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

TL;DR

This paper introduces a new encrypted control method using input-output history data and leveled fully homomorphic encryption, ensuring system stability and performance while maintaining data privacy.

Contribution

It proposes a novel controller representation that prevents destabilization and performance loss in encrypted control systems, with optimization techniques for practical implementation.

Findings

The encrypted controller maintains control performance comparable to the original.

Stability analysis confirms the system remains stable under encryption.

Simulation results demonstrate the feasibility of the proposed scheme.

Abstract

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 input-output history data to implement an encrypted dynamic controller that operates without destabilization and performance degradation. Implementation of this encrypted dynamic controller representation can be optimized via batching techniques to reduce the time and space complexities. 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.