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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| Published in: | Automatica (Oxford) Vol. 136; p. 110083 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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01.02.2022
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| ISSN: | 0005-1098, 1873-2836 |
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| Abstract | 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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| AbstractList | 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. |
| ArticleNumber | 110083 |
| Author | Mitra, Aritra Tabuada, Paulo Sundaram, Shreyas Mao, Yanwen |
| Author_xml | – sequence: 1 givenname: Yanwen surname: Mao fullname: Mao, Yanwen email: yanwen.mao@ucla.edu organization: Department of Electrical and Computer Engineering, University of California, Los Angeles, CA 90095, USA – sequence: 2 givenname: Aritra surname: Mitra fullname: Mitra, Aritra email: amitra20@seas.upenn.edu organization: Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104, USA – sequence: 3 givenname: Shreyas surname: Sundaram fullname: Sundaram, Shreyas email: sundara2@purdue.edu organization: School of Electrical and Computer Engineering at Purdue University, West Lafayette, IN 47907, USA – sequence: 4 givenname: Paulo surname: Tabuada fullname: Tabuada, Paulo email: tabuada@ucla.edu organization: Department of Electrical and Computer Engineering, University of California, Los Angeles, CA 90095, USA |
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| Keywords | Eigenvalue and sparse observability Resilient state secure state-reconstruction Polynomial time algorithm |
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| SubjectTerms | Eigenvalue and sparse observability Polynomial time algorithm Resilient state secure state-reconstruction |
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