On the computational complexity of the secure state-reconstruction problem
In this paper, we discuss the computational complexity of reconstructing the state of a linear system from sensor measurements that have been corrupted by an adversary. The first result establishes that the problem is, in general, NP-hard. We then introduce the notion of eigenvalue observability and...
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| Vydané v: | Automatica (Oxford) Ročník 136; s. 110083 |
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| Hlavní autori: | , , , |
| Médium: | Journal Article |
| Jazyk: | English |
| Vydavateľské údaje: |
Elsevier Ltd
01.02.2022
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| Predmet: | |
| ISSN: | 0005-1098, 1873-2836 |
| On-line prístup: | Získať plný text |
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| Shrnutí: | In this paper, we discuss the computational complexity of reconstructing the state of a linear system from sensor measurements that have been corrupted by an adversary. The first result establishes that the problem is, in general, NP-hard. We then introduce the notion of eigenvalue observability and show that the state can be reconstructed in polynomial time when each eigenvalue is observable by at least 2s+1 sensors and at most s sensors are corrupted by an adversary. However, there is a gap between eigenvalue observability and the possibility of reconstructing the state despite attacks — this gap has been characterized in the literature by the notion of sparse observability. To better understand this, we show that when the A matrix of the linear system has unitary geometric multiplicity, the gap disappears, i.e., eigenvalue observability coincides with sparse observability, and there exists a polynomial time algorithm to reconstruct the state provided the state can be reconstructed. |
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| ISSN: | 0005-1098 1873-2836 |
| DOI: | 10.1016/j.automatica.2021.110083 |