控制系统隐私保护研究综述

王继民; 张纪峰; 陈嘉龙

doi:10.16383/j.aas.c250082

控制系统隐私保护研究综述

doi: 10.16383/j.aas.c250082 cstr: 32138.14.j.aas.c250082

王继民^{1, 2,},
张纪峰^{3, 4,},
陈嘉龙^4,

1.
北京科技大学自动化学院北京100083
2.
工业过程知识自动化教育部重点实验室北京100083
3.
中原工学院自动化与电气工程学院郑州450007
4.
中国科学院数学与系统科学研究院, 数学科学全国重点实验室, 北京100190

基金项目: 国家自然科学基金(62433020, 62203045, T2293770)资助

详细信息

作者简介:
王继民：北京科技大学自动化学院副教授, 主要研究方向为隐私保护, 系统辨识和网络化控制系统. E-mail: jimwang@ustb.edu.cn

张纪峰：中国科学院数学与系统科学研究院研究员, 主要研究方向为隐私保护, 系统建模与辨识, 随机系统, 适应控制, 多个体系统和有限信息系统. 本文通信作者. E-mail: jif@iss.ac.cn

陈嘉龙：中国科学院数学与系统科学研究院博士研究生, 主要研究方向为隐私保护, 分布式优化和随机系统. E-mail: chenjialong@amss.ac.cn

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出版历程
- 收稿日期: 2025-03-06
- 录用日期: 2025-05-29
- 网络出版日期: 2025-07-14

A Survey of Privacy Protection in Control Systems

Wang Ji-Min^{1, 2
,},
Zhang Ji-Feng^{3, 4
,},
Chen Jia-Long^4
,

1.
School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083
2.
Key Laboratory of Knowledge Automation for Industrial Processes, Ministry of Education, Beijing 100083
3.
School of Automation and Electrical Engineering, Zhongyuan University of Technology, Zhengzhou 450007
4.
State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190

Funds: Supported by National Natural Science Foundation of China (62433020, 62203045,T2293770)

More Information

Author Bio:
WANG Ji-Min　Associate professor at the School of Automation and Electrical Engineering, University of Science and Technology Beijing. His research interest covers privacy protection, system identification, and networked control systems

ZHANG Ji-Feng　Researcher at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences. His research interest covers privacy protection, system modeling and identification, stochastic systems, adaptive control, multi-agent systems, and finite-bite information systems. Corresponding author of this paper

CHEN Jia-Long　A Ph.D. student at the Academy of Mathematics and Systems Science, Chinese Academy of Sciences. His research interest covers privacy protection, distributed optimization, and stochastic systems

摘要

摘要: 控制系统隐私保护是随着数字化、信息化和智能化的发展而诞生的新兴方向, 具有广泛的实际需求与应用价值, 是现代控制理论在新时代的重要发展. 鉴于此, 本综述从研究背景与意义、国内外现状、未来研究方向及总结与展望四个方面, 对该方向进行系统梳理. 控制系统隐私问题无处不在, 隐私保护对控制系统至关重要. 由于该方向具有交叉性、不确定性、实时性和应用性等特点, 其研究具有挑战性. 在国内外研究现状部分, 详细介绍基于系统结构的方法、基于确定性变换的方法和基于随机混淆或扰动的方法, 并着重阐述同态加密、安全多方计算、差分隐私等常见技术的理论基础及在控制系统中的应用. 针对面临的诸多挑战性问题, 总结未来重点研究方向, 尤其是隐私、控制与通信的一体化设计, 以及隐私保护与系统性能之间的权衡. 最后, 对该方向进行总结与展望, 旨在为相关研究人员提供参考, 进一步推动国家安全战略的实施.
- 隐私保护 /
- 信息安全 /
- 系统控制 /
- 参数辨识 /
- 分布式优化与博弈
Abstract: Privacy protection in control systems is an emerging research direction, arising with the development of digitalization, informatization, and intelligence. It has a wide range of practical needs and application value, representing an important development in modern control theory in the new era. In view of this, this review systematically surveys this direction from four aspects: Research background and significance, current research status both domestically and internationally, future research directions, and summary and outlook. Privacy issues in control systems are everywhere, privacy protection is critical to control systems. This direction is challenging due to its interdisciplinary nature, uncertainties, real-time requirements, and practical applications. In the current research status both domestically and internationally part, we provide a detailed introduction of the system structure-based method, the deterministic transformation-based method, and the stochastic obfuscation or perturbation-based method. In addition, we focus on elaborating the theoretical basis of commonly used technologies and applications in control systems, such as homomorphic encryption, secure multi-party computation, and differential privacy. In face of numerous challenging issues, we summarize key future research directions, especially the integrated design of privacy, control, and communication, as well as the trade-off between privacy protection and system performance. Finally, we provide a summary and an outlook for this direction, aiming to offer references for relevant researchers and further promote the implementation of national security strategies.
- Privacy protection /
- information security /
- systems control /
- parameter identification /
- distributed optimization and game theory
注释:

1) 1¹ 所列应用包括但不限于上述成果, 实际建模中可根据所需保护的敏感信息和实现的具体控制任务, 选择合适的隐私保护方法和控制模型.

2) 2² 此处与控制系统中常见的模型预测控制 (Model predictive control, MPC) 不同.

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图 1 状态分解示例

Fig. 1 An example of state decomposition

下载: 全尺寸图片幻灯片

表 1 基于确定性变换的方法

Table 1 The deterministic transformation-based method

方法类别	实现技术	应用场景	对应文献
同态加密	Paillier密码体制	机器学习	[74]
		离散时间参数估计	[22, 79]
		离散时间分布式优化	[26, 80, 86, 89−91, 94]
		离散时间分布式趋同	[81−84, 133]
		离散时间线性系统协同控制	[62, 85, 87−88, 95]
		云控制系统	[96−99]
		离散时间线性系统状态估计	[28, 66, 92−93, 102]
		联邦学习	[107]
		离散时间模型预测控制	[130]
	RSA密码体制	离散时间非线性系统控制	[103]
		离散时间线性系统控制	[104]
		离散时间系统状态估计	[134]
	ElGamal密码体制	离散时间线性系统协同控制	[72, 105]
	ElGamal密码体制	离散时间分布式优化	[100]
	Learning With Errors密码体制	离散时间线性系统控制	[41, 101]
		离散时间线性系统状态估计	[106]
		离散时间系统分布式最优控制	[135]
	全同态加密	联邦学习	[73]
	全同态加密	离散时间线性系统控制	[132]
安全多方计算	混淆电路	机器学习	[113, 129]
	混淆电路	基因分析	[122−123]
	秘密分享	机器学习	[110−112, 114−118]
		联邦学习	[119−121]
		基因分析	[124]
		线性方程组求解	[125−126]
		连续时间多项式控制	[127]
		离散时间模型预测控制	[131]
	隐私比较	离散时间系统Kalman滤波	[128]
其他变换	同构变换	离散时间线性二次最优控制	[14]
	仿射变换	离散时间分布式趋同	[52]
		离散时间系统状态估计	[54, 64−65]
		云控制系统	[67]
		连续时间分布式优化	[68]
		离散时间分布式最优控制	[69]
	时变变换	连续时间分布式趋同	[63]

下载: 导出CSV

表 2 添加扰动后的两次输出

Table 2 Two outputs after adding perturbation

	$ P(150\le M_i<250) $	$ P(250\le M_i<350) $
$ i=1 $	0.139	0.116
$ i=2 $	0.116	0.139

下载: 导出CSV

表 3 隐私预算$ \epsilon $为0.1、0.3和10时的两次输出

Table 3 Two outputs when $ \epsilon $ is 0.1, 0.3, and 10

		$ P(150\le M_i<250) $	$ P(250\le M_i<350) $
$ \epsilon=0.1 $	$ i=1 $	0.0487	0.0453
$ \epsilon=0.1 $	$ i=2 $	0.0453	0.0487
$ \epsilon=0.3 $	$ i=1 $	0.139	0.116
$ \epsilon=0.3 $	$ i=2 $	0.116	0.139
$ \epsilon=10 $	$ i=1 $	0.993	0.007
$ \epsilon=10 $	$ i=2 $	0.007	0.993

下载: 导出CSV

表 4 差分隐私方法

Table 4 Differential privacy method

应用场景	对应文献
离散时间分布式优化	[18, 47, 50, 148, 157, 165−172, 182]
离散时间分布式趋同	[149, 158, 160, 177−181]
离散时间线性系统控制	[148, 185−186, 189−191]
社交网络参数估计	[151]
离散时间系统Kalman滤波	[16, 150−151]
离散时间系统非线性观测器设计	[154]
离散时间系统区间观测器设计	[155]
离散时间系统线性二次Gauss控制	[156]
连续时间分布式趋同	[159, 161]
离散时间参数估计	[160−161, 171−172, 174]
离散时间分布式聚合博弈	[164, 190]
离散时间线性系统状态估计	[175, 194]
离散时间系统线性二次控制	[183]
机器学习	[182−183]
联邦学习	[186]
非线性不确定系统异常检测	[189]

下载: 导出CSV

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