Time: 9h30, Thursday, January 14, 2016
Location: Room 201, Building A5, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi
Abstract: Piecewise Bézier curves have interesting properties: they are simple but very rich geometrically and algorithmically easy to manipulate.  Furthermore, the set of piecewise Bézier curve (PBC) on an affine space is an affine space itself. This leads us to a very simple interpretation of deformations of such curves and allow to interpret some problem of optimal trajectory computation in a affine space into a parametrical optimization problem using approximation by piecewise Bézier curves. We show how to interpret computation of arc of trajectories for classical ODE as optimization of trajectories into piecewise Bézier curves space. Then, we apply this problem to control problems. Despite its naive shape, this approach leads to some very efficient algorithms and some very interesting links with very distinct mathematical domains.