Minimum variation solutions for sliding vector fields on the intersection of two surfaces in R3

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:292

Article

Dieci, Luca¹  Difonzo, Fabio¹ 

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

关键词: Filippov sliding motion;    Minimum variation solution;   

DOI  :  10.1016/j.cam.2015.02.026

来源: Elsevier

【 摘 要 】

In this work, we consider model problems of piecewise smooth systems in R-3, for which we propose minimum variation approaches to find a Filippov sliding vector field on the intersection Sigma of two discontinuity surfaces. Our idea is to look at the minimum variation solution in the H-1-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 H-1-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 R-3. (C) 2015 Elsevier B.V. All rights reserved.

【 授权许可】

Free