Activity
Introduction:
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.
Courses:
[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 generalpurpose software packages of wide applicability, it is clear that the onesizefitsall 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 structurepreserving 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 manmade 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 largescale 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 largescale 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 onboard 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 multiagent 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. 
Schedule:

Monday, June 25 
Tuesday, June 26 
Wednesday June 27 
Thursday, June 28 
Friday, June 29 
8:009:30 
Registration (8:009:00) and Opening(9:009:30) 




9:3011:00 
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

11:0011:30 
Coffee 
Coffee 
Coffee 
Coffee 
Coffee 
11:3013:00

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 
13:0015:30 
Lunch 
Lunch 
Lunch 
Lunch 
13:0013:30 Closing Lunch 
15:3016:30 
Geometric integration of Hamiltonian systems 
Distributed motion coordination of robotic networks

Computational Geometric Mechanics and Control 
Computational Geometric Mechanics and Control 

16:3017:00 
Coffee 
Coffee 
Coffee 
Coffee 

17:0018:00 
Distributed motion coordination of robotic networks 
Posters 
Computational Geometric Mechanics and Control 
LAB: Computational Geometric Mechanics and Control 

Registration:
Contact: gmcnetull [dot] es
To make the registration, please send the following information by email to gmcnetull [dot] es
First Name 
Family Name 
Institution 
Country 
FAX 
Email 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 email to gmcnetull [dot] es or by fax to the number +34922318145, no later than 31 May, 2007.
Financial Support:
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.
Lodging reservation:
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 email to gmcnetull [dot] es
First name 
Family name 
Institution 
Phone 
FAX 
Email address 
I want do the lodging reservation in the hotel........... for ....... person(s)
Date of arrival ........
Date of departure ........
Participants:
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 BalseiroUniv. 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 
LugoVilleda  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 
MuñozLecanda  Miguel C.  Technical University of Catalonia  Spain 
Padrón  Edith  University of La Laguna  Spain 
QuintanaPortilla  Gema  University of Cantabria  Spain 
Ramírez Jr.  Juan  Purdue University  USA 
Roldán  Charles  Purdue University  USA 
Rosado  Eugenia  Universidad Politécnica de Madrid  Spain 
SantaMaría Megía  Ignacio  Universidad Complutense de Madrid  Spain 
Santoso  Jenny  University of Stuttgart  Germany 
SanzSerna  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 
Committees:
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)
How to get here:
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 CastroUrdiales you could take a bus of the company BizkaibusEncartaciones (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