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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Bibliographic Details
Published in:IEEE transactions on automatic control Vol. 68; no. 12; pp. 1 - 14
Main Authors: Lu, An-Yang, Yang, Guang-Hong
Format: Journal Article
Language:English
Published: New York IEEE 01.12.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
Online Access:Get full text
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Summary: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.
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ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2023.3278839