A polynomial-time algorithm for the secure state estimation problem under sparse sensor attacks via state decomposition technique

This paper investigates the secure state estimation problem for cyber-physical systems (CPSs) under sparse sensor attacks. In the existing results, the secure state estimation is usually established as an NP-hard problem where combinatorial candidates should be checked since the set of attacked chan...

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Veröffentlicht in:	IEEE transactions on automatic control Jg. 68; H. 12; S. 1 - 14
Hauptverfasser:	Lu, An-Yang, Yang, Guang-Hong
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York IEEE 01.12.2023 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:	Algorithms Combinatorial analysis Cyber-physical systems Decoding Decomposition Effectiveness Eigenvalues Force Matrix decomposition Observability Observability (systems) polynomial-time algorithm Polynomials secure state estimation Security Sparse matrices sparse sensor attack state decomposition technique State estimation
ISSN:	0018-9286, 1558-2523
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Abstract	This paper investigates the secure state estimation problem for cyber-physical systems (CPSs) under sparse sensor attacks. In the existing results, the secure state estimation is usually established as an NP-hard problem where combinatorial candidates should be checked since the set of attacked channels is unknown. For avoiding brute force search, a novel state decomposition technique is proposed such that the state can be reconstructed by a simple majority vote. Necessary and sufficient conditions for the observability of the decomposition elements are given, and based on the obtained conditions, an effective algorithm for designing the decomposition matrix is also proposed. Then, a polynomial-time secure state estimation strategy is constructed based on the proposed state decomposition technique. It is shown that besides <inline-formula><tex-math notation="LaTeX">\text{2}~s</tex-math></inline-formula>-sparse eigenvalue observable systems, the secure state estimation problem can be solved in polynomial time for more general cases where each decomposition element is <inline-formula><tex-math notation="LaTeX">\mathbb {B}</tex-math></inline-formula>-observable for at least <inline-formula><tex-math notation="LaTeX">2s+1</tex-math></inline-formula> sensors. Finally, the effectiveness of the proposed methods is demonstrated by two simulations showing the decrease of computational complexity and the effectiveness under different cases.
AbstractList	This paper investigates the secure state estimation problem for cyber-physical systems (CPSs) under sparse sensor attacks. In the existing results, the secure state estimation is usually established as an NP-hard problem where combinatorial candidates should be checked since the set of attacked channels is unknown. For avoiding brute force search, a novel state decomposition technique is proposed such that the state can be reconstructed by a simple majority vote. Necessary and sufficient conditions for the observability of the decomposition elements are given, and based on the obtained conditions, an effective algorithm for designing the decomposition matrix is also proposed. Then, a polynomial-time secure state estimation strategy is constructed based on the proposed state decomposition technique. It is shown that besides <inline-formula><tex-math notation="LaTeX">\text{2}~s</tex-math></inline-formula>-sparse eigenvalue observable systems, the secure state estimation problem can be solved in polynomial time for more general cases where each decomposition element is <inline-formula><tex-math notation="LaTeX">\mathbb {B}</tex-math></inline-formula>-observable for at least <inline-formula><tex-math notation="LaTeX">2s+1</tex-math></inline-formula> sensors. Finally, the effectiveness of the proposed methods is demonstrated by two simulations showing the decrease of computational complexity and the effectiveness under different cases. This article investigates the secure state estimation problem for cyber–physical systems (CPSs) under sparse sensor attacks. In the existing results, the secure state estimation is usually established as an NP-hard problem where combinatorial candidates should be checked since the set of attacked channels is unknown. For avoiding brute force search, a novel state decomposition technique is proposed such that the state can be reconstructed by a simple majority vote. Necessary and sufficient conditions for the observability of the decomposition elements are given, and based on the obtained conditions, an effective for designing the decomposition matrix is also proposed. Then, a polynomial-time secure state estimation strategy is constructed based on the proposed state decomposition technique. It is shown that besides [Formula Omitted]-sparse eigenvalue observable systems, the secure state estimation problem can be solved in polynomial time for more general cases where each decomposition element is [Formula Omitted]-observable for at least [Formula Omitted] sensors. Finally, the effectiveness of the proposed methods is demonstrated by two simulations showing the decrease of computational complexity and the effectiveness under different cases.
Author	Lu, An-Yang Yang, Guang-Hong
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Snippet	This paper investigates the secure state estimation problem for cyber-physical systems (CPSs) under sparse sensor attacks. In the existing results, the secure... This article investigates the secure state estimation problem for cyber–physical systems (CPSs) under sparse sensor attacks. In the existing results, the...
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SubjectTerms	Algorithms Combinatorial analysis Cyber-physical systems Decoding Decomposition Effectiveness Eigenvalues Force Matrix decomposition Observability Observability (systems) polynomial-time algorithm Polynomials secure state estimation Security Sparse matrices sparse sensor attack state decomposition technique State estimation
Title	A polynomial-time algorithm for the secure state estimation problem under sparse sensor attacks via state decomposition technique
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