Controllability and Observability of Temporal Hypergraphs
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916365698334720 |
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| author | Dong, Anqi Mao, Xin Chen, Can |
| author_facet | Dong, Anqi Mao, Xin Chen, Can |
| contents | Numerous complex systems, such as those arisen in ecological networks, genomic contact networks, and social networks, exhibit higher-order and time-varying characteristics, which can be effectively modeled using temporal hypergraphs. However, analyzing and controlling temporal hypergraphs poses significant challenges due to their inherent time-varying and nonlinear nature, while most existing methods predominantly target static hypergraphs. In this article, we generalize the notions of controllability and observability to temporal hypergraphs by leveraging tensor and nonlinear systems theory. Specifically, we establish tensor-based rank conditions to determine the weak controllability and observability of temporal hypergraphs. The proposed framework is further demonstrated with synthetic and real-world examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_12085 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Controllability and Observability of Temporal Hypergraphs Dong, Anqi Mao, Xin Chen, Can Systems and Control Social and Information Networks Dynamical Systems 93Bxx, 92Dxx, 05C65 Numerous complex systems, such as those arisen in ecological networks, genomic contact networks, and social networks, exhibit higher-order and time-varying characteristics, which can be effectively modeled using temporal hypergraphs. However, analyzing and controlling temporal hypergraphs poses significant challenges due to their inherent time-varying and nonlinear nature, while most existing methods predominantly target static hypergraphs. In this article, we generalize the notions of controllability and observability to temporal hypergraphs by leveraging tensor and nonlinear systems theory. Specifically, we establish tensor-based rank conditions to determine the weak controllability and observability of temporal hypergraphs. The proposed framework is further demonstrated with synthetic and real-world examples. |
| title | Controllability and Observability of Temporal Hypergraphs |
| topic | Systems and Control Social and Information Networks Dynamical Systems 93Bxx, 92Dxx, 05C65 |
| url | https://arxiv.org/abs/2408.12085 |