Encrypted State Estimation in Networked Control Systems

In this paper, we propose a distributed state observer in which the data of measurements and state estimates are protected by homomorphic cryptosystem. The proposed observer network is composed of local observers, where each of them utilizes encrypted local measurement, encryption of plant input, and encrypted estimates transmitted from its neighbors. All the operations in the network are performed on encrypted data without decryption, and the full state is recovered in every local observer as an encrypted message. Assuming the characteristic polynomial and the minimal polynomial of the state matrix for the plant are the same, the parameters in the observers are chosen to be integers. This not only allows finitetime convergence for the state estimates, but also makes the encrypted dynamic observers operate for infinite time horizon.