“A Safety Study for Dynamical Systems on Heisenberg Lie Group of dimension 4”
Authors: Sultan Selcuk Sutlu, Bedia Akyar, Ayse Kara Hansen and Aysegul Kivilcim,Affiliation: Acibadem University, Turkey, IBC International Business College, Denmark, Aarhus University and Aalborg University
Reference: 2025, Vol 46, No 4, pp. 137-145.
Keywords: Safety, Heisenberg Lie group, dynamical systems
Abstract: The safety property of dynamical systems has typically been studied in Euclidean spaces. In this work, we extend the notion of safety to a non-Euclidean geometry. Motivated by the role of time as a fourth dimension in physical models, we construct the 4-dimensional Heisenberg Lie group H4 and investigate the safety problem of dynamical systems defined on this group. Unlike odd-dimensional Heisenberg Lie groups, which admit a unique structure, even-dimensional cases allow multiple forms; in particular, H4 possesses four distinct forms. Focusing on one such form, we provide a detailed analysis of dynamical systems on H4. Moreover, using a diffeomorphism between the (2n+1)-dimensional Heisenberg Lie group and the Euclidean space of the same dimension, we establish their equivalence, and we extend safety result for H4. Several examples are presented to illustrate the applicability of the theoretical results.
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DOI: 10.4173/mic.2025.4.1References:
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BibTeX:
@article{MIC-2025-4-1,
title={{A Safety Study for Dynamical Systems on Heisenberg Lie Group of dimension 4}},
author={Sutlu, Sultan Selcuk and Akyar, Bedia and Hansen, Ayse Kara and Kivilcim, Aysegul},
journal={Modeling, Identification and Control},
volume={46},
number={4},
pages={137--145},
year={2025},
doi={10.4173/mic.2025.4.1},
publisher={Norwegian Society of Automatic Control}
};