TY - JOUR
T1 - Mesh-Based Piecewise Affine Abstraction with Polytopic Partitions for Nonlinear Systems
AU - Jin, Zeyuan
AU - Shen, Qiang
AU - Yong, Sze Zheng
N1 - Funding Information: Manuscript received September 1, 2020; revised November 4, 2020; accepted November 16, 2020. Date of publication November 30, 2020; date of current version December 22, 2020. This work was supported in part by DARPA under Grant D18AP00073. Recommended by Senior Editor R. S. Smith. (Corresponding author: Sze Zheng Yong.) Zeyuan Jin and Sze Zheng Yong are with the School for Engineering of Matter, Transport and Energy, Arizona State University, Tempe, AZ 85281 USA (e-mail: [email protected]; [email protected]). Publisher Copyright: © 2017 IEEE.
PY - 2021/11
Y1 - 2021/11
N2 - This letter 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 subdomains/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 letter 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 subdomains/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.
KW - Model/controller reduction
KW - computational methods
KW - model validation
UR - https://www.scopus.com/pages/publications/85097416341
UR - https://www.scopus.com/pages/publications/85097416341#tab=citedBy
U2 - 10.1109/LCSYS.2020.3041312
DO - 10.1109/LCSYS.2020.3041312
M3 - Article
SN - 2475-1456
VL - 5
SP - 1543
EP - 1548
JO - IEEE Control Systems Letters
JF - IEEE Control Systems Letters
IS - 5
M1 - 9272993
ER -