1st International Summer School on Geometry, Mechanics and Control
Organizing Committee
Manuel de León Rodríguez, (CSIC, Madrid)
David Martín de Diego, (CSIC, Madrid)
Edith Padrón Fernández, (University of La Laguna)
Organizers of the Scientific Programme
Juan Carlos Marrero (University of La Laguna)
David Martín de Diego (CSIC, Madrid)
Eduardo Martínez (University of Zaragoza)
Miguel Muñoz Lecanda (Technical University of Catalonia)
|
Monday, June 25 |
Tuesday, June 26 |
Wednesday June 27 |
Thursday, June 28 |
Friday, June 29 |
8:00-9:30 |
Registration (8:00-9:00) and Opening(9:00-9:30) |
|
|
|
|
9:30-11:00 |
Geometric integration of Hamiltonian systems
|
Geometric integration of Hamiltonian systems |
Geometric integration of Hamiltonian systems |
Distributed motion coordination of robotic networks |
Geometric integration of Hamiltonian systems
|
11:00-11:30 |
Coffee |
Coffee |
Coffee |
Coffee |
Coffee |
11:30-13:00
|
Distributed motion coordination of robotic networks |
Distributed motion coordination of robotic networks |
Computational Geometric Mechanics and Control |
Optimal Control of PDEs
Until 13:30 |
Computational Geometric Mechanics and Control |
13:00-15:30 |
Lunch |
Lunch |
Lunch |
Lunch |
13:00-13:30 Closing Lunch |
15:30-16:30 |
Geometric integration of Hamiltonian systems |
Distributed motion coordination of robotic networks
|
Computational Geometric Mechanics and Control |
Computational Geometric Mechanics and Control |
|
16:30-17:00 |
Coffee |
Coffee |
Coffee |
Coffee |
|
17:00-18:00 |
Distributed motion coordination of robotic networks |
Posters |
Computational Geometric Mechanics and Control |
LAB: Computational Geometric Mechanics and Control |
|
Scholarships
A limited number of scholarships for PhD Student and advanced undergraduate students, that may cover registration fees, lodging expenses or/and travel expenses, will be provided by the organisers.
If you want to apply for a scholarship, please send us to here gmcnetull.es your CV (and grades certificate in case your are an undergraduate student) before April 30, 2007.
Contact: gmcnetull [dot] es
To make the registration, please send the following information by e-mail to gmcnetull [dot] es
First Name |
Family Name |
Institution |
Country |
FAX |
E-mail address
Are you a student or PhD student? Do you want to present a Poster?
Title of the Poster
|
The registration fee
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, coffee breaks and lunches along the Workshop
Payment should be made by transference to the following bank account
Bank: Cajacanarias
Account: 2065 0067 67 3000223636
IBAN: ES72 2065 0067 6730 0022 3636
BIC/SWIFT: CECAESMM065
Please, ask your bank to write explicitly in your transference order the name "GMC + surname of the participant" and send confirmation (your name and transfer details) by e-mail to gmcnetull [dot] es or by fax to the number +34922318145, no later than 31 May, 2007.
Lodging reservation
The number of rooms which have been reserved by the organization is limited, therefore we ask you to make the reservation as soon as possible.
Hotel Las Rocas (Hotel****) http://www.lasrocashotel.com/es/
PRICES
Single room: 73,83 Euros (Room + Breakfast) VAT included
Double room: 44,94 Euros per person (Room + Breakfast) VAT included
Hotel Miramar (Hotel***) http://www.miramardecastro.com/
PRICES
Single room: 50 Euros (Room + Breakfast) VAT included
Double room: 30 Euros per person (Room + Breakfast) VAT included
To make a hotel reservation, please send the following information by e-mail to gmcnetull [dot] es
First name |
Family name |
Institution |
Phone |
FAX |
E-mail address |
I want do the lodging reservation in the hotel........... for ....... person(s)
Date of arrival ........
Date of departure ........
Family Name | First Name | Institution | Country |
Aragüés Muñoz | Rosario | University of Zaragoza | Spain |
Bajars | Janis | Centrum voor Wiskunde an Informatica | Netherlands |
Barbero | Maria | Technical University of Catalonia | Spain |
Bassi | Luca | University of Bologna | Italy |
Bustillo Saiz | Paula | University of Cantabria | Spain |
Cortés | Jorge | Univ. of California (Santa Cruz) | USA |
de León | Manuel | CSIC, Madrid | Spain |
Díaz | Viviana | Universidad Nacional del Sur | Argentina |
Dragulete | Oana Mihaela | EPFL Lausanne | Switzerland |
Ferraro | Sebastián | CSIC, Madrid | Spain |
Grebow | Daniel John | Purdue University | USA |
Grillo | Sergio | Instituto Balseiro-Univ. Nacional de Cuyo | Argentina |
Hinic | Ana | Institute of Mathematics and Informatics | Serbia |
Iglesias | Ponte | CSIC, Madrid | Spain |
Leok | Melvin | Purdue University | USA |
Long | David | North Carolina State University | USA |
Lugo-Villeda | Luís Iván | Sant'Anna School of Advanced Studies | Italy |
Lukasik | Maciej | Warsaw University | Poland |
Marrero | Juan Carlos | Univ. La Laguna | Spain |
Martín de Diego | David | CSIC, Madrid | Spain |
Martínez | Eduardo | University of Zaragoza | Spain |
Martínez Campos | Cédric | CSIC, Madrid | Spain |
Moriano | Cristina | Universidad Antonio Nebrija | Spain |
Muñoz-Lecanda | Miguel C. | Technical University of Catalonia | Spain |
Padrón | Edith | University of La Laguna | Spain |
Quintana-Portilla | Gema | University of Cantabria | Spain |
Ramírez Jr. | Juan | Purdue University | USA |
Roldán | Charles | Purdue University | USA |
Rosado | Eugenia | Universidad Politécnica de Madrid | Spain |
Santa-María Megía | Ignacio | Universidad Complutense de Madrid | Spain |
Santoso | Jenny | University of Stuttgart | Germany |
Sanz-Serna | J M | University of Valladolid | Spain |
Shen | Bo | university Dortmund | Germany |
Sosa | Diana | University of La Laguna | Spain |
Tejado Balsera | Inés | University of Extremadura | Spain |
Turhan | Murat | EPFL Lausanne | Switzerland |
Vankerschaver | Joris | University of Ghent | Belgium |
Zadeh | Joseph | Purdue University | USA |
To arrive at Castro:
By car; use mappy or via Michelin to plan your trip.
If you arrive by plane, the best arrival airport is the one at Bilbao. From there, you must take a bus until TermiBus of Bilbao (frequence: half an hour, price: 1,50 euros, duration: half an hour). You can also take a taxi (20 euros). Teletaxi: 944800909. To go from Bilbao to Castro-Urdiales you could take a bus of the company Bizkaibus-Encartaciones (tel: 94 636 34 24). There is a bus each 30 minutes and the price is 2.42 euros, which lasts around 50 minutes. You take this bus at TermiBus station. This bus makes several stops in Castro. You can ask the drive about the best stop to go to the Hotel Las Rocas and/or Miramar (or to the Beach Brazomar, see the street guide).
If you come to Castro through Bilbao, a taxi could be another option (around 50 euros; tel 944800909)
The bus company ALSA (tel: 902 42 22 42) have routes to Castro Urdiales from Oviedo, Santander, San Sebastián, Vitoria, Pamplona and Zaragoza.
Where to go:
The conferences and coffee breaks will be at Centro Cultural "La Residencia", where CIEM is located.
Lodging will be at Hotel Las Rocas (in which the participants will have lunch) and Hotel Miramar.
In this Castro Urdiales street guide, the hotels Las Rocas and Miramar are in the squares C8 and B8, respectively. The location of CIEM is at square B7 (marked with an "8").
Here you have a printable version, from squares B6 to C8.
More information:
- Castro Urdiales street guid
- Centro Cultural "La Residencia" (CIEM)
- How to arrive at Castro Urdiales
- Lodging in Castro Urdiales
- Restaurants in Castro Urdiales
- Cultural activities in Castro Urdiales

The International Summer School on Geometry, Mechanics and Control is oriented to Ph.D. students and t postdoctoral students with undergraduate studies in Mathematics, Physics or Engineering, in particular to those who want to begin its research in geometrical aspects of mechanics, numerical integration, field theory and control theory. In this sense, the courses could be a complement to Ph.D. programs of different Universities. The main pretension is to form and attract young researchers of contrasted quality in the International context in leader topics around Mechanics, Differential Geometry and Control.
The School is also open to professionals who want to attend advanced and specialized courses oriented to geometrical techniques in those fields. It pretends to show an updated version of the knowledge of some basic problems in these topics and to present to the participants open problems and, in particular, the applications by means of specialized courses taught by the best international researchers in the respective fields.
The specific scientific profile of the School in 2007 is based on the research lines of Numerical Analysis (in particular, numerical integration), Geometric Mechanics and Control Theory with applications to Engineering, Robotics and Physics.
In 2007, the School will develop two research lines which will linked along the course. In each of the lines, it will be proposed discussion sessions and presentation of open problems and research to be done in the future.
-
Numerical integration and Geometric Mechanics
During the last decade, a remarkable effort has been made in the construction of geometric integrators for Lagrangian and Hamiltonian systems. The main idea consists in looking for numerical methods which preserve one or more geometric invariants associated to those systems (energy, first integrals, symplecticity ...).
-
Optimal Control Theory: Applications to Engineering
The mathematical theory of control is a broad area which, from a mathematical point of view, deals with three fundamental problems in Control Theory: modelling, analysis and design. For that, it is used different areas of Mathematics, for instance: Differential and Symplectic Geometry, Stability Theory of Dynamical Systems, Complex Analysis, Differential Analysis, Functional Analysis, Complexity Theory, etc. As it is expected, this approach implies the appearance of new problems in all those areas which suppose a fruitful interaction between them.
[PDF file]
Minicourse: Geometric integration of Hamiltonian systems |
Departament of Applied Mathematics University of Valladolid
NOTES [PDF] |
Contents: Numerical methods for the integration of ordinary differential equations have a long and distinguished history, but only flourished in connection with the digital computer fifty or sixty years ago. Typically those methods are universal in the sense that they may be applied to any differential system. While this feature has made it possible to build general-purpose software packages of wide applicability, it is clear that the one-size-fits-all approach cannot be optimal in all cases. It is therefore plausible to investigate whether special methods can be introduced to integrate restricted but significant special classes of differential systems. Often, the most salient feature of the special class under consideration is some geometric property of the solution flow and one attemps to design numerical methods that preserve that geometric property. This is the approach that originated in the eighties and now known as "Geometric integration". The most important example of geometric integration, both in terms of the range of applications (statistical simulations of gases and liquids, macromulecules, quantum chemistry, celestial mechanics, etc.) and of the volume of existing literature is the case of Hamiltonian systems. These are characterized geometrically by the symplecticness of their flows and one tries to design numerical integrators in such a way that the numerical solution also provides a symplectic transformation in phase space. The underlying hope is that symplectic integrators will better mimic the dynamic properties of Hamiltonian systems, particularly in long term integrations. In the minicourse I will first review the history of numerical methods (one hour) and then present some background on Hamiltonian systems (one hour). After these preliminaries I will present the families of available symplectic integrators (three hours). The course will conclude by analyzing to what extent symplectic integrators outperform their classical counterparts. |
Minicourse: Computational Geometric Mechanics and Control |
Department of Mathematics Purdue University
|
Contents: Geometric mechanics is concerned with the use of differential geometric and symmetry techniques in the study of Lagrangian and Hamiltonian mechanics. This approach serves as the theoretical underpinning of innovative control methodologies in geometric control theory that allow the attitude of satellites to be controlled using changes in its shape, as opposed to chemical propulsion. It is also the basis for understanding the ability of a falling cat to always land on its feet, even when released in an inverted orientation. Such control algorithms rely critically on the geometric structure inherent in the mechanical system, and it is therefore natural to develop numerical implementations that are based on discrete analogues of Lagrangian and Hamiltonian mechanics, and discrete differential geometric techniques. This provides a systematic framework for constructing geometric structure-preserving integrators and geometric controllers for mechanical systems. The minicourse will commence with a motivational overview of discrete geometry and mechanics, through the use of an illustrative example (one hour), followed by a discussion of the Lagrangian formulation of mechanics and its corresponding discretization (one hour). I will then show how exterior calculus is a generalization of vector calculus, introduce its discrete analogue, and discuss applications (two hours). Matrix Lie groups will be introduced, and applied to the construction of numerical schemes for rigid body dynamics (one hour), and the associated optimal control problem will be discussed (one hour). Prerequisites: This minicourse will build upon concepts introduced in the preceding minicourse on "Geometric integration of Hamiltonian systems," but will otherwise assume a familiarity with differential equations, elementary mechanics, vector calculus, and matrix algebra.
|
Minicourse: Distributed motion coordination of robotic networks |
University of California Santa Cruz
Talk 1 [PDF]; Talk 2 [PDF]; Talk 3 [PDF]; Talk 4 [PDF]; Talk 5 [PDF]
Material: File |
Contents: Motion coordination is a remarkable phenomenon in biological systems and an extremely useful tool in man-made groups of vehicles, mobile sensors and embedded robotic systems. Just like animals do, groups of mobile autonomous agents need the ability to deploy over a given region, assume a specified pattern, rendezvous at a common point, or jointly move in a synchronized manner. Robotic teams and large-scale swarms are being considered for a broad class of applications, ranging from environmental monitoring, to search and rescue operations, and space imaging. Biology provides clear evidence that large-scale groups of animals coordinate their motion in order to efficiently pursue a collective objective. The collective behavior arises from local interactions, driven by individual goals, and with limited information exchange. The emergence of complex global behavior from simple local rules is by itself fascinating, and has generated a large body of literature in biology, physics, mathematics, and computer science. Modern technological advances make the deployment of large groups of autonomous mobile agents with on-board computing and communication capabilities increasingly feasible and attractive. As a consequence, the interest of the control community for motion coordination has increased rapidly in the last few years. This course will present analysis and design tools for distributed motion coordination algorithms. The introduction of the mathematical analysis techniques and design methodologies presented in the course will be done through application setups and examples from cooperative control, mobile sensor networks, and multi-agent robotic systems. The broad objective of the course is to illustrate ways in which systems and control theory helps us analyze emergent behaviors in animal groups and design autonomous and reliable robotic networks. The course will begin with an introduction to distributed motion coordination algorithms in biology and engineering (1 hour). We will discuss some of the envisioned applications of robotic networks, and justify the need for modeling, analysis and design mathematical tools. Then, we will briefly discuss important notions from graph theory, distributed algorithms and linear iterations (1 hour). We will then be ready to model robotic networks and their interconnection topology, and introduce some complexity notions that characterize the execution of coordination algorithms (1 hour). The final lectures will be devoted to design and analyze cooperative strategies for different tasks, including rendezvous (1 hour), deployment (1 hour) and agreement (1 hour). In doing this, we will introduce beautiful mathematical tools that will help us analyze these problems.
Prerequisites: Familiarity with ordinary differential equations, dynamical systems and analysis.
References: S.Martínez, J. Cortés, and F. Bullo. Motion coordination with distributed information. IEEE Control Systems Magazine, 2006. Submitted. Available at http://www.soe.ucsc.edu/˜jcortes
|
Talk: Optimal Control of PDEs |
Eduardo Casas University of Cantabria SPAIN
TEXT [PDF]; SLIDES [PDF] |
Contents: This talk is an introduction to the Optimal Control Theory of Partial Differential Equations. We will formulate some different problems corresponding to distributed and boundary (Dirichlet and Neumann) controls of elliptic and parabolic equations. We will present the goals of the theory and the methods to achieve them will be exhibited through one example. Essentially we will consider the problem of the existence of a solution and its numerical approximation, providing error estimates for the discretization. The first and second order optimality conditions will be showed to be a key tool in the analysis of the control problem. |