2005 seminars

01-12-2005   María Barbero  

Tangent and cotangent bundle geometry

30-09-2005   Modesto Salgado  

k-symplectic and k-cosymplectic field theory

17-03-2005   Marina Delgado  

A numerical algorithm for singular LQ systems

21-24 February 2005   Stefano Stramigioli and Arjan van der Schaft  

Port-controlled hamiltonian systems   (Ph.D. course)

14-18 February 2005   Francesco Bullo  

Geometric control of mechanical systems   (Ph.D. course)

20-01-2005   Andrew Lewis  

Removing "control" from control theory I.  Motivation and problem formulation

20-01-2005   Andrew Lewis  

Removing "control" from control theory II.  Controllability theorems

1 December 2005

María Barbero, Department of Applied Mathematics IV, UPC, Barcelona

Tangent and cotangent bundle geometry

Dep. de Matemàtica Aplicada IV, Campus Nord UPC, edifici C3, 204a (biblioteca de Matemàtica); 16.00 h

Abstract   Natural geometric structures come up in optimal control theory for mechanical systems.  They are defined on the bundles TTQ, TT*Q, T*TQ, TT*TQ and TTTQ.  In this seminar we present some of them and their relationships.

30 September 2005

Modesto Salgado, Department of Geometry and Topology, Universidade de Santiago de Compostela

k-symplectic and k-cosymplectic field theory

Dep. de Matemàtica Aplicada IV, Campus Nord UPC, edifici C3, 204a (biblioteca de Matemàtica); 10.30 h

Abstract   We present these formalisms, whose starting point is the paper by Ch. Günther, J. Differential Geometry 25 (1987) 23-53.  One of the advantages of these formalisms is that the tangent and the cotangent bundles of a manifold are only needed to develop them, and they generalize, in a very clear way, the geometric description of the hamiltonian and lagrangian mechanics.

17 March 2005

Marina Delgado, Department of Mathematics, Universidad Carlos III de Madrid

A numerical algorithm for singular LQ systems

Dep. de Matemàtica Aplicada IV, Campus Nord UPC, edifici C3, 204a (biblioteca de Matemàtica); 15.30 h

Abstract   We present an algorithm to obtain the equations satisfied by singular arcs for singular linear-quadratic optimal control problems.   It is based in the reduction algorithm for DAE's.   The numerical implementation is based in the singular value decomposition.

21-24 February 2005   Ph.D. course

Arjan van der Schaft, Department of Applied Mathematics, University of Twente, and
Stefano Stramigioli, IMPACT Institute and EL-CE, University of Twente

Port-controlled hamiltonian systems

Centre de Recerca Matemàtica; 10.00 h (Mon, Wed), 11.00 h (Tue, Thu)

Contents  

1. Introduction to port-hamiltonian theory
2. Background on multi-body analysis
3. Infinite dimensional systems
4. Geometrical robotics and ports
5. Haptics and telemanipulation

14-18 February 2005   Ph.D. course

Francesco Bullo, Mechanical Engineering Department, University of California at Santa Barbara

Geometric control of mechanical systems

Centre de Recerca Matemàtica; 11.00 h

Contents  

1. Problem descriptions and motivation
2. Geometric modeling
3. Systems on groups
4. Controllability
5. Kinematic reduction and motion planning
6. Perturbation methods and oscillatory stabilization
7. Open questions

Bibliography  

1. F. Bullo and A. D. Lewis, Geometric control of mechanical systems, Texts in Applied Mathematics 49, Springer Verlag, New York, 2005.

20 January 2005

Andrew D. Lewis, Department of Mathematics & Statistics, Queen's University, Kingston, Ontario, Canada

Removing "control" from control theory II.  Controllability theorems

Dep. de Matemàtica Aplicada IV, Campus Nord UPC, edifici C3, 204a (biblioteca de Matemàtica); 15.30 h

Abstract   Carry on from part I of the talk, some results describing controllability are developed.   "Zeroth-order" and "first-order" results from the literature are given in the geometric formulation.   Finally, new second-order controllability results are stated.

20 January 2005

Andrew D. Lewis, Department of Mathematics & Statistics, Queen's University, Kingston, Ontario, Canada

Removing "control" from control theory I.  Motivation and problem formulation

Dep. de Matemàtica Aplicada IV, Campus Nord UPC, edifici C3, 204a (biblioteca de Matemàtica); 12.00 h

Abstract   In the usual formulation of nonlinear control theory, one has a drift vector field, representing the uncontrolled dynamics, and control vector fields, representing that part of the dynamics that one can control.   The choice of drift vector field and control vector fields is not unique, and therefore a formulation is developed that is independent of these choices.   Very little work has been done on this purely geometric formulation of control theory.   To give some idea of the sorts of problems that arise, we formulate some novel definitions of controllability.

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