The Filippov moments solution on the intersection of two and three manifolds
- Series
- Dissertation Defense
- Time
- Thursday, April 2, 2015 - 12:05 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Fabio Difonzo – School of Mathematics, Georgia Tech
We consider several possibilities on how to select a Filippov sliding
vector field on a co-dimension 2 singularity manifold, intersection of two
co-dimension 1 manifolds, under the assumption of general attractivity. Of specific
interest is the selection of a smoothly varying Filippov sliding vector field. As a
result of our analysis and experiments, the best candidates of the many possibilities
explored are based on so-called barycentric coordinates: in particular, we choose
what we call the moments solution. We then examine the behavior of the moments vector
field at the first order exit points, and show that it aligns smoothly with the exit
vector field. Numerical experiments illustrate our results and contrast the present
method with other choices of Filippov sliding vector field. We further generalize
this construction to co-dimension 3 and higher.