Search-based and Stochastic Solutions to the Zonotope and Ellipsotope Containment Problems

Adrian Kulmburg, Ivan Brkan, Matthias Althoff

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We introduce new techniques to check whether a zonotope is contained in another zonotope. This fundamental problem in control theory has many applications, such as the verification of invariant sets, formal verification of controllers, and fault detection. Our first method uses a search-based vertex enumeration to quickly and efficiently check containment. We also propose two stochastic methods that are able to rapidly disprove or confirm containment with a certain probability. Furthermore, we generalize the first approach to the case where the circumbody is an ellipsotope and generalize the stochastic methods to the case where both the inbody and the circumbody are ellipsotopes. We conclude by comparing the efficiency of our algorithms to currently available ones.

Original languageEnglish
Title of host publication2024 European Control Conference, ECC 2024
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1057-1064
Number of pages8
ISBN (Electronic)9783907144107
DOIs
StatePublished - 2024
Event2024 European Control Conference, ECC 2024 - Stockholm, Sweden
Duration: 25 Jun 202428 Jun 2024

Publication series

Name2024 European Control Conference, ECC 2024

Conference

Conference2024 European Control Conference, ECC 2024
Country/TerritorySweden
CityStockholm
Period25/06/2428/06/24

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