Seminar schedule

22-27 June 2009  

III International Summer School on Geometry, Mechanics, and Control  

8-12 June 2009   Mariano Santander  

Hamiltonian systems, integrability, and separability   (master course)

3 June 2009   María Barbero Liñán  

A panorama of tracking a submarine

2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997

22-27 June 2009

III International Summer School on Geometry, Mechanics, and Control ,
organised by the Geometry, Mechanics, and Control Network

Hotel Ametlla Mar, l'Ametlla de Mar, Catalonia, Spain

Courses  

• A. Bloch   Geometric control of mechanical and nonholonomic systems
• A.D. Lewis   Controllability theory
• V. Jurdjevic   Optimal control on Lie groups: integrable hamiltonian systems
• R. Ortega   Passivity-based control of physical systems: control by interconnection and state-feedback laws

8-12 June 2009   master course

Mariano Santander, Department of Theoretical Physics, University of Valladolid

Hamiltonian systems, integrability, and separability (details)

Facultat de Matemàtiques i Estadística, room 103.
Schedule: Monday--Friday, 12-14 h.

Contents  

• What is an integrable system? Integrability and symmetry
• Examples of integrable systems
• Identification and construction of integrable systems
• Integrability from bialgebras
• Integrability and superintegrability on spaces of constant curvature
• Geometry of the "curved" Kepler problem and harmonic oscillator
• Some conjectures and open problems

Basic bibliography  

• A. Perelomov, Integrable systems of classical mechanics and Lie algebras, Birkhauser, Basel, 1990
• V.I. Arnol'd, V.V. Kozlov, A.I. Neishtadt, Mathematical aspects of classical and celestial mechanics, Springer, Berlin, 1997

3 June 2009

María Barbero Liñán, Centre de recherche INRIA Nancy - Grand Est, Vandoeuvre-lès-Nancy

A panorama of tracking a submarine

Campus Nord UPC, edifici C3, 204a (biblioteca de Matemàtica); 12 h

Abstract:   In this talk, we introduce the problem of tracking trajectories in a control system and the applications to avoid obstacles.   We focus on the tracking problem for a submarine from a differential geometric viewpoint so as to obtain intrinsic solutions to the problem under study.   In order to revisit the results in the literature, notions of averaging methods and oscillatory controls are necessary.   Finally, we give insights into how to generalize the previous results in such a way that weaker assumptions and more general submarines can be considered.

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