Input-Output History Feedback Controller for Encrypted Control with Leveled Fully Homomorphic Encryption

Protecting the parameters, states, and input/output signals of a dynamic controller is essential for securely outsourcing its computation to an untrusted third party. Although a fully homomorphic encryption scheme allows the evaluation of controller operations with encrypted data, an encrypted dynamic controller with the encryption scheme destabilizes a closed-loop system or degrades the control performance due to overflow. This paper presents a novel controller representation based on inputoutput history data to implement an encrypted dynamic controller that operates without destabilization and performance degradation. An algorithm for efficient encrypted control computation is also proposed using single instruction/multiple data operations based on a batching technique. Furthermore, this study analyzes the stability and performance degradation of a closed-loop system caused by the effects of controller encryption. A numerical simulation demonstrates the feasibility of the proposed encrypted control scheme, which inherits the control performance of the original controller at a sufficient level.

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