Comparteix:

2001

24 October 2001
Juan J. Morales Ruiz, Department of Applied Mathematics II, UPC
Some ideas about the differential Galois theory of linear differential equations
Dep. de Matemàtica Aplicada IV, Campus Nord UPC, edifici C3, 204a (biblioteca de Matemàtica); 15.30 h: Abstract: The Galois theory of linear differential equations is a theory analogous to the classical Galois theory of polynomials: given a linear ordinary differential equation with coefficients in a differential field (for instance, the field of rational functions over the complex numbers), the Galois group gives us a mesure of the complexity of the solutions. In particular, by means of the Galois group we can characterize the integrability of the equation (i.e., solutions in closed form).

18 July 2001
Rubén Martín Grillo, Department of Applied Mathematics IV, UPC
A Lie group formulation of robot dynamics
Dep. de Matemàtica Aplicada IV, Campus Nord UPC, edifici C3, 204a (biblioteca de Matemàtica); 15.30 h: Abstract: This talk is mainly a review of the article [1]. The aim is to give a geometric formulation, based on Lie groups an riemannian geometry, of the equations ruling the dynamics of open chained robots, constituted of links with revolution and prismatic joints.
[1] F.C. Park, J.E. Bobrow and S.R. Ploen, "A Lie group formulation of robot dynamics", Int. J. Robotics Research 14 (1995) 609--618.

10 May 2001
Carlos López, Department of Applied Mathematics, University of Zaragoza
Geometry of optimal control
Dep. de Matemàtica Aplicada IV, Campus Nord UPC, edifici C3, 204a (biblioteca de Matemàtica); 16.30 h: Abstract:

28 March 2001
Jaume Franch, Department of Applied Mathematics IV, UPC
Transformation of optimal control Lagrange problems to Mayer problems with feedback linearized state equations
Dep. de Matemàtica Aplicada IV, Campus Nord UPC, edifici C3, 204a (biblioteca de Matemàtica); 15.30 h: Abstract: Optimal solution of classes of Mayer problems with feedback linearizable state equations possess unique structures. A number of special numerical algorithms are available to construct their optimal solution. This seminar will deal with the following question: what classes of optimal control Lagrange problems can be transformed to Mayer problems with feedback linearized state equations? Some necessary and some sufficient conditions will be given to this question.

22 February 2001
Sonia Martínez Díaz, Institute of Applied Mathematics and Fundamental Physics, CSIC
Motion control algorithms for mechanical systems with symmetry
Dep. de Matemàtica Aplicada IV, Campus Nord UPC, edifici C3, 304 (biblioteca de Telemàtica); 11.30 h: Abstract: We treat underactuated mechanical control systems with symmetry taking the viewpoint of the affine connection formalism. The series presented in the previous talk describing the evolution of the trajectories of the system is used here to investigate its behaviour under small-amplitude periodic forcing. Based on this, motion control algorithms are designed that solve the tasks of point-to-point reconfiguration, static interpolation, and stabilization around a point. We illustrate the theoretical results and the performance of the three motion algorithms in the blimp system.

21 February 2001
Jorge Cortés Monforte, Institute of Applied Mathematics and Fundamental Physics, CSIC
Underactuated mechanical control systems with symmetry. Controllability and series expansions
Dep. de Matemàtica Aplicada IV, Campus Nord UPC, edifici C3, 204a (biblioteca de Matemàtica); 15.30 h: Abstract: We develop tools for studying the control of underactuated mechanical systems that evolve on a configuration space with a principal fiber bundle structure. Taking the viewpoint of affine connection control systems, we derive reduced formulations of the Levi-Civita and the nonholonomic affine connections, along with the symmetric product, in the presence of symmetries and nonholonomic constraints. These results are then used to describe controllability tests that are specialized to this class of systems, including the notion of fiber configuration controllability. We also present a series expansion which describes the evolution of the trajectories of mechanical control systems starting from non-zero velocity. The use of these tools is shown in studying the planar rigid body with a variable direction (vectored) thruster, a robot manipulator with a passive joint, and the snakeboard robot.

24 January 2001
Antoni Ras, Department of Applied Mathematics IV, UPC
Riemannian geometry and hamiltonian dynamical systems [slides]
Dep. de Matemàtica Aplicada IV, Campus Nord UPC, edifici C3, 204a (biblioteca); 15.30 h: Abstract: In this session we will mainly review some results from the paper "Geometric approach to hamiltonian dynamics and statistical mechanics" by L. Casetti et al [cond-mat/9912092]. In particular, we will focus on two points:
- Correspondences between hamiltonian dynamical systems and riemannian geometry: trajectories vs. geodesics, chaos vs. curvature, ...
- Deduction of an analytical formula for the largest Lyapunov exponent through the Jacobi and Levi-Civita equation.

10 January 2001
Carles Batlle, Department of Applied Mathematics IV, UPC
(Nearly) exact computation of part of the Lyapunov spectrum for the buck converter [slides]
Dep. de Matemàtica Aplicada IV, Campus Nord UPC, edifici C3, 204a (biblioteca); 15.30 h: Abstract: We review a recently proposed method in which the Lyapunov exponents of a continuous-time dynamical system arise as the asymptotic solution of a system of differential equations related to the QR decomposition of the tangent application. Part of these equations are highly nonlinear and in general must be solved numerically. However, for the buck converter they can be solved exactly, once the numerical data of the target orbit is plugged in. We perform the computations for the 1-periodic orbits and show that they are in accordance with previous known results. Some possible avenues of future work will be presented.