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2005

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

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

Bibliography

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.