Classical and strong convexity of sublevel sets and application to attainable sets of nonlinear systems
Optimization and Control
2017-01-03 v2
Abstract
Necessary and sufficient conditions for convexity and strong convexity, respectively, of sublevel sets that are defined by finitely many real-valued -maps are presented. A novel characterization of strongly convex sets in terms of the so-called local quadratic support is proved. The results concerning strong convexity are used to derive sufficient conditions for attainable sets of continuous-time nonlinear systems to be strongly convex. An application of these conditions is a novel method to over-approximate attainable sets when strong convexity is present.
Keywords
Cite
@article{arxiv.1311.4989,
title = {Classical and strong convexity of sublevel sets and application to attainable sets of nonlinear systems},
author = {Alexander Weber and Gunther Reissig},
journal= {arXiv preprint arXiv:1311.4989},
year = {2017}
}
Comments
20 pages, 3 figures