南京理工大学学报（自然科学版）2025，Vol.49Issue(5)：547-556,10.DOI:10.14177/j.cnki.32-1397n.2025.49.05.004
基于LWE全同态加密的渐近动态跟踪控制
Asymptotic tracking control of dynamic reference under LWE fully homomorphic encryption
摘要
Abstract
This work investigates the problem of asymptotic tracking control of a dynamic reference under fully homomorphic encryption(FHE),which proposes a controller design method based on learning with errors(LWE)FHE scheme.The constructed fully homomorphic encrypted controller in this work can protect the controller parameters and the real-time information of the closed-loop system,addressing the limitation of current partially homomorphic encrypted controllers which fail to safeguard the controller parameters.Firstly,based on the LWE FHE scheme,a novel dynamic tracking encrypted controller operating is proposed.Then,this work shows that the noise induced by LWE FHE will not be amplified by multiplication to infinity,and provides a corresponding parameter design method for the controller.Finally,this article provides a sufficient condition of the modulus of the cryptosystems(the size of the message space),under which the actuator is able to restore the control inputs from the lower-bit information,and realizes the asymptotic tracking of a dynamic reference.The proposed method effectively reduces the modulus in the cryptosystem without degrading the convergence accuracy.The effectiveness of the designed encrypted controller is demonstrated through a simulation.关键词
隐私保护/全同态加密/动态跟踪控制/动态量化Key words
privacy protection/fully homomorphic encryption/dynamic tracking control/dynamic quantization分类
计算机与自动化引用本文复制引用
梁宪魁,冯帅..基于LWE全同态加密的渐近动态跟踪控制[J].南京理工大学学报（自然科学版）,2025,49(5):547-556,10.基金项目
国家自然科学基金(62303226) （62303226）
中央高校基本科研业务费专项资金(30922010714) （30922010714）
江苏省自然科学基金(BK20230921) （BK20230921）
