Welcome to III International Summer School on Geometry, Mechanics and Control organised by the Geometry,  Mechanics and Control (GMC) Network.

The third edition of the International Summer School on Geometry, Mechanics and Control will be held in Catalonia, Spain, and it will take place in L’Ametlla de Mar, June 22-27, 2009.

The school is oriented to young researchers, Ph.D. and postdoctoral students in Mathematics, Physics and Engineering, in particular those interested in focusing their research on geometric control and its applications to mechanical and electrical systems, and optimal control. It is intended to present an up-to-date view of some fundamental issues in these topics and bring to the participants attention some open problems, in particular problems related to applications.  The courses will be delivered by some of the best international scientists in the respective topics.

This Summer School is a post-graduate course of CSIC on science and physical technologies.

Important dates:

Registration: no later than 15 May, 2009

Scholarships: no later than 15 April, 2009


ANDREW D. LEWIS (Queen’s University, Kingston, Canada)

Controllability theory (5 hours)

Controllability is a fundamental problem in control theory, dealing with the problem of determining whether it is possible to steer a control system from one state to another.  The property of controllability underlies any control design methodology, and has deep connections to the theory of optimal control.  Despite its fundamental importance in control theory, the property of controllability remains somewhat poorly understood.

These lectures will begin at a low level, introducing the problem of controllability, considering simple but illustrative examples, and considering the mechanisms for controllability.  Then some simple theorems concerning controllability will be stated and sometimes proved.

Basic theorems concerning the structure of the reachable set will be provided and discussed.

What will then follow is a survey of known results, plus counterexamples illustrating the limits of applicability of these results.  The emphasis will be on the techniques and tools used in the study of controllability.

Material [PDF]


ANTHONY BLOCH (University Michigan, USA)

Geometric Control of Mechanical and Nonholonomic Systems (7 hours)

This course will discuss the the geometry and dynamics of mechanical systems and various techniques for their control. The theory of geometric mechanics gives a general framework for analyzing aspects of mechanical systems theory, in particular notions of symmetry and conservation laws and stability. The theory extends in a natural fashion to nonlinear control theory where one is interested in controllability and stabilization of systems defined on manifolds. These lectures will cover the following topics: Key examples of mechanical and control systems; theory of geometric mechanics including the theory of Lagrangian systems, Hamiltonian systems and nonholonomic systems; topics in nonlinear control theory; controllability of nonholonomic systems, stability and stabilization of mechanical and nonholonomic systems including the energy momentum method and controlled Lagrangians; optimal control of mechanical systems and subRiemannian geometry.

A basic textbook is the book Nonholonomic Mechanics and Control Theory, by A Bloch, with J. Baillieul, P. Crouch and J.Marsden, but many other sources will be used as well.

Material [PDF]


VELIMIR JURDJEVIC (University of Toronto, Canada)


Optimal Control on Lie Groups: Integrable Hamiltonian systems (5 hours)


Material [PDF]



ROMEO ORTEGA (Laboratoire des Signaux et Systèmes, LSS/CNRS/Supélec, France)


Passivity-Based Control of Physical Systems: Control by Interconnection and State-Feedback Laws (6 hours)


Material [PDF]

As vividly illustrated by the quintessential Watt's governor a natural procedure to modify the behavior of a dynamical system is to interconnect it with another dynamical system. Examples of this approach abound in modern high-performance practical applications and are proven to be very robust and reliable. These include, among many others, mechanical suspension and flapper systems, flotation devices, damping windings and impedance matching filters in electrical systems. (It may be even argued that biological and medical applications, of great current interest, are best studied invokinginterconnection principles instead of simplistic causeeffect preconceptions.)

Adopting the interconnection perspective allows us to formulate the control problem in terms of the physical properties of the systems like energy-shaping and damping injection, it furthermore underscores the role of interconnection to achieve these objectives. This should be contrasted with the classical actuator-plant-sensor paradigm that leads to a signal-processing view of control in which the systems physical properties are di±cult to incorporate.

In our previous works we have proposed a mathematical framework to design controllers using the aforementioned systems interconnection perspective that we called Control by Interconnection (CbI). Towards this end we restricted ourselves to systems described by Port-Hamiltonian (PH) models, which suitably describe the dynamics of many physical processes, and where the importance of the energy function, the interconnection pattern and the dissipation of the system is highlighted. In CbI the controller is another PH system connected to the plant (through a power-preserving interconnection) to add up their energy functions. In spite of the conceptual appeal of formulating the control problem as the interaction of dynamical systems, the current version of CbI imposes a severe restriction on the plant dissipation structure that stymies its practical application.

The purpose of this course is to propose some extensions to the CbI method to make it more widely applicable|in particular, to overcome the dissipation obstacle [1]. Furthermore, we establish the connections between CbI and Standard PassivityBased Control (PBC). Standard PBC, where energy shaping is achieved via static (or dynamic) state feedback, is one of the most successful controller design techniques [2] [3]. However, the control law is usually derived either from an uninspiring and non-intuitive "passive output generation" viewpoint or from an, equally restrictive, model matching perspective-where a quadratic storage function is assigned to the error dynamics. We prove in this talk that Standard PBC is obtained restricting CbI to a suitable subset of the state space|providing a nice geometric interpretation to Standard PBC.

The application of the methods is illustrated with the following practical examples: electromechanical systems (double-fed induction machines, synchronous motors and micro-electromechanical systems), power system stabilizers, switched power converters and underactuated mechanical systems.


[1] R. Ortega, A. van der Schaft, F. Casta~nos and A. Astolfi, Control by state{modulated interconnection of port{Hamiltonian systems, IEEE Trans. Automat. Contr., Vol. 53, No. 11, pp. 2527{2542, 2008.

[2] R. Ortega, A. Loria, P. J. Nicklasson and H. Sira{Ramirez, Passivity-Based Control of Euler{Lagrange Systems, Springer-Verlag, Berlin, Communications and Control Engineering, 1998.

[3] A. Astolfi, D. Karagiannis and R. Ortega, Nonlinear and Adaptive Control with Applications, Springer-Verlag, Berlin, Communications and Control Engineering, 2007.



The school is organized as follows. First, two basic courses will be given, one on Geometric Control, in which problems related with different aspects of controllability will be discussed, and another one on Geometric Control of Mechanical systems; they will be followed by a shorter one on Optimal Control on Lie Groups. From these courses, two different applications will be dealt with: one is oriented to electric networks and the other one will present a complex system and the necessary tools for its development and coordination.


Monday 22

Tuesday 23

Wednesday 24

Thursday 25

Friday 26





Geometric Control of Mechanical and Nonholonomic Systems


Geometric Control of Mechanical and Nonholonomic Systems


 Session for young researchers

Passivity-Based Control of Physical Systems: Control by Interconnectionand State-Feedback Laws


Passivity-Based Control of Physical Systems: Control by Interconnectionand State-Feedback Laws











Controllability theory


Optimal Control on Lie Groups: Integrable Hamiltonian systems



Controllability theory


Optimal Control on Lie Groups: Integrable Hamiltonian systems



Lunch break

Lunch break


Lunch break

Lunch break



Geometric Control of Mechanical and Nonholonomic Systems


Geometric Control of Mechanical and Nonholonomic Systems



Passivity-Based Control of Physical Systems: Control by Interconnectionand State-Feedback Laws


Passivity-Based Control of Physical Systems: Control by Interconnectionand State-Feedback Laws










Optimal Control on Lie Groups: Integrable Hamiltonian systems


Controllability theory



Optimal Control on Lie Groups: Integrable Hamiltonian systems


Controllability theory




Contact: gmcnetatull [dot] es

In order to register, please send the following information by e-mail togmcnetatull [dot] es

First Name
Family Name
E-mail address

Are you a student or PhD student?


The standard registration fee for participants is 200 Euros
The fee for students and retired scientists is 100 Euros
The registration fee includes: conference materials and coffee breaks.

Payment should be made by bank order to the following bank account


Bank: Cajacanarias

Account: 2065 0067 61 1400223636

IBAN: ES31 2065 0067 6114 0022 3636



Please, ask your bank to write explicitly in your transference order the name "3GMC + surname of the participant" and send confirmation (your name and transfer details) by e-mail to gmcnetatull [dot] es (gmcnetatull [dot] es) or by fax to the number +34922318145, no later than 15 May, 2009



Financial Support:


A limited number of scholarships for PhD and advanced undergraduate students will be provided by the organisers in order to partially cover for travel and/or lodging expenses.

If you want to apply for a scholarship, please send here gmcnetatull [dot] es your CV (and grades certificate in case you are an undergraduate student) by April 15, 2009.


Lodging reservation:


Urb. Roques Daurades

Cala Bon Capó 43860

L’Ametlla de Martel.

Phone 34 977 45 77 91

fax. 34 977 45 77 92

Single room: 95,25 Euros (Room + Breakfast+lunch + dinner) VAT included

Double room: 63,50 Euros per person (Room + breakfast + lunch + dinner) VAT included

To do the reservation of the accomodation (or the fligth)  you can send to gmcnetull [dot] es with the following information

Type of room (Double, Single or other type)

Check-in date:

Check-out date:

For information of the price of rooms for three or four persons to ask in gmcnetull [dot] es



Family Name Name  Institution  Country
Aguilar Cesar Queen's University Canada
Balseiro Paula CONICET Argentina
Barbero Liñán  María  INRIA Nancy Grand-Est France
Bhowmik Subrata Technical University of Denmark, Lyngby Denmark
Bloch Anthony University of Michigan  USA
Bright Ido The Weizmann Institute of Science Israel 
Bruveris Martins  Imperial College London UK
Caponigro Marco SISSA/ISAS, Trieste Italy
Casas Fernando Universitat Jaume I Spain
Colombo Leonardo Universidad de La Plata Argentina
Colomé Figueras Adrià Universitat Politècnica de Catalunya Spain
de León  Manuel ICMAT, CSIC Spain 
De Nicola Antonio University of La Laguna Spain
Diaz Viviana Universidad Nacional del Sur  Spain
Ellis  David  Imperial College London UK
Farokhi Farhad Sharif University of Technology Iran
Fernandez Javier Instituto Balseiro - Centro Atómico Bariloche Argentina
Ferraro Sebastián Universidad Nacional del Sur  Argentina
Franch Jaume UPC Spain
Gallardo Abel Technical University or Catalonia Spain
García Naranjo Luís  EPFL Switzerland
Garrone Enrico Università degli Studi of Turin Italy
Gay-Balmaz Francois EPFL Switzerland
Ghezzi Roberta University of Trieste Italy
Gràcia Xavier Technical University of Catalonia  Spain 
Grillo Sergio Instituto Balseiro - Centro Atómico Bariloche Argentina
Grosch Patrick Instituto de Robotica e Informatica Industrial Spain
Hochgerner Simon EPFL Switzerland
Iglesias  David  ICMAT, CSIC Spain
Jiménez Fernando ICMAT, CSIC Spain
Jurdjevic Velimir  Univerty of Toronto Toronto
Koiller Jair Fundação Getulio Vargas/RJ Brazil
Kule Memet MEB Halil Akkanat Çok Programlı Lisesi Turkey 
Lewis Andrew Queen’s University Canada
Long David  North Carolina State University USA
Manno Giovanni University of Milano-Bicocca Italy
Marrero Juan Carlos University of La Laguna Spain
Martín de Diego David  ICMAT, CSIC Spain 
Martínez Eduardo Universidad de Zaragoza Spain
Martínez Campos Cédric  ICMAT, CSIC Spain
Muñoz Lecanda  Miguel Technical University of Catalonia  Spain 
Ohsawa TomoKi University of Michigan  USA
Ortega Romeo Laboratoire des Signaux et Systèmes, Spélec France
Padrón Edith University of La Laguna Spain
Perez Martinez Mª Carmen Universidad de Cádiz Spain
Pietrzkowski Gabriel Institute of Mathematics of the Polish Academy of Sciences Poland
Prieto Pere Daniel Technical University of Catalonia Spain
Pugliese Fabrizio Università di Salerno Italy
Rodriguez de la Peña Thalia Universidad Carlos III de Madrid  Spain
Rodríguez Olmos Miguel University of Manchester UK
Román-Roy Narciso Technical University  of Catalonia Spain
Salgado Modesto University of Santiago de Compostela Spain
Salnikov Vladmir Institute Camille Jordan, Universite Claude Bernard Lyon 1** France
Santos Patricia ISEC/CMUC Portugal
Sarras Ioannis Universite Paris-Sud France
Shermenev Alexander General Physics Institute Russia
Stern Ari University of California, San Diego USA
Tobella Alomar  Enric  Technical University of Catalonia Spain
Tronci Cesare EPFL Switzerland
Velho Roberto Federal University of Rio de Janeiro Brazil
Vilariño Silvia Universidad de Santiago de Compostela Spain
Zakharova Anastasia Grenoble INP France



Oganizer Committe

Miguel Carlos Muñoz Lecanda (UPC)

Narciso Román Roy (UPC)

Xavier Gràcia Sabaté (UPC)

David Martín de Diego (CSIC)

Edith Padrón Fernández (ULL)


Organizers of Scientific Programme

Manuel de León Rodríguez, CSIC

Juan Carlos Marrero González, ULL

Miguel Carlos Muñoz Lecanda, UPC

Eduardo Martínez Fernández, UNIZAR



How to get here:

Travel information

Transfer and transport from the Airport to the city centre

For an in-depth review of all the transport methods between the airport and Barcelona city centre Click Here or click on the most appropriate transport means below to go directly to that information.

Taxis (click for more info) - a Taxi offers a low-cost and convenient way to get to the city centre - the fare is around 25 euros and the journey takes around 25 - 30 mins (depending on traffic)

Aerobus (click for more info) ( Shuttle bus service) - Express bus service that runs regularly between the airport and the city centre. 4.25 euros for a single ticket and takes about 25 -30 minutes (depending on traffic)

Private car hire transfer - arrange a private car hire in advance of your trip. 

Trains from the Airport (Click for more info) the RENFE train will take you from Barcelona airport to the city centre where you can change for the metro system at either Barcelona Sants (Sants Estacio) or Passeig de Gracia stations. Tickets 2.80 euros. Journey time is about 25 minutes.

Barcelona Car hire ( Click for more info) Cheap car hire is available from terminal B. This page lists all the main car hire rental companies at Barcelona airport with contact information.

Travelling by train from Barcelona to L’Ametlla de Mar

Train timetable:

More information on the Barcelona-Sants Station web-page:

In order to arrive from the train station in L’Ametlla de Mar to the hotel, please follow the indications in the Interactive map:

Travelling by car from Barcelona to L’Ametlla de Mar

Take the Highway AP-7, Tarragona direction. Then, keep in the highway  AP-7 until you get to the exit 39  “l’Ametlla / El Perelló”.

Take the road TV-3025 to l'Ametlla de Mar.

(Another option is to take the main road – N 340).

Once on town: at the town entrance, follow the indications on the road. There's yellow signs that indicate the route to the Hotel Ametlla Mar.

More information: At the web page of L’Ametlla de Mar

Telephones of interest

HIFE Buses 977 440 300
RENFE (train) information 902 240 202
Reus Airport (35km) 977 771 911
Barcelona Airport (140km) 932 983 838
Taxis in l'Ametlla 977 456 468
  977 456 259
  977 493 322
  977 456 094