This document provides an overview and summary of a book containing articles presented at three workshops on advances in control, signals, and systems theory, with an emphasis on physical modeling. The workshops covered electrical and mechatronic systems, mathematical tools, and chemical processes and life sciences. The book is organized into three parts corresponding to the workshops. It presents key contributions and surveys on topics like modeling of multi-body mechanical systems, sliding mode control, Hamiltonian modeling, nonlinear parameter estimation, underactuated mechanical systems, motion planning for pendulums, mechanical suspension systems, MEMS modeling and control, flatness characterization, nonholonomic mechanics, controlled Lagrangians, input delay compensation, genetic regulatory networks, cancer modeling, ventilation modeling,

2. Lecture Notes
in Control and Information Sciences 407
Editors: M. Thoma, F. Allgöwer, M. Morari

4. Jean Lévine and Philippe Müllhaupt (Eds.)
Advances in the Theory
of Control, Signals
and Systems with
Physical Modeling
ABC

5. Series Advisory Board
P. Fleming, P. Kokotovic,
A.B. Kurzhanski, H. Kwakernaak,
A. Rantzer, J.N. Tsitsiklis
Editors
Jean Lévine
CAS, Unité Mathématiques et Systèmes
MINES-ParisTech
35, rue Saint-Honoré
77300 Fontainebleau
France
E-mail: jean.levine@mines-paristech.fr
Philippe Müllhaupt
Laboratoire d’Automatique
Faculté des Sciences
de l’Ingénieur
Station 9
CH-1015 Lausanne
Switzerland
E-mail: philippe.muellhaupt@epfl.ch
ISBN 978-3-642-16134-6 e-ISBN 978-3-642-16135-3
DOI 10.1007/978-3-642-16135-3
Lecture Notes in Control and Information Sciences ISSN 0170-8643
Library of Congress Control Number: 2010936509
c 2010 Springer-Verlag Berlin Heidelberg
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6. Advances in the Theory of Control, Signals, and
Systems, with Physical Modeling
Jean L´evine1 and Philippe M¨ullhaupt2
1 Introduction
This book gathers articles that have been invited for presentation in the framework
of a Bernoulli Programme, held at the Bernoulli Center in Lausanne (Switzerland)
from January to June 2009.
This Programme mainly consisted of three workshops aiming at reviewing the
advances in the theory of control, signals, and systems, with a particular emphasis
on their relationship to physical modeling.
More precisely, the aim of this series of three workshops was to
• bring together knowledge and know-how from the communities of control, sig-
nals and systems,
• focus on the theoretical advances in these areas and examine the possibilities of
new convergences between them,
• contribute to the enhancement of the dialogue between theoretical laboratories
and more practically oriented units and industries.
In the 60’s, control, signals and systems had a common linear algebraic back-
ground and, according to their evolution, their respective backgrounds have now
dramatically differed. Recovering such a common background, especially in the
nonlinear context, is currently a fully open question.
In most contributions, emphasis has been put on physical modeling, which serves
as an Ariadne’s thread between the diverse fields of interest. This idea is not new,
however. As an example, mechanical system modeling, which heavily relies on ana-
lytical mechanics and in particular its conservation laws, has greatly inspired control
theory. As another example, control of chemical processes also gained in the use of
1 Centre Automatique et Syst`emes, Unit´e Math´ematiques et Syst`emes, Mines-ParisTech,
E-mail: jean.levine@mines-paristech.fr
2 Laboratoire d’Automatique, Ecole Polytechnique F´ed´erale de Lausanne
E-mail: philippe.muellhaupt@epfl.ch

7. VI Jean L´evine and Philippe M¨ullhaupt
sophisticated modeling software tools based on theories of mass balance conser-
vation and entropy laws. Hence one purpose of this program was to force the in-
teraction of probably uncorrelated disciplines thanks to these theoretical modeling
aspects.
Another important aspect of the conferences was to present and develop new
applications of the above approaches, and contribute to the enhancement of the dia-
logue between theoretical laboratories and more practically oriented research units
and industries, in both classical areas and emerging fields of research.
The first workshop, entitled Electrical and Mechatronical Systems Workshop
looked at various applications stemming from Mechatronics, Electrical and Me-
chanical Engineering, such as MEMS, eletrical machines, robots and car suspension.
From the modeling and methodological side, finite dimensional systems (described
by ordinary differential equations or difference equations) and infinite dimensional
systems (delayed systems, distributed systems, PDEs’, non-integer derivations)
were approached for control and signal processing, as well as model-free tech-
niques Indeed, the influence of physical modeling contributed to outline some con-
vergences. In particular, a unifying Lagrangian formalism has been sketched so as
to integrate electrical, electronical, magnetic and mechanical aspects of systems,
potentially leading to significant simplifications in the analysis of control systems.
Both finite dimensional and infinite dimensional models are shown to ease some es-
timation, adaptative control and observation problems. New applications in emerg-
ing fields of mechatronic systems, such as MEMS, or new suspension technologies,
have been presented, showing that Mechanics, Mechatronics and Electronics remain
a major source of inspiration for control and system theorists.
The aim of the second workshop, entitled Mathematical Tools Workshop, was to
serve as a think tank for mathematical paradigms in the fields of Control, Signals
and Systems. Again, both finite dimensional and infinite dimensional models have
been explored. Various approaches, in the framework of differential geometry and
algebra have been examined. Group theory and Riemannian Geometry appeared in
many presentations with, in particular, robotics, mechanical systems or quantum
control as background applications. Recent advances, in the fields of hamiltonian,
lagrangian, quantum, energy-based and flat or non flat control systems have also
been presented.
Finally, the third and last workshop, entitled Chemical and Life Science Work-
shop, concerned new approaches in the analysis of biomedical, biomechanical and
reaction systems, possibly coupled with fluid dynamics, with many challenging ap-
plications such as cancer treatment and diagnosis. Important results concerning uni-
fying approaches to deal with complex chemical and biochemical reactions have
been presented taking into account the network structure of the reactions while en-
suring robustness with respect to various unknown parameters and perturbations.
The influence of noisy data in the biological and chemical reaction systems has also
been approached. Time-scales, transients and bifurcations in ecological systems,
population dynamics and biological systems have also received a great attention
and their control theoretical perspectives have been envisaged.

8. Advances in Control, Signals and Systems VII
The reader will find in the present volume key contributions and surveys, giving a
precise account of the above topics. The book is organized in three parts, according
to the three aforementioned workshops. In each part, the articles follow the alpha-
betic order of the first author. This order has been prefered to a more sophisticated,
but often artificial, clustering by sub-themes. We hope that these readings will be
most inspiring and informative to PhD students and researchers in Mathematics,
Electrical, Mechanical, Chemical or Bio Engineering, and more generally to every
people of both the academic and industrial spheres curious of the recent develop-
ments in control, signals and systems.
We are very grateful both to the Swiss National Science Foundation for funding
such an endeavor and to the Centre Bernoulli for providing the required infrastruc-
ture. In particular, we thank Mrs. Christiane De Paola, Talya Van Woerden, Sabrina
Martone, and Rana Gherzeddine for the important administrative and organisational
work and Mr. Marc Perraudin for maintaining the internet server. Last, but not least,
we are deeply indebted to Prof. Tudor Ratiu for his constant encouragements to
organize the above program.
Jean L´evine and Philippe M¨ullhaupt
Mines-ParisTech and EPFL

10. Contents
Part I: Electrical and Mechatronical Systems
Modeling and Control of Multi-Body Mechanical Systems:
Part I A Riemannian Geometry Approach . . . . . . . . . . . . . . . . . . . 3
Suguru Arimoto
Modeling and Control of Multi-Body Mechanical Systems:
Part II Grasping under Rolling Contacts between Arbitrary
Shapes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
Suguru Arimoto
Sliding Mode Control for a High-Speed Linear Axis Driven
by Pneumatic Muscles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Harald Aschemann, Dominik Schindele
Using Hamiltonians to Model Saturation in Space Vector
Representations of AC Electrical Machines . . . . . . . . . . . . . . . . . . 41
Duro Basic, Al Kassem Jebai, Fran¸cois Malrait, Philippe Martin,
Pierre Rouchon
Iterative Learning Control Using Stochastic Approximation
Theory with Application to a Mechatronic System . . . . . . . . . . . 49
Mark Butcher, Alireza Karimi
Elimination Theory for Nonlinear Parameter Estimation. . . . . 65
John Chiasson, Ahmed Oteafy

11. X Contents
Controlling Underactuated Mechanical Systems: A Review
and Open Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Zhong-Ping Jiang
Time Scaling in Motion Planning and Control of Tree-Like
Pendulum Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Matthias Krause, Joachim Rudolph, Frank Woittennek
Mechanical Version of the CRONE Suspension . . . . . . . . . . . . . . 99
Alain Oustaloup, Xavier Moreau
Electrostatic MEMS: Modelling, Control, and
Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
Guchuan Zhu
Part II: Mathematical Tools
Flatness Characterization: Two Approaches . . . . . . . . . . . . . . . . . 127
Felix Antritter, Jean L´evine
Nonholonomic Mechanics, Dissipation and Quantization . . . . . 141
Anthony M. Bloch
Controlled Lagrangians . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153
Dong Eui Chang
Compensation of Input Delay for Linear, Nonlinear,
Adaptive, and PDE Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
Miroslav Krstic
Boundary Value Problems and Convolutional Systems over
Rings of Ultradistributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Hugues Mounier, Joachim Rudolph, Frank Woittennek
Wei-Norman Technique for Control Design of Bilinear
ODE Systems with Application to Quantum Control . . . . . . . . 189
Markku Nihtil¨a
Interval Methods for Verification and Implementation of
Robust Controllers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Andreas Rauh, Harald Aschemann
Rational Interpolation of Rigid-Body Motions . . . . . . . . . . . . . . . 213
J.M. Selig
Contact Geometry and Its Application to Control . . . . . . . . . . . 225
Peter J. Vassiliou

12. Contents XI
Part III: Chemical Processes and Life Sciences
Piecewise Affine Models of Regulatory Genetic Networks:
Review and Probabilistic Interpretation . . . . . . . . . . . . . . . . . . . . . 241
Madalena Chaves, Jean-Luc Gouz´e
A Control Engineering Model for Resolving the TGF-β
Paradox in Cancer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
Seung-Wook Chung, Carlton R. Cooper, Mary C. Farach-Carson,
Babatunde A. Ogunnaike
A Mathematical Model of Air-Flow Induced Regional
Over-Distention during Mechanical Ventilation: Comparing
Pressure-Controlled and Volume-Controlled Modes . . . . . . . . . . 269
P.S. Crooke, A.M. Kaynar, J.R. Hotchkiss
Positive Feedbacks Contribute to the Robustness of the
Cell Cycle with Respect to Molecular Noise . . . . . . . . . . . . . . . . . 283
Didier Gonze, Marc Hafner
Guaranteed and Randomized Methods for Stability
Analysis of Uncertain Metabolic Networks . . . . . . . . . . . . . . . . . . . 297
Heinz Koeppl, Stefano Andreozzi, Ralf Steuer
Coexistence of Three Predators Competing for a Single
Biotic Resource . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
Claude Lobry, Tewfik Sari, Karim Yadi
Control Problems for One-Dimensional Fluids and Reactive
Fluids with Moving Interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323
Nicolas Petit
A Port-Hamiltonian Formulation of Open Chemical
Reaction Networks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
Arjan van der Schaft, Bernhard Maschke
Bifurcations of Dynamical Systems, Logistic and Gompertz
Growth Laws in Processes of Aggregation . . . . . . . . . . . . . . . . . . . 349
Alex Shoshitaishvili, Andrei Raibekas
Global Uncertainty Analysis for a Model of TNF-Induced
NF-κB Signalling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
Steffen Waldherr, Jan Hasenauer, Malgorzata Doszczak,
Peter Scheurich, Frank Allg¨ower
Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379