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References

Marcelo Forets edited this page Aug 13, 2020 · 52 revisions

Zonotopes

  • Guibas, L. J., Nguyen, A. T., & Zhang, L. (2003, January). Zonotopes as bounding volumes. In SODA (Vol. 3, pp. 803-812). pdf

  • Althoff, M., Stursberg, O., & Buss, M. (2010). Computing reachable sets of hybrid systems using a combination of zonotopes and polytopes. Nonlinear analysis: hybrid systems, 4(2), 233-249. pdf

  • Froitzheim, S. (2016). Efficient conversion of geometric state set representations for hybrid systems (Doctoral dissertation, Bachelor’s thesis, RWTH Aachen University). pdf

  • Althoff, M., & Krogh, B. H. (2012, April). Avoiding geometric intersection operations in reachability analysis of hybrid systems. In Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control (pp. 45-54). pdf

  • An Efficient Algorithm for Vertex Enumeration of Two-Dimensional Projection of Polytopes Amit Gurung and Rajarshi Ray

  • http://www.lsv.fr/~fribourg/MPRI_2019_Girard_Zonotopes.pdf

Minkowski sum

Minkowski difference

Triangulations

Polygon intersection

More on intersections

Disjointness check

  • Chazelle, B., & Dobkin, D. P. (1980, April). Detection is easier than computation. In Proceedings of the twelfth annual ACM symposium on Theory of computing (pp. 146-153).

Enumerations

  • Löhne, A. (2020). Approximate Vertex Enumeration. arXiv preprint arXiv:2007.06325.

  • Awasthi, P., Kalantari, B., & Zhang, Y. (2018, March). Robust vertex enumeration for convex hulls in high dimensions. In International Conference on Artificial Intelligence and Statistics (pp. 1387-1396).

Star sets

  • Tran, H. D., Lopez, D. M., Musau, P., Yang, X., Nguyen, L. V., Xiang, W., & Johnson, T. T. (2019, October). Star-based reachability analysis of deep neural networks. In International Symposium on Formal Methods (pp. 670-686). Springer, Cham. pdf

Theses

  • Le Guernic, C. (2009). Reachability analysis of hybrid systems with linear continuous dynamics (Doctoral dissertation). pdf. Tags: support function, zonotope, zonotope-hyperplane intersection.

  • Althoff, M. (2010). Reachability analysis and its application to the safety assessment of autonomous cars (Doctoral dissertation, Technische Universität München). pdf, M. Althoff's PhD thesis. Tags: zonotope, zonotope order reduction, interval matrix, matrix zonotope.

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