Implementation of Ellipsoidal Operations in CORA 2022

17 pages•Published: December 13, 2022

Abstract

Tool presentation: Ellipsoids are a broadly applied set representation for formal anal- yses, such as set-based observers, or reachability analysis. While ellipsoids are not closed under frequently used set operations like Minkowski sum or intersection, their widespread popularity can be attributed to their compact numerical representation and intuitive na- ture. As a result, there already exist toolboxes that implement many operations for el- lipsoids. That said, most are either no longer maintained, or implement only a subset of necessary ellipsoidal operations. Thus, we implement all common set operations, as well as recent research results on ellipsoids as a class in the Continuous Reachability Analyzer (CORA) - a free MATLAB toolbox for continuous reachability analysis. Previously, CORA already contained implementations for many ellipsoidal operations, which, however, were lacking in speed, accuracy, and functionality. Here, we describe the implementation of the ellipsoid class in CORA and compare it against the popular, but no longer maintained, Ellipsoidal Toolbox (ET).

Keyphrases: cora, ellipsoidal operations, ellipsoidal toolbox, ellipsoids

In: Goran Frehse, Matthias Althoff, Erwin Schoitsch and Jeremie Guiochet (editors). Proceedings of 9th International Workshop on Applied Verification of Continuous and Hybrid Systems (ARCH22), vol 90, pages 1-17.

Links:	https://easychair.org/publications/paper/8hnJ
	https://doi.org/10.29007/p328

BibTeX entry

@inproceedings{ARCH22:Implementation_Ellipsoidal_Operations_CORA,
  author    = {Victor Gaßmann and Matthias Althoff},
  title     = {Implementation of Ellipsoidal Operations in CORA 2022},
  booktitle = {Proceedings of 9th International Workshop on Applied Verification of Continuous and Hybrid Systems (ARCH22)},
  editor    = {Goran Frehse and Matthias Althoff and Erwin Schoitsch and Jeremie Guiochet},
  series    = {EPiC Series in Computing},
  volume    = {90},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2398-7340},
  url       = {/publications/paper/8hnJ},
  doi       = {10.29007/p328},
  pages     = {1-17},
  year      = {2022}}

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