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    Area of Science:

    • Control Systems Engineering
    • Cybersecurity
    • Signal Processing

    Background:

    • Linear discrete-time systems are vulnerable to stealthy attacks that compromise data integrity.
    • Existing methods struggle with unknown system dynamics and stealthy, non-sparse attacks.

    Purpose of the Study:

    • To develop a robust data recovery method for linear systems under stealthy attacks.
    • To identify and compensate for attacks in systems with unknown dynamics.

    Main Methods:

    • A novel encoding scheme with subdecoding matrices tailored for 1-D attack-stealthy subspaces.
    • Subspace projection technique for stealthy attack parameter identification.
    • Development of n parallel attack identification filters to determine the attack subspace.

    Main Results:

    • A necessary and sufficient condition for determining the targeted subspace was established.
    • A composite encoding matrix was designed to bound the recovery error covariance trace.
    • The proposed approach demonstrated effectiveness in a flight vehicle simulation.

    Conclusions:

    • The novel encoding scheme and subspace projection effectively identify and compensate for stealthy attacks in linear systems with unknown dynamics.
    • The method offers a significant advancement in secure data recovery for critical systems.