The Filippov moments solution on the intersection of two and three manifolds

Series: 
Dissertation Defense
Thursday, April 2, 2015 - 12:05
1 hour (actually 50 minutes)
Location: 
Skiles 006
,  
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.