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c© 2008 MTNSAll rights reserved. No part of the publication may be reproduced in any form by print, photoprint, microfilmor any other means without permission from the organizers.

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Contents

Welcome v

Sponsors vi

Committees vii

Announcing MTNS 2010 viii

Additional Information 1Steering Committee Meeting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Opening Reception . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Banquet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1Internet Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Plenary Lectures 2Symmetry Breaking and Synchrony Breaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Integrating human and robot decision-making dynamics . . . . . . . . . . . . . . . . . . . . . . . . 3Nonlinear observer design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5New Directions in the Application of Model Order Reduction . . . . . . . . . . . . . . . . . . . . . 7Contagion as a Practical Example of Informatic Support of the Analysis of Complex Interdependent

Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Semi-Plenary Lectures 11Controllability of distributed parameter systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11System theory over finite algebras — count your blessings . . . . . . . . . . . . . . . . . . . . . . . 13When Control Theory Meets Neuroscience . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15New perspectives in algebraic systems theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17Estimation and Identification of Metabolic Systems Models from Time-Series Data . . . . . . . . 19Use of Dynamic Quantizers for Discrete-Valued Input Systems . . . . . . . . . . . . . . . . . . . . 21Duality of Infinite Dimensional Linear Programming and Its Applications to Control Problems . . 23Control in a Behavioral Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25Nonlinear model predictive control without terminal constraints: stability, performance and design 27The Role of Lie Brackets in Stability of Linear and Nonlinear Switched Systems . . . . . . . . . . . 29Structured versus Unstructured Perturbations for Analysis of Dynamical Systems . . . . . . . . . . 30Overdetermined Multidimensional Systems: A Survey . . . . . . . . . . . . . . . . . . . . . . . . . 31Problems of control and system theory of biochemical reaction systems . . . . . . . . . . . . . . . . 33On the zero-modules of spectral factors using state space methods – the role of a coupled Sylvester-

homogeneous linear equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34A unifying formalism of instabilities, nonlinear dynamics, and statistical mechanics for unsteady

shear flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

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Special Sessions at MTNS 2008 37

Program at a Glance 40

Detailed program listing 45Monday, July 28 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45Tuesday, July 29 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50Wednesday, July 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Thursday, July 31 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57Friday, August 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

List of Abstracts 68Monday, July 28 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68Tuesday, July 29 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86Wednesday, July 30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105Thursday, July 31 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105Friday, August 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

Index of Authors, Chairs, and Organizers 136

Welcome to MTNS 2008

On behalf of the Organizing Committee of MTNS 2008, I welcome you to the 18th edition ofMTNS, the International Symposium on the Mathematical Theory of Networks and Systems.

The symposium is organized every two years and traditionally covers areas involving awide range of research directions in mathematical systems, networks and control theory.Mathematical methods which play a role in the areas mentioned above stem from a broadrange of fields of pure and applied mathematics, including ordinary and partial differentialequations, real and complex analysis, numerical analysis, probability theory and stochasticanalysis, operator theory, linear and commutative algebra as well as algebraic and differ-ential geometry. There is a wide range of applications ranging from problems in biology,communications and mathematical finance to problems in chemical engineering, aerospaceengineering and robotics. More recent themes include Linear Matrix Inequalities and newparadigms in traditional control areas, new systematic approaches to model reduction withresultant broad range of model-reduction applications, new uses of commutative algebra andalgebraic geometry in the behavioral approach to system theory, especially to multidimen-sional system theory, as well as the inux of new opportunities for application of engineeringparadigms in emerging areas such as mathematical biology and finance.

MTNS 2008 features a total of 20 plenary and semi-plenary talks by some of the leadingresearchers in the area of systems and control. In addition MTNS 2008 has 15 invited SpecialSessions covering a variety of these recent developments, as well as Regular Sessions on some20 additional identifiable topics for a total of some 300 presentations; unfortunately, noone person can go to all of them! Members of the Steering Committee as well as the LocalOrganizing Committee were actively involved in the planning and organizing of the program;I would like to express my sincere thanks to the members of these committees. I would alsolike to express special gratitude to all those who helped organize special sessions; this workgoes a long way toward ensuring the success of MTNS.

MTNS 2008 received generous support from the Air Force Office of Scientific Researchand the National Science Foundation as well as from various colleges and departments atVirginia Tech. This support was crucial enabling many young researchers to participate inMTNS 2008.

We hope that you will find the 18th edition of MTNS interesting and stimulating.

Joseph A. Ball,MTNS 2008 Symposium Chair

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Sponsors

• Air Force Office of Scientific Research (PR08-959)

• National Science Foundation (DMS-0758242)

• Virginia Bioinformatics Institute.

• Virginia Tech College of Engineering

• Virginia Tech College of Science

• Virginia Tech Department of Mathematics

• Virginia Tech Department of Electrical & Computer Engineering

• Virginia Tech Department of Aerospace & Ocean Engineering

• Virginia Tech Interdisciplinary Center for Applied Mathematics

Cooperative Agreement: This conference has been organized in cooperation withthe Society for Industrial and Applied Mathematics (SIAM).

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Committees

MTNS Steering Committee/Program Committee

Athanasios C. Antoulas Yoshito OhtaJoseph A. Ball (Vice Chair: 2006-2008) Pablo Parrilo

Vincent D. Blondel Giorgio PicciChristopher Byrnes Andre C. M. Ran

Bart de Moor Anders RantzerHarry Dym Joachim Rosenthal

Tryphon T. Georgiou Malcolm C. SmithUwe Helmke Olof Staffans

J. William Helton Paul van DoorenMargreta Kuijper Arjan van der Schaft

Aleksandr Borisovich Kurzhanski Victor VinnikovAnders Lindquist Yutaka Yamamoto (Chair: 2006-2008)

Iven Mareels Eva Zerz

Honorary members

• Charles A Desoer

• Israel Gohberg

• Robert W.Newcomb

• Armen H. Zemanian

MTNS 2008 Organizing Committee

• Joseph A. Ball (Chair)

• Athanasios C. Antoulas

• Christopher A. Beattie

• Tryphon T. Georgiou

• Serkan Gugercin

• Ekehard Sachs

• Craig A. Woolsey

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Announcing MTNS 2010

19th International Symposium onMathematical Theory of Networks and Systems

Eotvos Lorand University,BudapestJuly 5-9, 2010

MTNS 2010 will take place on the campus of the Faculty of Sciences of the Eotvos LorandUniversity, in a complex of newly erected buldings in the south of Buda, next to the Danube,having excellent technical equipment, air-conditioning, and other facilities (including inter-net connections), to host conferences of the size of MTNS. See

http://www.elte.hu/kepcsarnok/lagymanyos

Lunch will be provided on site. The conference site is in walking distance of most majorhotels - at which reservations have been made for MTNS 2010.

The technical organization will be carried out by Scope Ltd., a company located in ourInstitute, MTA SZTAKI, with an excellent record in conference organization, including theIFAC World Congress in Budapest, 1984, and more recently, the World Science Forums inBudapest.

The formal division of responsibilites will be:

General chair: Gyorgy Michaletzky, Dean of Faculty of ScienceIPC Chair: Laszlo Gerencser,

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http://www.elte.hu/kepcsarnok/lagymanyos

Additional Information

Steering Committee Meeting

Steering Committee meeting (includes lunch): Tuesday July 29, 12:30 - 14:30 at the Old Guard (inside thePreston Center restaurant at the conference site)

Opening Reception

Sunday, July 27 starting 18:00 in Latham Ballroom

Banquet

Wednesday, July 30 starting 18:30 in Latham BallroomGuest Musicians: No Strings Attached - a prominent hammer dulcimer folk band playing traditional

music of the future (http://www.enessay.com/index.html)

Internet Connection

Free wireless service is available; some public terminals will be available.

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http://www.enessay.com/index.html

Plenary Lectures

Symmetry Breaking and Synchrony Breaking

Martin Golubitsky, Ohio State University

Monday, July 28, 09:00–10:00, Latham A/B

A coupled cell system is a network of interacting dynamical systems. Coupled cell modelsassume that the output from each cell is important and that signals from two or more cellscan be compared so that patterns of synchrony can emerge. Network architecture is a graphthat indicates which cells have the same phase space, which cells are coupled to which, andwhich couplings are the same. We ask: Which part of the qualitative dynamics observed incoupled cells is the product of network architecture and which part depends on the specificequations?

In our theory local network symmetries replace sym-metry as a way of organizing network dynamics, andsynchrony-breaking replaces symmetry-breaking as a basicway in which transitions to complicated dynamics occur.In this talk we will survey some of the theory and some ofthe interesting examples. In older work we showed how thesymmetries of quadrupedal gaits led to a ’simplest’ structurefor quadruped locomotor central pattern generators and tothe prediction of an unusual gait. In more recent work wehave shown that feed forward structures in networks canlead naturally to a simple method for constructing nonlin-ear filter/amplifiers.

Martin Golubitsky is Distinguished Professor of Mathematical and Physical Sciences atThe Ohio State University. His research has been in the theory and application of bifurcationsin the presence of symmetry, a subject on which he has co-authored three graduate texts.Recently, Golubitsky has studied network dynamics with an eye towards applications inneuroscience. He is a past president of SIAM and a Fellow of the American Academy ofArts and Sciences. In September Golubitsky will become the Director of the MathematicalBiosciences Institute.

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Integrating human and robot decision-making dynamics

Integrating human and robot decision-making dynamics

Naomi Ehrich Leonard, Princeton University

Tuesday, July 29, 09:00–10:00, Latham A/B

The superior ability of humans to recognize pattern and extract structure from data makeshuman decision-making invaluable to performance of complex tasks in uncertain, changingenvironments. On the other hand, there is tremendous advantage to automating cooperativetasks with multi-agent robotic systems as has been witnessed, for example, in the growingsuccess of mobile sensor networks. Of great interest is to investigate how humans androbots can best jointly contribute to decision-making. Psychologists and behavioral scientistsperform experiments with human subjects and develop models to study human decision-making; for example, there is an ample literature on a class of sequential binary decision-making called the two-alternative forced-choice task [1,2,3]. In this task, the human subjectchooses between two options at regular time intervals and receives a reward after each choice.Interestingly, these experiments show convergence of the aggregate behavior to rewards thatare often suboptimal.

We introduce a decision-making problem associated witha complex task that integrates human and robotic decision-making dynamics with feedback. The setting is a human-supervised collective robotic foraging problem, where thehuman decision-making takes the form of a two-alternativeforced-choice task and the reward report is a feedback fromthe robots. This allows direct use of the results from psy-chology to study how the human will behave.

To explore the integrated decision dynamics, we presenttwo models of human decision-making: one is the win-stay,lose-switch model and the other is a deterministic limitof the popular drift diffusion model. With these modelswe prove convergence of the human behavior to the ob-served aggregate decision-making for reward structures withmatching points. Since behavior converges to suboptimalperformance, we show how adaptive laws for the robot feed-back that use only local information can be applied to helpthe human make optimal decisions.

This is joint work with Ming Cao and Andrew Stewart. Papers are electronically availableat http://www.princeton.edu/∼naomi.

[1] D. M. Egelman, C. Person, and P. R. Montague. A computational role for dopaminedelivery in human decision-making. Journal of Cognitive Neuroscience, 10:623–630, 1998.

[2] R. Herrnstein. Rational choice theory: necessary but not sufficient. American Psy-chologist, 45:356–367, 1990.

[3] P. R. Montague and G. S. Berns. Neural economics and the biological substrates of

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http://www.princeton.edu/�naomi

PLENARY LECTURES

valuation. Neuron, 36:265–284, 2002.

Naomi Ehrich Leonard is Professor of Mechanical and Aerospace Engineering and as-sociated faculty member of the Program in Applied and Computational Mathematics atPrinceton University where she has been since 1994. In 2001 she was the Lise Meitner GuestProfessor at Lund University, Sweden and in 2007 a Visiting Professor at University of Pisa,Italy. She received the B.S.E. degree in mechanical engineering from Princeton University in1985. From 1985 to 1989, she worked as an engineer in the electric power industry. She re-ceived the M.S. and Ph.D. degrees in electrical engineering from the University of Marylandin 1991 and 1994. Her research is in nonlinear control and dynamics with current interestsin cooperative control for multi-agent systems, mobile sensor networks, adaptive ocean sam-pling, collective behavior in animal groups and decision dynamics in mixed human/robotteams. She became an IEEE Fellow in 2007 and received the Mohammed Dahleh Award(2005), John D. and Catherine T. MacArthur Foundation Fellowship (2004), AutomaticaPrize Paper award (1999), ONR Young Investigator Award (1998) and NSF CAREER Award(1995). She has served as associate editor for Automatica and SIAM Journal on Control andOptimization.

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Nonlinear observer design

Nonlinear observer design

Alessandro Astolfi, Imperial College London

Wednesday, July 30, 09:00–10:00, Latham A/B

The problem of observer design for nonlinear, deterministic, finite-dimensional systems isdiscussed. We initially provide a survey of existing results for linear and nonlinear systems,pointing out open problems and directions of research. We then focus on the problem ofglobal observer design for nonlinear systems, highlighting the role of normal forms, of input-state-output properties, of invariant manifolds and of an extended notion of homogeneity.The classical results in [5, 6] and Luenberger’s ideas [9, 10], with their nonlinear enhancementproposed in [8] and further developed in [12, 1], are the point of departure for the constructionof global observers. We discuss in detail three global design methodologies. The design in [4],applicable to uniformly observable systems, exploits the notion of output-to-state-stabilityto construct a state norm estimator which is used to tune on-line a high-gain observer.This design guarantees global convergence of the estimation error within the domain ofdefinition of the trajectories. The design in [7], applicable to general nonlinear systems,exploits Luenberger’s ideas (and their nonlinear counterpart) and the notion of invariantmanifold to construct globally convergent (adaptive) state and parameter estimators. Thedesign in [2], applicable to systems in triangular forms, relies upon the newly developednotion of homogeneity in the bi-limit, and uses observer backstepping and dynamic scalingto recursively design globally convergent observers. The applicability of these global observerdesigns to the problem of global output feedback stabilization is also discussed [11, 2, 3].

References[1] V. Andrieu and L. Praly. On the existence of

Kazantzis-Kravaris/Luenberger observers. SIAM Journal ofControl and Optimization, 45:432–456, 2006.

[2] V. Andrieu, L. Praly, and A. Astolfi. Homogeneousapproximation, recursive observer design and output feed-back. SIAM Journal of Control and Optimization, (to ap-pear).

[3] A. Astolfi, D. Karagiannis, and R. Ortega. Nonlinearand Adaptive Control with Applications. Springer Verlag,London, 2008.

[4] A. Astolfi and L. Praly. Global complete observabilityand output-to-state stability imply the existence of a glob-ally convergent observer. Mathematics of Control, Signals,and Systems, 18(1):32–65, 2006.

[5] J.-P. Gauthier and I. Kupka. Deterministic Observa-tion Theory and Applications. Cambridge University Press,2001.

[6] J.-P. Gauthier and I.A.K. Kupka. Observability and observers for nonlinear systems.SIAM J. Control and Optimization, 32(4):975–994, 1994.

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PLENARY LECTURES

[7] D. Karagiannis, D. Carnevale, and A. Astolfi. Invariant manifold based reduced-orderobserver design for nonlinear systems. IEEE Trans. Autom. Control, (to appear).

[8] N. Kazantzis and C. Kravaris. Nonlinear observer design using Lyapunov’s auxiliarytheorem. Systems and Control Letters, 34:241–247, 1998.

[9] D.G. Luenberger. Observing the state of a linear system. IEEE Trans. MilitaryElectronics, 8:74–80, 1964.

[10] D.G. Luenberger. An introduction to observers. IEEE Trans. Autom. Control,16(6):596–602, 1971.

[11] L. Praly and A. Astolfi. Global asymptotic stabilization by output feedback under astate norm detectability assumption. In 44nd Conference on Decision and Control and 2005European Control Conference, pages 2634–2639, 2005.

[12] M.Q. Xiao and A.J. Krener. Nonlinear observer design in the Siegel domain. SIAMJournal of Control and Optimization, 41:932–953, 2002.

Alessandro Astolfi was born in Rome, Italy, in 1967. He graduated in electrical engineer-ing from the University of Rome in 1991. In 1992 he joined ETH-Zurich where he obtaineda M.Sc. in Information Theory in 1995 and the Ph.D. degree with Medal of Honour in1995 with a thesis on discontinuous stabilization of nonholonomic systems. In 1996 he wasawarded a Ph.D. from the University of Rome “La Sapienza” for his work on nonlinear ro-bust control. Since 1996 he is with the Electrical and Electronic Engineering Department ofImperial College, London (UK), where he is currently Professor in Non-linear Control The-ory. From 1998 to 2003 he was also an Associate Professor at the Dept. of Electronics andInformation of the Politecnico of Milano. Since 2005 he is also Professor at Dipartimento diInformatica, Sistemi e Produzione, University of Rome “Tor Vergata”. He has been visitinglecturer in “Nonlinear Control” in several universities, including ETH-Zurich (1995-1996);Terza University of Rome (1996); Rice University, Houston (1999); Kepler University, Linz(2000); SUPELEC, Paris (2001). His research interests are focused on mathematical controltheory and control applications, with special emphasis for the problems of discontinuousstabilization, robust stabilization, robust and adaptive control, and observer design. He isauthor of more than 70 journal papers, 20 book chapters and 160 papers in refereed confer-ence proceedings. He is co-editor of three books, including the book “Analysis and Designof Nonlinear Control Systems – In Honor of Alberto Isidori” (Springer Verlag), and author(with D. Karagiannis and R. Ortega) of the monograph “Nonlinear and Adaptive Controlwith Applications” (Springer Verlag). He is Associate Editor of Systems and Control Let-ters, Automatica, IEEE Trans. Automatic Control, the International Journal of Control,the European Journal of Control, the Journal of the Franklin Institute, the IMA Journal ofMathematical Control and Information and he is subject Editor of the International Journalof Adaptive Control and Signal Processing. He has also served in the IPC of various inter-national conferences. A. Astolfi has been the recipient of the 2007 IEEE Control SystemsSociety Antonio Ruberti Young Researcher Prize. The Prize is given annually to “recognizedistinguished cutting-edge contributions by a young researcher to the theory or applicationof systems and control”.

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New Directions in the Application of Model Order Reduction

New Directions in the Application of Model Order Reduction

Danny C. Sorensen, Rice University

Thursday, July 31, 09:00–10:00, Latham A/B

Model order reduction (MOR) has played an important role in reducing computation time inimportant applications such as circuit simulation and structural analysis. Related method-ology such as proper orthogonal decomposition and principal component analysis has seennumerous applications in areas such as computational fluid dynamics and protein dynamics.This methodology speeds computation and reduces storage requirements by replacing a large-scale system of differential or difference equations by one of substantially lower dimensionthat has nearly the same response characteristics.

New applications of MOR are beginning to emerge whichhave intriguing possibilities for the widespread use of thistechnology. Traditional applications have concerned dimen-sion reduction of a single system. However, there are numer-ous important applications where there is a need to model avery large number of interactive systems all of the same typeor to conduct parametric studies involving a large numberof experiments such as a Monte Carlo study.

This talk will provide a brief review of existing MORtechniques and then will give an overview of current exam-ples that suggest an exciting future for model reduction. Re-cent work has been done by several researchers in areas suchas 1) probabilistic analysis of aerodynamic applications in-volving shape variations, 2) modeling of large systems of in-teracting neurons, 3) the dynamics of polymer solutions andmelts. These systems share the common need to conductvery large numbers of computational experiments. Such ex-periments become intractable without the order of magnitude reductions in computationtime achievable through model order reduction.

Danny Sorensen is Noah Harding Professor and Chair of Computational and AppliedMathematics at Rice University. Dr. Sorensen received his B.S. in Mathematics from Uni-versity of California, Davis in 1972 and his Ph.D. in Mathematics from University of Cali-fornia, San Diego in 1977. He was an Assistant Professor of Mathematics at University ofKentucky from 1977-1980. He then joined the Mathematics and Computer Science Divisionof Argonne National Laboratory where he became a Senior Computer Scientist. He joinedthe faculty of Rice University in 1989.

While at Argonne National Laboratory, he was one of the founders of the AdvancedComputing Research Facility. This facility was one of the first to provide public access to avariety of parallel computers, and served as a model for a number of similar facilities thatwere established across the nation. His interest in scientific computing education has contin-

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PLENARY LECTURES

ued at Rice U. where he established an interdisciplinary degree program in ComputationalScience and Engineering. He also has served on the executive committee for the Keck Cen-ter for Training in Computational Biology. He is a member of the executive board for theComputational Science Research Institute at Sandia National Laboratory.

Professor Sorensen’s research interests are in computational mathematics with emphasison numerical linear algebra, control, and high performance scientific computing. He has alsoworked extensively in the area of nonlinear numerical optimization. His current researchactivities involve iterative techniques for the solution of very large scale algebraic eigenvalueproblems and linear systems of equations. He is currently working in the related area of modelreduction for dynamical systems. He has been involved in several software developmentefforts including LAPACK and most recently the development of ARPACK. The latter is afreely available software package for the solution of very large scale symmetric/non-symmetricregular or generalized eigenvalue problems. This is one of the few available software packagesfor the solution of large nonsymmetric eigenvalue problems. ARPACK underlies the EIGScommand in Matlab. It has been used widely throughout the world on a wide variety oflarge scale applications. The package is based on the implicitly restarted Arnoldi methodthat was developed by Professor Sorensen.

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Contagion as a Practical Example of Informatic Support of the Analysis of Complex Interdependent Systems

Contagion as a Practical Example of Informatic Support of the Analysis ofComplex Interdependent Systems

Christopher Barrett, Virginia Bioinformatics Institute

Friday, August 1, 09:00–10:00, Latham A/B

This talk outlines an interaction-based approach to the behavioral analysis of large complexsystems. Policy problems typically consist of a large number of interacting physical, tech-nological, and- importantly- human/societal components. Examples of such systems involvebiological systems, functioning societal infrastructures such as urban regional transporta-tion systems, electrical power markets and grids, the Internet, ad-hoc communication andcomputing systems, public health, etc. All these share the feature of being networks; thatis, individual agents/entities/ components interact in particular ways with a specified set ofcomponents.

Computer simulation tools provide a compelling way tostudy such systems. Moreover, seemingly purely quantita-tive changes in HPC have created opportunities for qual-itative changes in the way information can be integratedin analysis of these large heterogeneous systems. In par-ticular, we will discuss examples of, and some issues with,expanded use of knowledge held as procedural informationin combination with measured data.

We develop the topic in an illustrative context of decisionsupport for public health planning related to epidemics ofinfectious diseases. There are 4 lines of thought in the exam-ple: (i) detailed representation: an interaction-based, highperformance computing oriented, modeling environment forsituation assessment and course of action analysis, (ii) Ser-vice oriented HPC-based cyber-architecture for coordinat-ing and scaling models, data and decision support systems,(iii) ideas of synthetic information: integrating diverse mea-sured and simulated data to synthesize new composite system knowledge, and (iv) somedirections of theoretical foundations of interaction-based systems.

Chris Barrett received his Ph.D. in bioinformation systems from the California Instituteof Technology in 1985. Prior to joining VBI, he worked for 17 years at the Los AlamosNational Laboratory (LANL). While at LANL, he was leader of the Basic and AppliedSimulation Science Group and built up a research group active in theoretical and appliedresearch in intelligent systems, distributed systems, and advanced computer simulation. Hehas scientific experience in simulation, scientific computation, algorithm theory and develop-ment, system science and control, engineering science, biosystems analysis, decision science,cognitive human factors, testing and training. His achievements include the developmentof large-scale, high performance simulation systems, and the development of a distributed

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PLENARY LECTURES

computing approach for detailed simulation-based study of mobile, packet-switched digitalcommunications systems. Dr. Barrett has received Distinguished Service Awards from LosAlamos National Laboratory, the Alliance for Transportation Research, the Royal Instituteof Technology in Stockholm, and Artificial Life and Robotics, Oita University, Japan. He iscurrently director of the Virginia Bioinformatics Laboratory-National Capitol Region and thedirector of the Virginia Bioinformatics Institute Network Dynamics and Simulation ScienceLaboratory.

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Semi-Plenary Lectures

Controllability of distributed parameter systems

Birgit Jacob, TU Delft

Monday, July 28, 14:30–15:30, Latham C

Intuitively the concept of controllability concerns the problem of steering a system intoa given state in a certain time. When dealing with controllability problems one has todistinguish between finite-dimensional systems modelled by ordinary differential equationsand distributed parameter systems modelled by partial differential equations or evolutionequations. According to the Hautus-Popov lemma a finite-dimensional system is controllableif and only if a certain block matrix has full rank. In the finite-dimensional context a systemis controllable for some time if it is controllable for all time. This is no longer true fordistributed parameter systems.

In this talk we discuss different concepts of controllabilityfor distributed parameter systems and apply them to sev-eral examples such as the heat equation and the Schrodingerequation in R2. A distributed parameter system is calledexact controllable in time t0 if for every pair of initial andfinal states, one can find an input function such that thestate of the system matches both the initial condition attime t = 0 and the final condition at time t = t0. Work-ing with distributed parameter systems the control usuallyacts through the right hand side of the partial differentialequation or through the boundary conditions. It has beennoted in the literature that exact controllability rarely holdsif the input space is one dimensional, and therefore we studyweaker notions such as null controllability and approximatecontrollability as well. Note, that in the finite-dimensionalcontext the concepts of exact controllability, approximatecontrollability and null controllability are all equivalent. Inapplications, null controllability is often sufficient. For example, the finite cost condition isimplied by null controllability and thus the existence of a unique optimal solution to variousquadratic cost minimization problems is guaranteed. There is a large literature on the topic.

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SEMI-PLENARY LECTURES

We refer the reader to e.g., the survey article by Russell, or the books by Lions, Lasieckaand Triggiani, and Curtain and Zwart.

There are different tools to address controllability problems. In this talk we mainlyfocus on theoretical operator methods and moment methods. In 1992, Russell and Weissgeneralized the Hautus-Popov lemma to systems described by bounded operators and theyconjectured that the generalized Hautus-Popov lemma characterizes exact controllability forall distributed parameter systems. It was shown later that the conjecture holds for severalclasses of distributed parameter systems. However, in general the conjecture fails to hold. Fora wide class of distributed parameter systems the controllability problem can be translatedinto a weighted interpolation problem by vector valued analytic functions. This enables usto characterize controllability in terms of Carleson measures and Carleson embeddings.

Birgit Jacob received the M.Sc degree in mathematics from the University of Dortmund,Germany, in 1992 and the Ph.D degree in mathematics from the University of Bremen, Ger-many, in 1995. She held PostDoc positions at the University of Twente in the Netherlands,the University of Leeds in the UK and the Berlin University of Technology in Germany. Since2006 she has been with the Delft Institute of Applied Mathematics at the Delft Universityof Technology in the Netherlands, where she is an Associate Professor in Analysis.

Her current research interests include the area of infinite-dimensional systems and oper-ator theory, particularly well-posed linear systems,operator semigroups, controllability, ob-servability, transfer functions, the spectrum of block operator matrices and Volterra equa-tions.

She is a member of the Editorial Board of the international journal Operators and Ma-trices.

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System theory over finite algebras — count your blessings

System theory over finite algebras — count your blessings

Margreta Kuijper, University of Melbourne

Monday, July 28, 14:30–15:30, Alumni Assembly Hall

Strong connections exist between linear system theory and the theory of linear error controlcodes. Some of these connections

a) are obvious and well-established: linear convolutionalcodes over finite fields are linear discrete-time systems overfinite fields. It is then not surprising that fundamental lin-ear algebraic notions such as row reducedness from systemtheory are instrumental in minimal polynomial encoder de-sign.

b) are less obvious but well-established: the decodingof Reed-Solomon block codes can be phrased as a minimalpartial realization/interpolation problem.

c) are quite obvious but not well-established: polyno-mial block codes over finite fields, such as the ubiquitousbinary CRC codes, are linear discrete-time systems over fi-nite fields. Their dual systems are the rateless shift registercodes.

In this talk we first give an overview of these connectionsand the historical and conceptual relevance of the behavioralviewpoint in making these connections. We see that thesystem theoretic results over infinite fields carry through effortlessly to the finite field case –no counting needed.

We then turn to linear codes over finite rings. We give an overview of recently developedlinear algebraic results for such rings and show how these give rise to fundamental resultson discrete-time systems over finite rings. These fundamentals have applications for linearcodes over finite rings and nonlinear codes over finite fields. Here the fact that the ring isfinite is crucial—this time counting is needed. We end by addressing current research areassuch as the area of rateless coding for packet transmission over the internet.

Margreta Kuijper is an Associate Professor at the Department of Electrical and ElectronicEngineering of the University of Melbourne (Australia) where she have been employed since1995. From 1992 to 1995 she was a postdoctoral fellow at the Mathematics Departmentof the University of Groningen, the Netherlands. From 1988 to 1992 she worked at theCenter of Mathematics and Computer Science (CWI), Amsterdam, where she obtained herPhD degree in 1992 in conjunction with Tilburg University, the Netherlands. She is theauthor of the book “First-order representations of linear systems” (Birkhauser, 1994). Shereceived her M.Sc. degree cum laude in 1985 from Vrije Universiteit (VU), Amsterdam.In the years 1985-1988 she held an Engineer position in the area of systems and controlat the National Aerospace Laboratory (NLR), Amsterdam. In her research she is mainly

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interested in the interplay between system theory and communications. Her major currentresearch interests are in polynomial matrix theory, behavioral system theory, convolutionalcoding, Reed-Solomon coding, systems and codes over finite fields and rings, coding forpacket transmission, data compression for correlated sources.

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When Control Theory Meets Neuroscience

When Control Theory Meets Neuroscience

Iven Mareels, University of Melbourne

Monday, July 28, 14:30–15:30, Latham A/B

From its very onset cybernetics was interested in communication and control as it is im-plemented in either engineered systems or biology. Indeed much of the seminal work ofNorbert Wiener, John Von Neumann and Claude Shannon was motivated by the fact thattheir theories and insight would lead to elucidating how the mind works.

In this lecture we review some of the basic questions theywere interested in, like memory capacity and computationalcapacity of the brain, and compare some of their predictionswith measurements and neuroscience estimates that havebeen made more recently.

Of particular interest to systems theory people is thefact that in order to elucidate how learning works, espe-cially in motor control, neuroscience researchers are partic-ularly interested in motor control in interactions with theenvironment that are described as “unstable”, like drillingor writing or standing/walking. Indeed in view of recentadvances in our understanding of feedback entropy and in-variance entropy, control theory can shed light on the min-imum required feedback information rate that is necessaryfor a stable feedback loop to exist, and may settle the ques-tion on whether or not a feedback loop exists. The latteris of great interest, for example the “simple” question, Dohumans use feedback during walking ? is still open.

Next we review the ideas of feedback entropy. First we consider linear systems subjectto additive white Gaussian noise in the state transition map and the observation map, andask “What is the minimum data rate to achieve stabilization?”. Subsequently we posethe same question in a nonlinear setting and introduce the concept of topological feedbackentropy, which is an open-loop system property. It turns out that the minimum data ratefor stabilization (invariance) is precisely the plant’s topological feedback entropy.

Finally we conjecture extensions in the context of a network of dynamically interconnectedsystems.

To illustrate how these results may be relevant to neuroscience we infer an estimate for theinformation rate that must be achieved in the human nervous system in order for a personto stand or walk. The estimates are based on very simplified models for walking/motionthat appear to capture the essence of walking. These estimates are aligned with and providemathematical support for estimates arrived at from a behavioural neuroscience perspective.

Iven Mareels was born in Aalst Belgium on 11 August 1959. He obtained the (ir) Mastersof Electromechanical Engineering from Gent University, Belgium in 1982 and the PhD in

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Systems Engineering from the Australian National University, Canberra, Australia in 1987.Since 1996, he is a Chair Professor of Electrical and Electronic Engineering, at the Depart-ment of Electrical and Electronic Engineering, the University of Melbourne. Since June2006, he leads the National Institute for Communications Technology Australia, VictoriaResearch Laboratory’s program in ICT for Life Sciences. He is also Associate Dean of theFaculty of Engineering.

Previously he was a Reader at the Australian National University (1990-1996), a lecturerat the University of Newcastle (1988-1990) and the University of Gent (1986-1988).

He has received several awards in recognition of his research and teaching. In 2005, hewas named IEEE CSS Distinguished Lecturer, and in 1994 received the Vice-Chancellor’sAward for Excellence in Teaching from the Australian National University. He is a co-editorin chief, together with Prof. A. Antoulas of Systems & Control Letters. He has receivedseveral awards for his publications.

He is Fellow of the Academy of Technological Sciences and Engineering, Australia, aFellow of the Institute of Electrical and Electronics Engineers (USA), a member of the Societyfor Industrial and Applied Mathematics, a Fellow of the Institute of Engineers Australia,Vice-Chair and founding member of the Asian Control Association, and a member of theorganising committee for the Asian Control Conference. Until Dec 2005 he was a memberof the Board of Governors of the Control Systems Society IEEE. He is registered with theInstitute of Engineers Australia as a professional engineer. He is Chair of the NationalCommittee for Automation, Control and Instrumentation. He holds the award of IEEEDistinguished Lecturer Control Systems Society 2005.

He has extensive experience in consulting for both industry and government. He hasstrong interests in education. He has taught a broad range of subjects in both mechanical andelectrical engineering curricula. He was one of the developers of the Bachelor of Engineeringat the Australian National University. His research interests are in adaptive and learningsystems, nonlinear control and modelling. At present he has strong research interests inmodelling and controlling of large scale systems, both engineered as well as natural systems.

Iven Mareels has published widely, 3 research monographs, in excess of 100 journal publi-cations and 150 conference publications. He holds 3 patents. He has supervised to completion25 PhD students and is currently supervising 9 PhD students.

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New perspectives in algebraic systems theory

New perspectives in algebraic systems theory

Alban Quadrat, INRIA Sophia-Antipolis

Tuesday, July 29, 14:30–15:30, Alumni Assembly Hall

The purpose of this talk is to present the algebraic analysis approach to mathematical sys-tems theory developed in recent years. Algebraic analysis, pioneered by B. Malgrange andthe Japanese school of M. Sato, is a mathematical theory which studies linear systems ofpartial differential equations based on module theory, homological algebra and sheaf theory.Ideas, techniques and results of algebraic analysis have recently been extended to differentclasses of linear systems such as discrete systems, differential time-delay systems, multidi-mensional systems or infinite-dimensional systems.

The module-theoretic approach to linear systems devel-oped within algebraic analysis gives a unified mathemati-cal framework (common concepts, techniques, results, algo-rithms and implementations) for the study of the structuralproperties of different classes of multidimensional linear sys-tems and infinite-dimensional linear systems and for thestudy of synthesis problems (e.g., optimal control, stabiliza-tion problems). In particular, the module characterizationsof the structural properties developed in this approach areintrinsic in the sense that they do not depend on particu-lar representations of the linear system (e.g., state-space orinput-output representations for 1D linear systems, Roesseror Fornasini-Marchesini models for multidimensional sys-tems). Within algebraic analysis, the behavioural approachto linear systems can be found again and more intrinsicallydeveloped. Using powerful tools of homological algebra, wecan then obtain general characterizations for the moduleproperties corresponding to the system properties. Finally, using constructive algebra (e.g.,non-commutative Grobner or Janet bases) and symbolic computation, those homologicalcharacterizations can be made constructive over certain classes of multidimensional systems(e.g., differential time-delay systems, under-determined systems of partial differential or dif-ference equations) and can be implemented in dedicated symbolic computation packages(e.g., OreModules, OreMorphisms, JanetOre, QuillenSuslin, Stafford).

Alban Quadrat was born in 1973 at Le Chesnay in France. After studies in pure andapplied mathematics at the University of Versailles and a Master’s Degree at the Universityof Orsay (Paris XI) in control theory and signal processing, he was awarded a PhD thesisin mathematics by the Ecole Nationale des Ponts et Chausses (one of the oldest FrenchEngineering Institutes in France) under the supervision of Jean-Francois Pommaret (1999).

Following his employment as a postdoctorate, under the guidance of J. R. Partington,at the Department of Pure Mathematics at the University of Leeds (United Kingdom), he

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joined, as a researcher, INRIA Sophia-Antipolis (a branch of The French National Institutefor Computer Science and Control located near Nice, France) in 2001.

He is an associated editor of the journal “Multidimensional Systems and Signal Pro-cessing”. His main interests are algebra (algebraic analysis, module theory, homologicalalgebra, symbolic computation), mathematical systems theory (multidimensional systems,behavioural approach, infinite-dimensional systems, stabilization problems), (algebraic, dif-ferential and non-commutative) geometry, mathematical physics, and history of science.

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Estimation and Identification of Metabolic Systems Models from Time-Series Data

Estimation and Identification of Metabolic Systems Models from Time-Series Data

Eberhard Voit, Georgia Institute of Technology

Tuesday, July 29, 14:30–15:30, Latham A/B

Arguably the most challenging task of biomathematical systems modeling is the estimationof parameter values. Until recently, this task was typically pursued by characterizing modelcomponents and processes one at a time and subsequently merging all “local” descriptionsinto one comprehensive model. Recent advances in molecular and systems biology have pro-vided us with a strikingly different estimation strategy, which is based on experimentallydetermined time series of observations at the genomic, proteomic, or metabolic levels. Thesetime profiles contain enormous information about the structure, dynamics and regulatorymechanisms that govern the biological systems of interest. However, extraction and integra-tion of this information into fully functional, explanatory models is a daunting task. Theestimation methods developed to date face significant problems in three distinctly differentclasses:

• Computational issues, including: slow algorithmic progress toward the error minimumor lack of convergence; very complicated error surfaces with numerous local minima;substantial time requirements for integration of differential equations.

• Data related issues, including: overly noisy data; missing data; missing time series;collinearity between time series; solution spaces with equal error; non-informative, e.g.,essentially constant, time profiles.

• Mathematical issues, including: distinctly different, yet equivalent solutions; non- equiv-alent solutions with similar error; invalid assumptions regarding the chosen processdescriptions; error compensation among and within equations.

• Issues of model quality beyond goodness of fit, including: lack of diagnostic tools beyondthe residual error; lack of model fit for data not used in the estimation; model failure inextrapolations; lack of criteria for optimality of the obtained parameters; lack of criteriafor determining the appropriateness of the chosen mathematical representations; lack ofmethods for assessing whether residual errors are due to idiosyncrasies or noise in thedata, an invalid model structure, inadequate computational methods, or a combinationthereof.

Many articles have acknowledged and discussed various computational issues in great detailand some have addressed issues related to data and models. However, there has been littleif any substantial discussion of model validity and quality beyond residual errors, except forthe common statement that the estimated parameter set may not be unique. Here I discussa novel approach to metabolic systems estimation, called Dynamic Flux Estimation (DFE),that resolves several of the issues mentioned above. This approach consists of two distinctsteps. The first consists of an entirely model-free and assumption-free data analysis, which

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immediately reveals inconsistencies within the data, and between data and the alleged systemtopology. The second step addresses the mathematical formulation of the processes in thebiological system. In contrast to all currently available methods, this step allows quantitativediagnostics of whether–or to what degree–the assumed formulations are appropriate or inneed of improvement. DFE is a natural extension of stoichiometric and flux balance analysisin that it focuses on the stoichiometry at all nodes in the investigated system. However, inDFE the system is typically not in a steady state and its transient dynamics is utilized as acrucial indicator of the regulation within the system.

Eberhard Voit received Master’s degrees in biology andmathematics and a Ph.D. in theoretical biology from theUniversity at Cologne, Germany. He subsequently held fac-ulty and research positions at the University of Michigan,the Medical University of South Carolina, and in Tasmania,Australia.

Voit currently holds an endowed chair in the W.H. Coul-ter Department of Biomedical Engineering at Georgia Tech,with the rank of Professor and Georgia Research AllianceEminent Scholar. He also holds the faculty rank of Profes-sor at Emory Medical School as well as joint appointmentsin Georgia Tech’s College of Computing and School of Bi-ology. Voit currently serves as the inaugural director ofGeorgia Tech’s new Integrative BioSystems Institute.

Voit is one of the leading experts in Metabolic Pathway Analysis and Biochemical SystemsTheory and has authored or co-authored close to two hundred articles and book chapters.He has authored several books, two of which have been translated into Chinese. Voit hasbeen an invited speaker at numerous international conferences and taught several tutorialsand workshops on the subject within the U.S., as well as in Canada, Japan, Portugal, andTaiwan.

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Use of Dynamic Quantizers for Discrete-Valued Input Systems

Use of Dynamic Quantizers for Discrete-Valued Input Systems

Toshiharu Sugie

Tuesday, July 29, 14:30–15:30, Latham C

The control of systems containing discrete-valued (quantized) signals is one of the most ac-tively studied topics in the field of systems and control. Discrete-valued signals are commonin many types of control systems, such as mechanical systems, chemical plants, networkedsystems, hybrid systems, and biological systems. This is due in part to the various devicesembedded in these systems, such as D/A converters, PWM amplifiers, ON/OFF actuators,qualitative sensors, and communication encoders/decoders. As an example of discrete-valuedsignals in biological systems, the activation/inhibition (ON/OFF) operation of gene expres-sion is often used as a control input in gene regulatory networks.

In these studies, one of the central issues is how to de-sign the quantizer which maps the continuous-valued sig-nal to the discrete-valued signal. Though the quantizerswhich are commonly used are static, we are interested inthe dynamic quantizers which determine their output basedupon the past input sequence. In this talk, we show howmuch advantage we can get by using the dynamic quantiz-ers. First, the performance of the dynamic quantizers isanalyzed. Based on the result, an optimal dynamic quan-tizer and its performance are given in a closed form. Thesystem composed of a given linear plant and the quantizer isan optimal approximation of the linear plant in terms of theinput/output relation. This result is extended to the closedloop control systems. The advantage of the dynamic quan-tizers are demonstrated through some experimental resultsas well as various numerical examples.

References

[1] S. Azuma and T. Sugie: Optimal Dynamic Quantizers for Discrete-Valued Input Con-trol, Automatica, Vol. 44, No. 2, 396-406 (2008.2)

[2] S. Azuma and T. Sugie: Synthesis of Optimal Dynamic Quantizers for Discrete-ValuedInput Control, IEEE Trans. on Automatic Control, to appear (2008.12)

[3] Y. Minami, S. Azuma, and T. Sugie: An Optimal Dynamic Quantizer for FeedbackControl with Discrete-Valued Signal Constraints, Proc. of the 46th IEEE CDC, New Orleans,pp. 2259–2264 (2007.12)

[4] M. Ishikawa, I. Maruta, T. Sugie: Practical Controller Design for Discrete-valuedInput Systems using Feedback Modulators, Proc. of ECC2007, Kos, Greece, pp. 3269–3274(2007.7)

Toshiharu Sugie was born in Osaka, Japan in 1954. He received the B.E., M.E., and Ph.D.degrees in engineering form Kyoto University, Japan, in 1976, 1978 and 1985, respectively.

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Since 1998, he has been Professor at the Department of Systems Science, Kyoto University.He was a research member of Musashino Electric Communication Laboratory in NipponTelegraph and Telephone Public Corporation, Japan (1978-1980), a research associate atthe Department of Mechanical Engineering, University of Osaka Prefecture (1984-1988),and an associate professor at the Department of Applied Systems Science, Kyoto University(1988-1997).

His research interests are in robust control, nonlinear control, identification for control,and their application to mechanical systems. He published a few books, one of which wonthe Best Book Award from the Society of Instrument and Control Engineers, Japan (SICE)in 1994. He also received Best Paper Awards from SICE in 1994, 2000, 2003 and 2007, andfrom the Institute of Systems, Control and Information Engineers, Japan in 1991, 1998 and2008.

Dr. Sugie has served as an Associate Editor of Automatica since 1997. He was alsoan Associate Editor of textitAsian Journal of Control (1998-2005) and textitInternationalJournal of Systems Science (2003-2005). He is an IEEE Fellow.

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Duality of Infinite Dimensional Linear Programming and Its Applications to Control Problems

Duality of Infinite Dimensional Linear Programming and Its Applicationsto Control Problems

Yoshito Ohta, Kyoto University

Wednesday, July 30, 10:30–11:30, Latham C

There are many robust control problems which can be expressed as an infinite dimensionallinear programming problems even though the underlying system is finite dimensional. Forexample, the `1 control problem which minimizes the `1 norm of the impulse response ofa closed loop map becomes a linear programming problem with infinitely many variablesand infinitely many constraints. Another example is a parameter dependent linear matrixinequality.

An elementary result for finite dimensional linear pro-gramming problems is that the dual problem takes the sameoptimal value if one of them has non-empty feasible set andtakes finite optimal value. This relation between primal anddual problems is not only theoretically but also computa-tionally important.

In this talk, we consider the duality of infinite-dimensional linear programming problems with possibly anunbounded operator. Then we derive computational meth-ods based on the duality. Furthermore, we consider its im-plications to control problems.

With some mild conditions, it can be shown that thedual problem defined on the dual space takes the same op-timal value as the primal problem. If we approximate bothprimal and dual problems in finite dimensional spaces, wehave upper and lower bounds for the optimal value. Weconsider conditions that guarantee the convergence of lowerand upper bounds to the primal optimal cost when the dimensions of the primal and dualproblems increase. A sufficient condition for such gap free approximations is the existenceof an appropriately defined pseudo-interior point.

Examples of control problems to which the framework of this talk can be applied are the`1 control problem with additional frequency domain constraints and the L2 gain analysisproblem for linear parameter varying (LPV) systems. We will show how to derive gap freeapproximations for the dual problems for these particular control problems.

Yoshito Ohta received a Bachelor of Engineering Degree, a Master of Engineering Degree,and a Doctor of Engineering Degree in Electronic Engineering in 1980, 1982, and 1986respectively, all from Osaka University, Suita, Japan. In 1983, he joined the Departmentof Electronic Engineering, Osaka University as a Research Associate. In 1991, he becamea Lecturer at the Department of Computer-Controlled Machinery, Osaka University, and in1999 he became a Professor at the Department of Computer-Controlled Mechanical Systems,

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Osaka University. In 2006, he joined the Department of Applied Mathematics and Physics,Kyoto University, where he is currently a Professor. From 1986 to 1988, he was a VisitingScientist at the Laboratory for Information and Decision Systems, Massachusetts Instituteof Technology, USA. He received the Best Paper Prize of SICE (Tomoda Award) in 1992from the Society for Instrument and Control Engineers in Japan.

Dr. Ohta served as an Associate Editor of the IEEE Transactions on Automatic Controlfrom 2001 to 2005. He is currently an Associate Editor of Automatica and an Associate Ed-itor of European Journal of Control. His research interest is robust control, convex analysis,and networked control systems.

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Control in a Behavioral Framework

Control in a Behavioral Framework

H. L. Trentelman, University of Groningen

Wednesday, July 30, 10:30–11:30, Alumni Assembly Hall

In this talk I will present an overview of developments over the past years within thebehavioral approach to control.

As is well known, in the behavioral approach the set ofall trajectories that satisfy the laws of the system (called thebehavior), is considered as the mathematical model. Thismathematical model (behavior) can of course be describedby mathematical equations in terms of differential or differ-ence equations, algebraic equations, transfer matrices, etc.,in many different ways. Any such choice of mathematicalequations is called a representation of the behavior.

Controllers are behaviors to be designed. Interconnectinga given (plant) behavior with a controller behavior meansthat given components of the plant trajectories should be-come elements of the controller behavior as well. These com-ponents are called the control variables of the plant. In aclassical input/output framework the control variables typ-ically consist of the plant control inputs and measured out-puts. Interconnecting plant and controller behavior yieldsthe controlled behavior.

In this context I will discuss a number of basic control theoretic issues. Firstly, I willaddress the following question: given a plant behavior, which ’desired’ behaviors can beachieved by interconnecting it with a suitable controller behavior. Behaviors that can beachieved in this way are called implementable. Next, I will consider the stabilization prob-lem: given a plant behavior, under what conditions does there exist a controller behaviorsuch that the resulting controlled behavior is stable. Essential notions here are the behav-ioral versions of stabilizability and detectability. I will also consider pole assignment in thebehavioral context. Thirdly, I will consider the problem of parametrization of all stabilizingcontrollers, thus establishing the behavioral version of the well known Youla parametriza-tion. This parametrization will be applied to find conditions for the existence of stabilizingcontrollers with a priori given input/output structure. Finally I will give discuss some im-portant developments in the problem of synthesis of dissipative systems and the behavioralversion of the problem of robust stabilization.

Dr. Trentelman has been professor in Systems and Control at the Mathematics Depart-ment of the University of Groningen since 2004. From 1991 to 2004 he served as associateprofessor at the same Department. From 1985 to 1991 he was assistant professor, andlater associate professor, at the Mathematics Department of the University of Technologyat Eindhoven, the Netherlands. From 1981 to 1985 he has worked as a research associate

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for the Dutch Organization for Scientific Research at the University of Groningen, where heobtained his Ph.D. degree in Mathematics in 1985. Dr. Trentelman is associate editor ofSystems and Control Letters, and is past associate editor of the SIAM Journal on Controland Optimization.

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Nonlinear model predictive control without terminal constraints: stability, performance and design

Nonlinear model predictive control without terminal constraints: stability,performance and design

Lars Gruene, University of Bayreuth

Wednesday, July 30, 10:30–11:30, Latham A/B

Model predictive control (MPC) is an optimization based control technique for stabilizationand tracking widely used in industry and theoretically investigated since the late 1970s. Inorder to guarantee stability of the closed loop, in most of the literature stabilizing terminalconstraints for the underlying finite time optimal control problem are imposed. Only quiterecently it was shown in papers by Jadbabaie and Hauser as well as by Grimm, Messina, Teeland Tuna that for nonlinear MPC schemes without terminal constraints closed loop stabilitycan be expected under rather general conditions. The key requirement in these results is asufficiently large optimization horizon.

In the first part of this talk we will give a tutorial in-troduction into nonlinear model predictive control and itsstability. In the second part we will present a method forcomputing non-conservative estimates for the optimizationhorizon needed in order to achieve stability and guaran-teed performance of the closed loop. This method combinesideas from relaxed dynamic programming as introduced byRantzer and coworkers with a suitable asymptotic control-lability assumption and leads to conditions which are check-able by solving (small) linear programs. The main purposeof our analysis is the derivation of design guidelines for MPCschemes which ensure stability and good performance forsmall optimization horizons and thus allow for a fast onlinesolution of the finite horizon optimal control problem. Thisprocedure will be illustrated in the final part of the talk byboth finite and infinite dimensional examples.

Lars Grune has been a Professor for Applied Mathemat-ics at the University of Bayreuth, Germany, since 2002. He received his Diploma and Ph.D.in Mathematics in 1994 and 1996, respectively, from the University of Augsburg. From 1997until 2002 he was a scientific assistant and lecturer at the J.W. Goethe University in Frank-furt/M. He held several visiting positions, including a guest professorship at the UniversityParis IX Dauphine, France, in 2004, a visit at the University of Melbourne, Australia, in2001 and the University of Padua, Italy, in 2000 and a one year stay at the University LaSapienza in Rome, Italy, 1998-1999, supported by a DFG research grant.

Lars Grune served as an Associate Editor for several conferences, including the IFACNOLCOS Symposium and the IEEE Conference on Decision and Control, and he is currentlyan Associate Editor for the journals Mathematics of Control, Signals and Systems (MCSS)and Journal of Applied Mathematics and Mechanics (ZAMM).

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His research interests lie in the area of mathematical control theory and dynamical sys-tems, in particular on numerical and optimization-based methods for stability analysis andstabilization of nonlinear systems.

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The Role of Lie Brackets in Stability of Linear and Nonlinear Switched Systems

The Role of Lie Brackets in Stability of Linear and Nonlinear SwitchedSystems

Daniel Liberzon, University of Illinois at Urbana-Champaign

Thursday, July 31, 14:30–15:30, Latham C

We give an overview of recent work exploring the link between commutation relations amonga family of asymptotically stable vector fields and stability properties of the correspondingswitched system (or, more generally, a differential inclusion). We discuss both linear andnonlinear systems.

In the linear case, a complete characterization of the classof Lie algebras guaranteeing stability is available. Com-muting systems and systems with nilpotent or solvable Liealgebras are covered as special cases of this result.

The nonlinear results are far less complete, but they re-veal an interesting connection with the bang-bang principleof optimal control. Specifically, our approach is to con-sider an optimal control problem of finding the “most un-stable” trajectory for an associated control system, and usethe maximum principle to show that there exists an opti-mal solution which is bang-bang with a bound on the totalnumber of switches.

Stability conditions involving Lie brackets suffer fromlack of robustness with respect to perturbations of systemdynamics. At the end of the talk, we discuss some possibil-ities for making them more widely applicable.

Daniel Liberzon was a student in the Department of Mechanics and Mathematics atMoscow State University from 1989 to 1993 and received the Ph.D. degree in mathemat-ics from Brandeis University in 1998 (under the supervision of Prof. Roger W. Brockettof Harvard University). Following a postdoctoral position in the Department of ElectricalEngineering at Yale University from 1998 to 2000, he joined the University of Illinois atUrbana-Champaign, where he is now an associate professor in the Electrical and ComputerEngineering Department and a research associate professor in the Coordinated Science Lab-oratory. Dr. Liberzon’s research interests include nonlinear control theory, analysis andsynthesis of switched dynamical systems, control with limited information, and uncertainand stochastic systems. He is the author of the book “Switching in Systems and Control”(Birkhauser, 2003). Dr. Liberzon is a recipient of the IFAC Young Author Prize (2002),the NSF CAREER Award (2002), and the Donald P. Eckman Award from the AmericanAutomatic Control Council (2007). He currently serves as Associate Editor for the IEEETransactions on Automatic Control.

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Structured versus Unstructured Perturbations for Analysis of DynamicalSystems

Mark Embree, Rice University

Thursday, July 31, 14:30–15:30, Latham A/B

The matrices that drive linear dynamical systems are often endowed with considerable struc-ture, ranging from real versus complex entries, the nonzero pattern, and self-adjoint orHamiltonian properties; these reflect fundamental aspects of the physics of the underlyingproblem. One might naturally seek to exploit this structure when analyzing properties ofthe dynamical system, such as distance to instability, transient behavior, and the effect ofuncertainty; such developments are have grown into the field of structured perturbation the-ory. Early work in this vein was proposed by Hinrichsen and Pritchard two decades ago,through their study of the real- versus complex- distance to instability, with numerous resultsfollowing for a variety of matrix structures.

It quickly became clear that the effects of structuredperturbations were rather more challenging to characterizethan those due to less glamorous generic complex perturba-tions. However, in many situations those generic complexperturbations, when cast in the correct inner product spaceand with respect to the proper solution operator for theproblem, do indeed better reveal aspects of system behav-ior, such as transient growth.

This perspective, articulated by Trefethen, becomes par-ticularly particularly relevant when studying linearizationsof nonlinear systems. In this talk we shall survey the dis-tinctions between structured and unstructured perturba-tions. We will address those questions best addressed byeach style of analysis, then focus on two classes of problems:matrix pencils arising from descriptor systems, and polyno-mial eigenvalue problems arising from damped mechanicalsystems.

Mark Embree is an Associate Professor of Computational and Applied Mathematics atRice University in Houston, Texas. After undergraduate studies at Virginia Tech, he com-pleted his D.Phil. in Numerical Analysis at the Oxford University Computing Laboratoryunder the direction of Andy Wathen. He remained in Oxford for post-doctoral research withNick Trefethen, which led to their book on Spectra and Pseudospectra: The Behavior ofNonnormal Matrices and Operators (Princeton, 2005). He moved to Houston in 2002, wherehe resides with his wife and three children.

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Overdetermined Multidimensional Systems: A Survey

Overdetermined Multidimensional Systems: A Survey

Victor Vinnikov, Ben Gurion University

Thursday, July 31, 14:30–15:30, Alumni Assembly Hall

I will discuss linear multidimensional input/state/output systems with the evolution of thewhole state vector prescribed in each direction. This is in contrast to the more conven-tional models where either the evolution of the state is prescribed in only one direction (theFornasini–Marchesini model) or the state vector is decomposed into several partial states withthe evolution of each partial state prescribed in a different direction (the Givonne–Roessermodel).

The fact that the evolution of the whole state is pre-scribed in several independent directions means that thesystem equations are overdetermined. It is assumed that thestate operators appearing in the different evolution equa-tions commute so that the system equations are compatiblefor the zero input signal and arbitrary initial state. Compat-ibility analysis of the system equations then leads to addi-tional algebraic structure among the state, input and outputoperators (the so called vessel conditions) and to admissi-blity conditions for the input signal in the form of certaindifference equations. There are analogous admissibility dif-ference equations for the corresponding output signal.

Because of the admissibility conditions for the input andoutput signals, the frequency domain analysis for an overde-termined system leads to functions on an algebraic curve(rather than to functions of several independent variables).More specifically, the transfer function for say a 2D overde-termined system is (under certain assumptions) a bundle map between flat vector bundleson a compact Riemann surface, or equivalently, between kernel bundles for determinantalrepresentations of a plane algebraic curve.

I will survey the interrelations between overdetermined multidimensional systems andother subjects (such as operator theory and scattering theory), their applications, and thevarious aspects of their theory. I will also discuss how do overdetermined systems fit withinthe general behavioural approach to multidimensional systems.

References:J. A. Ball, C. Sadosky and V. Vinnikov, Conservative linear systems, unitary colliga-

tions and Lax-Phillips scattering: multidimensional generalizations, Internat. J. Control 77(2004), no. 9, 802–811.

J. A. Ball and V. Vinnikov, Hardy spaces on a finite bordered Riemann surface, multi-variable operator model theory, and Fourier analysis along a unimodular curve, OperatorTheory: Adv. Appl. 129, 37–56 (2001).

J. A. Ball and V. Vinnikov, Overdetermined Multidimensional Systems: State Space and

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Frequency Domain Methods, Mathematical Systems Theory (D. Gilliam and J. Rosenthal,eds.), Inst. Math. and its Appl. Volume Series, Vol. 134, Springer-Verlag, New York (2003),63–120.

M. S. Livsic, N. Kravitsky, A. S. Markus, and V. Vinnikov, Theory of commuting non-selfadjoint operators, Mathematics and Its Applications, vol. 332, Kluwer, Dordrecht, 1995.

Victor Vinnikov got his Ph. D. in Mathematics in 1988 from Ben Gurion University(Beer Sheva, Israel) under the direction of Moshe Livsic. He spent 2 years at Harvard as apost-doctoral fellow, and was at the Weizmann Institute of Science (Rehovot, Israel) beforejoining the Department of Mathematics of Ben Gurion University in January 2000. Hismain research interests are in multivariable operator theory and multidimensional systemtheory; he is also interested in algebraic geometry (theta functions, Jacobian varieties andmoduli spaces of vector bundles, determinantal representations), in linear matrix inequalities(LMIs), and in noncommutative positivity and noncommutative convexity.

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Problems of control and system theory of biochemical reaction systems

Problems of control and system theory of biochemical reaction systems

Jan H. van Schuppen

Friday, August 1, 14:30–15:30, Latham A/B

Progress in the life sciences can benefit from, besides experimental and descriptive research,also from the mathematical sciences for modeling, system identification, system theory, andcontrol theory.

The following research issues will be discussed during thelecture:

• Modeling of a metabolic network for Baker’s yeast(Saccharomyces cerevisiae) and of a genetic networkfor Escherichia coli in regard to nitrogen assimilation.

• Biochemical reaction systems and their algebraic prop-erties.

• Modeling of very large biochemical reaction systemspreferably of the complete cell by methods of hierar-chical system theory, modularity, and algebraic decom-position.

• System identification of rational (positive) systems.

• System reduction of biochemical reaction systems.

• Control for biotechnology including rational drug de-sign and production of food substances.

Jan H. van Schuppen is affiliated with the the researchinstitute Centrum voor Wiskunde en Informatica (CWI) inAmsterdam, The Netherlands and with the Department of Mathematics of the VU UniversityAmsterdam (part time).

Van Schuppen’s research interests include control of hybrid systems and of discrete-eventsystems, stochastic control, realization, and system identification. In applied research hisinterests include control and system theory for the life sciences, engineering problems ofcontrol of motorway traffic, and of communication networks.

He is Editor-in-Chief of the journal Mathematics of Control, Signals, and Systems, wasAssociate Editor-at-Large of the journal IEEE Transactions Automatic Control, and wasDepartment Editor of the journal Discrete Event Dynamic Systems.

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On the zero-modules of spectral factors using state space methods – therole of a coupled Sylvester-homogeneous linear equation

Gyorgy Michaletzky, Eotvos Lorand University

Friday, August 1, 14:30–15:30, Alumni Assembly Hall

The study of zeros of transfer functions has already a long history. Schrader and Sain (1989)published a survey on the notions and results of zeros of linear time invariant systems, in-cluding invariant zeros, system zeros, input-decoupling zeros, output-decoupling zeros andinput-output-decoupling zeros, as well. The connection of these zeros to invariant subspaceswas considered e.g. by A. S. Morse (1973) and later under more general assumptions (not as-suming the minimality of the realization) by H. Aling and J. M. Schumacher (1984) showingthat the combined decomposition of the state space considering Kalman’s canonical decom-position and Morse’s canonical decomposition in the same lattice diagram corresponds tothe various notions of multivariate zeros.

The book written by J. Ball, I. Gohberg and L. Rodman(1990) uses the concept of left (and right) zero pairs. Thisoffers the possibility of analyzing – together with the posi-tion of the zeros – the corresponding zero directions, as well.The zeros play an important role in the theory of spectralfactors. See e.g. A. Lindquist et al. (1993).

The starting point of the present paper to give state-space descriptions of the module-theoretic notion of thezeros of multivariate transfer functions defined by B. F.Wyman and M. K. Sain (1983) and to extend this analysisto the connection between the zero-modules of a rationalspectral density and its spectral factors, without using e.g.the full-rank condition of the spectral density.

In this module theoretic approach for a rational transferfunction F the action g → Fg is considered. Now if Φ =FF ∗, where F ∗ denotes the adjoint of the function F , thenone might expect that the (right) zeros arising from the

action g → F ∗g appear among the right zeros of Φ, but if h is a right-zero function of Fthen to produce from this a right-zero function of Φ another function g is needed for whichh = F ∗g (at least locally, around the zero location). It can be proved that if F is a left-invertible spectral factor then essentially this property holds. But in case of general spectralfactors the so-called finite zeros of F appear among the finite zeros of Φ but the generic zeroscorresponding to the kernel of F are transformed to finite zeros of Φ.

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On the zero-modules of spectral factors using state space methods – the role of a coupled Sylvester-homogeneous linear equation

Curriculum vitae – Gyorgy MichaletzkyEducation

B.S. Mathematics, L. Eotvos University, Budapest, Hungary, 1975title of the diploma thesis: Control on Lie-groups,

M.S. Mathematics, L. Eotvos University, Budapest, Hungary, 1980title of the dissertation: Sufficient and pairwise sufficient σ-fields

Ph. D. Probability Theory and Statistics, L. Eotvos University,Budapest, Hung. Acad. of Sciences, Budapest, Hungary, 1984title of the dissertation: Sufficient σ - fields, the structure of statistical spaces

Doctor of the Hungarian Academy of Sciences, 2000title of the dissertation: Realization theory of stationary processes and their applications.

Academic positions1990- Head of the Dept. of Prob. Theory and Statist, L. Eotvos University, Hungary.1997-2005 Head of Mathematics Departmental Group, Faculty of Science,

Eotvos Lorand University.2003-2005 vice Dean Faculty of Science, Eotvos Lorand University, Hungary2005- Dean, Faculty of Science, Eotvos Lorand University, Hungary1997-2001 Szechenyi Professor Scholarship, Ministry of Education, Hungary.1994- Chief Research Officer (part time) Laboratory of Operations Research and Decision

Systems, Computer and Automation Institute of Hungarian Academy of Sciences, Hungary.Scientific and Professional Societies and BoardsJanos Bolyai Mathematical SocietyStatistics Committee of the Hungarian Academy of Sciences, 1993-Mathematics Committee of the Hungarian Academy of Sciences, 1993-1996, 1999-Society of Industrial and Applied Mathematics, 1995-Hungarian Actuarial Society, 1992-Research areasRealization theory, sufficient statistics, stochastic optimization, functional analytic methods.

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A unifying formalism of instabilities, nonlinear dynamics, and statisticalmechanics for unsteady shear flows

Bernd R. Noack, Berlin Institute of Technology

Friday, August 1, 14:30–15:30, Latham C

Unsteady shear flows, like wakes, jets, and mixing layers, display a rich kaleidoscope ofphenomena associated with instabilities, transition, and turbulence. Presented efforts tomodel these phenomena are rooted in stability analysis, non-linear dynamics, and statisticalmechanics. We propose a finite-time thermodynamics (FTT) formalism which – for the firsttime – unifies a large class of these shear flow models. The flow attractor is shown to bea partial thermal equilibrium state, interpolating between linear instability and statisticalequilibrium. Results are elaborated for vortex shedding behind a circular cylinder and arereviewed for other fluid motion with simple periodic to complex broad-band dynamics. FTTpredicts the first and second field moments and allows to derive turbulence models in arigorous manner. Moreover, the formalism can be applied to a large class of nonlineardynamical systems and enables fully nonlinear, infinite horizon control.

Prof. Dr.-Ing. habil. Dr.rer.nat. Bernd R. Noack headsthe group ”Reduced-Order Modelling for Flow Control” atthe Faculty V ”Transport and Machine Systems” of theBerlin Institute of Technology, Germany. He develops feed-back flow control solutions for cars, airplanes and trans-port systems — in an interdisciplinary effort with Profs. B.Ahlborn, H.-C. Hege, R. King, M. Morzynski, G. Tadmorand others colleagues. The key for efficient turbulence ma-nipulation is a novel concept of attractor control — synergiz-ing reduced-order modeling (ROM) for fluid flows, nonlineardynamics, statistical physics and control theory.

He has co-authored more than 80 publications and 2patents on ROM and flow control. Dr. Noack’s researchachievements have been acknowledged by German, Euro-pean and American honors including the 2005 Richard vonMises award from the International Association of AppliedMathematics and Mechanics (GAMM).

Born in 1966, Dr. Noack studied physics in Gottingen, were he received his M.S. in 1989and PhD in 1992. In the sequel, he had positions at the Max-Planck Society, GermanAerospace Center, Gottingen University and the United Technologies Research Center (CT,USA) before he joined the Berlin Institute of Technology in 2000.

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Special Sessions at MTNS 2008

1. Modeling and Design of Air Transport Networks organized by Natalia Alexandrov

SSAlex1 Friday morning: Assembly

2. Model Reduction organized by A. C. Antoulas and Christopher Beattie

ModelRed Monday afternoon: Drillfield

3. Interpolation and Related Topics organized by Vladimir Bolotnikov

SSBolo1 Monday morning: Solitude

SSBolo2 Monday afternoon: Solitude

SSBolo3 Tuesday morning: Solitude

SSBolo4 Friday afternoon: Assembly

4. Network Dynamics and Control organized by Konda Reddy Chevva

SSChevva1 Tuesday afternoon: Duck Pond

5. Coding Theory organized by Josep Climent and Joachim Rosenthal

SSClRos1 Monday morning: Assembly

SSClRos2 Tuesday afternoon: Assembly

SSClRos3 Thursday morning: Assembly

6. Analysis and Optimization of Queueing Networks organized by Martin Day and Amar-jit Budhiraja

SSDayBud1 Friday morning: Latham C

SSDayBud2 Friday afternoon: Latham C

7. Hamilton-Jacobi Equations, Viscosity Solutions, and Max-Plus Analysis organized byMartin Day and William McEneaney

SSDayMc1 Tuesday morning: Latham C

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SPECIAL SESSIONS AT MTNS 2008

SSDayMc2 Thursday morning: Latham C

8. Infinite Dimensional Systems organized by Michael A. Demetriou, Birgit Jacob, MiroslavKrstic, Ralph C. Smith and George Weiss

SSDemi1 Monday afternoon: Latham E/F

SSDemi2 Tuesday morning: Latham A/B

SSDemi3 Tuesday afternoon: Latham A/B

SSDemi4 Thursday morning: Latham A/B

SSDemi5 Thursday afternoon: Latham A/B

9. Inverse Problems in Systems, Control and Estimation organized by Per Enqvist

SSEnqvist1 Tuesday morning: Drillfield

SSEnqvist2 Tuesday afternoon: Drillfield

10. Geometric Control of Quantum Mechanical Systems organized by Uwe Helmke andNavin Khaneja

SSHelmKh1 Monday morning: Latham E/F

11. Real Algebraic Geometry, Applications and Related Topics organized by Bill Heltonand Pablo A. Parrilo

SSHelPar1 Friday morning: Latham A/B

SSHelPar2 Friday afternoon: Latham A/B

12. Control Theory and Mechanics organized by Andrew D. Lewis

SSLewis1 Monday morning: Latham C

SSLewis2 Monday afternoon: Latham C

13. Distributed Decision Making in Networking and Control organized by Anders Rantzerand Pablo A. Parrilo

SSRantPar Thursday afternoon: Cascades

14. Control of Complex Networks and Environmental Applications organized by DanielJ. Stilwell and Maurizio Porfiri

SSStilPor1 Thursday morning: Cascades

SSStilPor2 Friday morning: Cascades

15. Classical PDE Control Studies organized by David Russell

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SPECIAL SESSIONS AT MTNS 2008

SSRussell1 Monday morning: Latham A/B

SSRussell2 Friday morning: Latham E/F

16. Multidimensional System Theory, Multivariable Operator Theory, and Applicationsorganized by Dmitry S. Kaliuzhnyi-Verbovetskyi and Victor Vinnikov

SSKVV1 Tuesday afternoon: Solitude

SSKVV2 Thursday morning: Solitude

SSKVV3 Thursday afternoon: Solitude

17. Algebraic and Behavioral Methods in Systems and Control Theory organized by EvaZerz

(a) SSZerz1 Monday afternoon: Latham A/B

(b) SSZerz2 Tuesday morning: Assembly

(c) SSZerz3 Thursday afternoon: Latham E/F

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