In this paper, we propose a secure two-party computation protocol for dynamic controllers using a secret sharing scheme. The proposed protocol realizes outsourcing of controller computation to two servers, while controller parameters, states, inputs, and outputs are kept secret against the servers. Unlike previous encrypted controls in a single-server setting, the proposed method can operate a dynamic controller for an infinite time horizon without controller state decryption or input re-encryption. We show that the control performance achievable by the proposed protocol can be made arbitrarily close to that attained by the unencrypted controller. Furthermore, system-theoretic and cryptographic modifications of the protocol are presented to improve the communication complexity. The feasibility of the protocol is demonstrated through numerical examples of PID and observer-based controls.

翻译：本文提出了一种利用秘密共享方案实现动态控制器的安全两方计算协议。该协议能够将控制器计算任务外包至两个服务器，同时确保控制器参数、状态、输入及输出对服务器保持机密。与以往单服务器环境下的加密控制方案不同，本方法能够在无限时间范围内运行动态控制器，而无需对控制器状态进行解密或对输入进行重新加密。我们证明，所提协议所能达到的控制性能可以无限逼近未加密控制器的性能。此外，本文提出了协议在系统理论与密码学层面的改进方案，以降低通信复杂度。通过PID控制与基于观测器的控制数值算例，验证了该协议的可行性。