On the alternating target tracking of a point cloud on Riemannian manifolds

Hyunjin Ahn; Seung-Yeal Ha

doi:10.1063/5.0203618

On the alternating target tracking of a point cloud on Riemannian manifolds

Chaos. 2024 May 1;34(5):053122. doi: 10.1063/5.0203618.

Authors

Hyunjin Ahn¹, Seung-Yeal Ha²

Affiliations

¹ Department of Mathematics, Myongji University, Gyeonggi-do 17058, Republic of Korea.
² Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 08826, Republic of Korea.

PMID: 38717421
DOI: 10.1063/5.0203618

Abstract

We study finite-time and asymptotic tracking of a given moving target configuration. For this, we proposed two multi-agent systems on Riemannian manifolds based on Filippov's framework. For asymptotic tracking, we adopt a piecewise C1-vector field on Riemannian manifolds resulting from switching moving targets, whereas for finite-time tracking, we use a piecewise C0 and non-Lipschitzian vector field on Euclidean space. For both multi-agent systems, we provide several sufficient frameworks for the desired asymptotic or finite-time tracking that are formulated in terms of system parameters, a preassigned switching moving target configuration, kernel functionals, and initial data.