Implementation of Polyhedral Operations in CORA 2024

19 pages•Published: October 10, 2024

Mark Wetzlinger, Viktor Kotsev, Adrian Kulmburg and Matthias Althoff

Abstract

Tool presentation: Polyhedra are a common set representation with widespread appli- cations in many areas of research, including convex geometry, reachability analysis, and invariant set computation. Their popularity stems from a tight relation to linear program- ming. Apart from some basic set operations with analytic formulae, the implementation of many polyhedral set operations in tools is not well documented. For this reason, we describe the evaluation of common set operations on polyhedra, including their runtime complexity, and provide an overview of their implementation as a dedicated class in the MATLAB tool Continuous Reachability Analyzer (CORA) for set-based computing. In particular, we highlight the handling of unbounded and degenerate sets. Finally, we com- pare our implementation to the popular multi-parametric toolbox.

Keyphrases: cora, polyhedra, polytopes, set based computing, set representations

In: Goran Frehse and Matthias Althoff (editors). Proceedings of the 11th Int. Workshop on Applied Verification for Continuous and Hybrid Systems, vol 103, pages 163-181.

Links:	https://easychair.org/publications/paper/81TW
	https://doi.org/10.29007/wb9s

BibTeX entry

@inproceedings{ARCH-COMP24:Implementation_Polyhedral_Operations_CORA,
  author    = {Mark Wetzlinger and Viktor Kotsev and Adrian Kulmburg and Matthias Althoff},
  title     = {Implementation of Polyhedral Operations in CORA 2024},
  booktitle = {Proceedings of the 11th Int. Workshop on Applied Verification for Continuous and Hybrid Systems},
  editor    = {Goran Frehse and Matthias Althoff},
  series    = {EPiC Series in Computing},
  volume    = {103},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/81TW},
  doi       = {10.29007/wb9s},
  pages     = {163-181},
  year      = {2024}}

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