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    This study introduces a secure state estimation method for artificial neural networks (ANNs) using homomorphic encryption (HES). It enables secure estimation over limited bandwidth networks without data decryption, ensuring data integrity.

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    Area of Science:

    • Control Systems Engineering
    • Cybersecurity
    • Artificial Intelligence

    Background:

    • Secure state estimation is crucial for systems with noisy data and limited communication.
    • Artificial neural networks (ANNs) are increasingly used but require secure data handling.
    • Open, bandwidth-limited networks pose challenges for transmitting sensitive measurement data.

    Purpose of the Study:

    • To develop a secure state estimation algorithm for ANNs under unknown-but-bounded noises.
    • To ensure data security during transmission over bandwidth-limited networks using novel encryption.
    • To enable state estimation directly from encrypted data without decryption.

    Main Methods:

    • A novel homomorphic encryption scheme (HES) combining encoding-decoding mechanism (EDM) and Paillier encryption.
    • Development of a secure set-membership state estimation algorithm operating on encrypted data.
    • Derivation of secure state estimator gains using optimization and Lagrange multiplier method.

    Main Results:

    • Sufficient conditions for the existence of an ellipsoidal set under noise and HES constraints were determined.
    • The proposed secure state estimation algorithm effectively computes estimates from encrypted data.
    • The method ensures data security throughout the estimation process.

    Conclusions:

    • The developed secure state estimation approach is effective for ANNs in noisy, bandwidth-limited environments.
    • The homomorphic encryption scheme provides robust data protection during transmission and estimation.
    • This work advances secure and reliable state estimation in networked control systems.