AI Article Synopsis
- The study focuses on tracking a moving target using two different multi-agent systems built on Riemannian manifolds.
- For asymptotic tracking, a smooth piecewise vector field is utilized for targets that switch positions, while for finite-time tracking, a piecewise non-smooth vector field in Euclidean space is used.
- The research provides frameworks that outline the necessary conditions for achieving both types of tracking based on system parameters, target configurations, and initial data.
Article 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.
Download full-text PDF |
Source |
|---|---|
| http://dx.doi.org/10.1063/5.0203618 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
A Riemannian multimodal representation to classify parkinsonism-related patterns from noninvasive observations of gait and eye movements.
Biomed Eng Lett
January 2025
Biomedical Imaging, Vision and Learning Laboratory(BivL2ab), Universidad Industrial de Santander (UIS), Bucaramanga, 680002 Santander Colombia.
Parkinson's disease is a neurodegenerative disorder principally manifested as motor disabilities. In clinical practice, diagnostic rating scales are available for broadly measuring, classifying, and characterizing the disease progression. Nonetheless, these scales depend on the specialist's expertise, introducing a high degree of subjectivity.
View Article and Find Full Text PDFKernel Stein Discrepancy on Lie Groups: Theory and Applications.
IEEE Trans Inf Theory
December 2024
Department of CISE, University of Florida, Gainesville, FL 32611 USA.
Distributional approximation is a fundamental problem in machine learning with numerous applications across all fields of science and engineering and beyond. The key challenge in most approximation methods is the need to tackle the intractable normalization constant present in the candidate distributions used to model the data. This intractability is especially common for distributions of manifold-valued random variables such as rotation matrices, orthogonal matrices etc.
View Article and Find Full Text PDFFractional Sobolev spaces on Riemannian manifolds.
Math Ann
June 2024
Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092 Zürich, Switzerland.
This article studies the canonical Hilbert energy on a Riemannian manifold for , with particular focus on the case of closed manifolds. Several equivalent definitions for this energy and the fractional Laplacian on a manifold are given, and they are shown to be identical up to explicit multiplicative constants. Moreover, the precise behavior of the kernel associated with the singular integral definition of the fractional Laplacian is obtained through an in-depth study of the heat kernel on a Riemannian manifold.
View Article and Find Full Text PDFEnvironmentally and statistically robust matched-field source localization based on information geometry principles.
J Acoust Soc Am
December 2024
Key Laboratory for Polar Acoustics and Application of Ministry of Education (Harbin Engineering University), Ministry of Education, Harbin, 150001, China.
Matched-field processing (MFP) achieves underwater source localization by measuring the correlation between the array and replica signals, with traditional MFP being equivalent to estimating the Euclidean distance between the data cross-spectral density matrix (CSDM) and replica matrices. However, in practical applications, random inhomogeneities in the marine environment and inaccurate estimation of CSDM reduce MFP performance. The traditional minimum variance matched-field processor with environmental perturbation constraints perturbs a priori environment parameters to obtain linear constraints and yields the optimal weight vectors as the replica vectors.
View Article and Find Full Text PDFGeometric properties of almost pure metric plastic pseudo-Riemannian manifolds.
Heliyon
December 2024
Ataturk University, Faculty of Science, Department of Mathematics, Erzurum 25240, Turkiye.
This paper investigates the geometric and structural properties of almost plastic pseudo-Riemannian manifolds, with a specific focus on three-dimensional cases. We explore the interplay between an almost plastic structure and a pseudo-Riemannian metric, providing a comprehensive analysis of the conditions that define pure metric plastic -Kählerian manifolds. In this context, the fundamental tensor field is symmetric and also represents another pure metric.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!