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.

翻译：保护动态控制器的参数、状态及输入/输出信号对安全地将计算任务外包给不可信第三方至关重要。虽然全同态加密方案允许对加密数据执行控制器运算，但采用该加密方案的动态控制器会因溢出导致闭环系统失稳或控制性能下降。本文提出一种基于输入-输出历史数据的控制器新表达方式，可构建在免于失稳与性能退化条件下运行的加密动态控制器。通过批处理技术对该加密动态控制器表达方式进行优化实现，可降低时间与空间复杂度。进一步地，本研究分析了控制器加密效应引发的闭环系统稳定性与性能退化问题。数值仿真验证了所提加密控制方案的可行性，该方案能以足够精度继承原始控制器的控制性能。