TY - GEN
T1 - Search-based and Stochastic Solutions to the Zonotope and Ellipsotope Containment Problems
AU - Kulmburg, Adrian
AU - Brkan, Ivan
AU - Althoff, Matthias
N1 - Publisher Copyright:
© 2024 EUCA.
PY - 2024
Y1 - 2024
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85200606337&partnerID=8YFLogxK
U2 - 10.23919/ECC64448.2024.10590884
DO - 10.23919/ECC64448.2024.10590884
M3 - Conference contribution
AN - SCOPUS:85200606337
T3 - 2024 European Control Conference, ECC 2024
SP - 1057
EP - 1064
BT - 2024 European Control Conference, ECC 2024
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2024 European Control Conference, ECC 2024
Y2 - 25 June 2024 through 28 June 2024
ER -