given their density, there is no roomfor connections at that layer. There-fore, two of the upper (metal) layersare dedicated to establishing the nec-essary connections between the indi-vidual transistors and the externalsupply voltage source; these layersare known collectively as the powergrid supply network. The trend in VLSIdesign has been following Moore’slaw, which states that the number oftransistors on an integrated circuitdoubles every 18 to 24 months. Thisfact, however, has made communica-tion between the transistors ratherthan processing within the transistors,a bottleneck in chip performance.

One of the issues in this context ispower supply. In order to ensureproper operation of the chip, eachtransistor needs to be supplied with aconstant voltage. There is usually oneexternal voltage source per chip,whose voltage needs to be distributedto all of the transistors. One of thechallenging problems in the physicalverification of the overall chip ischecking the integrity of the voltageon the power grid. In particular, it isnecessary to ensure that each transis-tor receives a voltage whose value iswithin a given range.

This verification proceeds by mod-eling the power grid supply network,which involves the discretization ofMaxwell’s equations, taking intoaccount the particular geometry of theseven layers making up the chip. Thisprocess leads to linear RLC (resistor-inductor-capacitor) circuits withroughly as many nodes as there aretransistors. Besides the external volt-age supply source, each transistoroperating at a given time is modeledas an input current source. Thus, a

typical model for the power grid maycontain about 10 million state vari-ables and 1 million inputs. Such mod-els can be simulated only after theyhave been appropriately reduced tomodels of complexity a few hundredstate variables. Furthermore, thereduced models must be imple-mentable as RLC circuits.

Thus, although model-reductionmethods (such as balanced trunca-tion) with important attributes arewell known in the systems and con-trol community, they often cannot becarried out in large-scale applications.A further constraint arising in thepower-grid problem is that thereduced model must be passive (thatis, realizable in terms of RLC compo-nents). A general methodology forsolving passivity-preserving model-reduction problems applicable tolarge-scale systems is based on thedevelopment of iterative methods.Our approach in this regard showsthat the key ingredients of one suchmethod are the spectral zeros of theoriginal system. Furthermore,through the Hamiltonian matrix ofthe system one can compute a passivereduced-order system by means ofiterative eigenvalue computationsapplied to the Hamiltonian matrix.

Q. In your opinion, what are someof the fundamental open problemsin system theory?

Thanos: One of the fundamentalresearch challenges facing system the-ory is dealing with complexity, forwhich there already exist severalremedies. In our framework, theresulting algorithms must satisfy thefollowing constraints. First, they mustbe efficient, that is, scale—at most—with the square of the problemdimension n; second, they must pro-duce an answer in a given amount oftime; and third the solution must beaccurate enough for the application athand (which is a problem given thatcomputers are finite-precisiondevices). In addition, system-theoreticproperties such as stability and pas-sivity must be preserved. Thus, model

reduction for complex and structuredsystems satisfying these broad numer-ical and system-theoretic criteria is animportant, mostly open, problem.

Here is a partial list of more spe-cific problems:

» Model reduction for uncertainsystems described by boundaryvalue partial differential equa-tions (PDEs) and after discretiza-tion by differential-algebraicequations (DAEs).

» Development and validation ofcontrol algorithms for complexsystems, as they arise, forinstance, in active control ofhigh-rise buildings, based onreduced models.

» Model reduction and dataassimilation, for instance, inweather prediction. In dataassimilation, together withequations describing the sys-tem, measurements are avail-able. Hence, what is needed is asort of reduced complexityobserver or Kalman filter.

» The study of microelectro-mechanical systems (MEMS),more generally, the study ofmulti-physics systems, and theassociated model-reductionproblems that must respect themultiphysics aspect of thesesystems.

» Design and verification of VLSIchips.

» Prediction and engineering of thefunction of complex moleculesby means of molecular dynamicssimulations. In this case, sam-pling issues arise because of themultiple scales involved, rang-ing all the way from femtosec-onds to milliseconds.

» Nanostructure simulation. Manynano-devices are currently beingdeveloped. After the physics ofthese new devices has been clar-ified, the next task consists inverifying that they work asintended. Given the complexi-ties involved, this task is expect-ed to require simulations thatdepend on model reduction.

18 IEEE CONTROL SYSTEMS MAGAZINE » JUNE 2007

Q. Have you thought about yournext book?

Thanos: It will probably be a revi-sion of the SIAM book.

Q. Many readers know your name aseditor-in-chief of Systems and ControlLetters (SCL). Can you talk a littleabout the history of SCL, as well assome of the topics that it has covered?

Thanos: SCL was founded by JanWillems. The first issue appeared in July1981. He and Roger Brockett were edi-tors-in-chief for the first seven years.Thereafter, and until 1995, Jan was thesole editor-in-chief. When Jan steppeddown, Iven Mareels of the University ofMelbourne and I took over as editors-in-chief. We have tried to keep the qualitystandard high while at the same timeputting on center stage recent results in avariety of areas by means of specialissues. Thus, during the past decade wehad special issues on topics that include

nonlinear systems (twice), adaptive con-trol, behavioral system theory, Lie theoryand its applications in control, hybridsystems, learning systems, chaos andsynchronization, and optimization andcontrol of distributed parameter systems.

Q. How would you describe yourvision for SCL, and its publicationniche, say, in comparison to IEEE Trans-actions on Automatic Conrol (TAC)?

Thanos: In many ways SCL, TAC,and Automatica are comparable. Iwould say that SCL is somewhat moretheory friendly than Automatica, and itspublication procedure is somewhat lessinvolved than that of TAC. I think thatSCL is perceived as more flexible thanboth. This perception gives SCL a repu-tation of being more open minded fornew ideas and less of a referee-pain.Finally, it is worth mentioning that SCLis listed in the citation indices of mathe-matics, engineering, and econometrics.

Q. Which courses do you prefer toteach at Rice?

Thanos: I like teaching signalsand linear systems at all levels. Inthe past few years I have concen-trated on teaching model reductionto both undergraduate and gradu-ate students. These courses are partsystem theory and part numericallinear algebra, with applications inthe foreground. The graduatecourses are often taught jointlywith colleagues from the Computa-tional and Applied MathematicsDepartment at Rice.

Q. How do occupy yourself outsideof teaching and research?

Thanos: I enjoy reading Greek lit-erature.

Q. Thank you for speaking withIEEE CSM.

Thanos: It was my pleasure!

Ari ArapostathisUniversity of Texas at Austin

For contributions in

nonlinear and stochastic

control and applications

in power systems.

Ari Arapostathis re-ceived a Ph.D. in elec-trical engineering in

1982 from the University of California,Berkeley. Since 1982, he has been at theUniversity of Texas at Austin, where heis professor of electrical and computer

engineering, and an affiliate of the com-putational and applied mathematicsgraduate program. His research inter-ests include stochastic and adaptivecontrol theory, hybrid systems, andapplications to interconnected powersystems. He has served on the editorialboard of the IEEE Transactions on Auto-matic Control and the Journal of Mathe-matical Systems, Estimation, and Control.

Richard D. BraatzUniversity of Illinois at Urbana-Champaign

For contributions in

robust control of

industrial systems.

Richard Braatz receiv-ed a B.S. degree fromOregon State Universi-ty in 1988 and M.S.

and Ph.D. degrees from the CaliforniaInstitute of Technology in 1991 and

1993, respectively. He is currently theMillennium Chair and professor at theUniversity of Illinois at Urbana-Cham-paign, where he holds appointments infour engineering departments.

Prof. Braatz’s research interests arein the robust control of industrial sys-tems with high system complexity,nonlinearities, spatial variations,unstable zero dynamics, and input,output, and state constraints. Prof.Braatz is a coauthor of two patents,over 100 journal papers, and threebooks, including Identification andControl of Sheet and Film Processes andFault Detection and Diagnosis in Indus-trial Systems. He is a recipient of theDonald P. Eckman Award, the CurtisW. McGraw Research Award, theIEEE Transactions on Control SystemsTechnology Outstanding PaperAward, and the Antonio RubertiYoung Researcher Prize. Prof. Braatzis the chair of the IEEE CSS TechnicalCommittee on Industrial Process Con-

2007 CSS Fellows

Election to the grade of IEEE Fel-

low acknowledges outstanding

contributions and exceptional profes-

sional distinction. We are pleased to

present the IEEE Control Systems

Society members who have been

accorded this honor for 2007.