Observer-based Control for Linear Continuous-Time Systems with Fully Homomorphic Encryption

This paper is concerned with designing an encrypted observer-based controller for linear continuous-time systems. To be specific, this paper deploys a fully homomorphic encryption (FHE) scheme to directly compute control inputs in an encrypted form without decryption, thus avoiding data eavesdropping. Note that the deployment of FHE in observer-based controllers inevitably faces challenges in handling quantization errors due to the quantization required by the encryption-decryption processes. That motivates us to propose a novel encrypted form for computations of the continuous-time controller, and present rigorous stability analysis based on its virtual dynamics. Consequently, stability criteria are formulated in terms of tractable conditions associated with quantization gains and sampling intervals. Numerical results on DC motor control corresponding to several quantization gains and sampling intervals demonstrate the validity of our method.