کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4638262 | 1631999 | 2016 | 14 صفحه PDF | دانلود رایگان |
In this work, we consider model problems of piecewise smooth systems in R3R3, for which we propose minimum variation approaches to find a Filippov sliding vector field on the intersection ΣΣ of two discontinuity surfaces. Our idea is to look at the minimum variation solution in the H1H1-norm, among either all admissible sets of coefficients for a Filippov vector field, or among all Filippov vector fields. We compare the resulting solutions to other possible Filippov sliding vector fields (including the bilinear and moments solutions). We further show that–in the absence of equilibria–also these other techniques select a minimum variation solution, for an appropriately weighted H1H1-norm, and we relate this weight to the change of time variable giving orbital equivalence among the different vector fields. Finally, we give details of how to build a minimum variation solution for a general piecewise smooth system in R3R3.
Journal: Journal of Computational and Applied Mathematics - Volume 292, 15 January 2016, Pages 732–745