TY - GEN
T1 - Mesh-Based Piecewise Affine Abstraction with Polytopic Partitions for Nonlinear Systems
AU - Jin, Zeyuan
AU - Shen, Qiang
AU - Yong, Sze Zheng
N1 - Publisher Copyright:
© 2021 American Automatic Control Council.
PY - 2021/5/25
Y1 - 2021/5/25
N2 - This paper considers the problem of piecewise affine abstraction with polytopic partitions of nonlinear systems, i.e., the over-approximation of nonlinear dynamics by a pair of piecewise affine functions over polytopic subdo-mains/partitions in the sense of the inclusion of all possible trajectories. Specifically, to tackle the 'boundary effect' that may make the over-approximation incorrect for polytopic partitions, we propose two mesh-based affine abstraction approaches based on expanding the partitions to simultaneously find the polytopic partitions and the pair of piecewise functions over the partitions. The effectiveness of the proposed approaches are compared with existing methods using hyperrectangular partitions, and demonstrated by computing abstractions of swarm dynamics and applying them for swarm intent identification.
AB - This paper considers the problem of piecewise affine abstraction with polytopic partitions of nonlinear systems, i.e., the over-approximation of nonlinear dynamics by a pair of piecewise affine functions over polytopic subdo-mains/partitions in the sense of the inclusion of all possible trajectories. Specifically, to tackle the 'boundary effect' that may make the over-approximation incorrect for polytopic partitions, we propose two mesh-based affine abstraction approaches based on expanding the partitions to simultaneously find the polytopic partitions and the pair of piecewise functions over the partitions. The effectiveness of the proposed approaches are compared with existing methods using hyperrectangular partitions, and demonstrated by computing abstractions of swarm dynamics and applying them for swarm intent identification.
UR - http://www.scopus.com/inward/record.url?scp=85111923081&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85111923081&partnerID=8YFLogxK
U2 - 10.23919/ACC50511.2021.9483441
DO - 10.23919/ACC50511.2021.9483441
M3 - Conference contribution
AN - SCOPUS:85111923081
T3 - Proceedings of the American Control Conference
SP - 4453
EP - 4458
BT - 2021 American Control Conference, ACC 2021
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2021 American Control Conference, ACC 2021
Y2 - 25 May 2021 through 28 May 2021
ER -