Scalable Zonotopic Under-approximation of Backward Reachable Sets for Uncertain Linear Systems
Abstract
Zonotopes are widely used for over-approximating forward reachable sets of uncertain linear systems for verification purposes. In this paper, we use zonotopes to achieve more scalable algorithms that under-approximate backward reachable sets of uncertain linear systems for control design. The main difference is that the backward reachability analysis is a two-player game and involves Minkowski difference operations, but zonotopes are not closed under such operations. We under-approximate this Minkowski difference with a zonotope, which can be obtained by solving a linear optimization problem. We further develop an efficient zonotope order reduction technique to bound the complexity of the obtained zonotopic under-approximations. The proposed approach is evaluated against existing approaches using randomly generated instances and illustrated with several examples.
Cite
@article{arxiv.2107.01724,
title = {Scalable Zonotopic Under-approximation of Backward Reachable Sets for Uncertain Linear Systems},
author = {Liren Yang and Necmiye Ozay},
journal= {arXiv preprint arXiv:2107.01724},
year = {2022}
}