Relationship Between the Number of Agents and Sparse Observability Index
The state estimation problem in the presence of malicious sensor attacks is commonly referred to as a secure state estimation problem. Central to addressing this problem is the concept of the sparse observability index, defined as the largest integer <inline-formula><tex-math notation="...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
IEEE
2025-01-01
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| Series: | IEEE Open Journal of Control Systems |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/10989748/ |
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| Summary: | The state estimation problem in the presence of malicious sensor attacks is commonly referred to as a secure state estimation problem. Central to addressing this problem is the concept of the sparse observability index, defined as the largest integer <inline-formula><tex-math notation="LaTeX">$ \delta$</tex-math></inline-formula> for which the system remains observable after the removal of any <inline-formula><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula> sensors. This index plays a critical role in quantifying the resilience of the system, as a higher <inline-formula><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula> enables unique state reconstruction despite the presence of more compromised sensors. In this study, for undirected multi-agent systems consisting of <inline-formula><tex-math notation="LaTeX">$ n$</tex-math></inline-formula> agents, we analyze the relationship between the number of agents <inline-formula><tex-math notation="LaTeX">$ n$</tex-math></inline-formula> and the sparse observability index <inline-formula><tex-math notation="LaTeX">$ \delta$</tex-math></inline-formula> for effective secure state estimation. In particular, we consider four typical graph structures: path, cycle, complete, and complete bipartite graphs. Our analysis reveals that <inline-formula><tex-math notation="LaTeX">$\delta$</tex-math></inline-formula> does not increase monotonically with <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula>, and that resilience is intricately tied to the underlying network structure. Notably, we demonstrate that the system exhibits enhanced resilience when the number of agents <inline-formula><tex-math notation="LaTeX">$n$</tex-math></inline-formula> is a prime number, although the specifics of this relationship vary depending on the graph topology. |
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| ISSN: | 2694-085X |