基于博弈论的信息物理融合系统安全控制
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摘要
对于远程复杂的操控系统,信息物理融合系统(Cyber-physical system, CPS)主要依靠无线网络实现从传感器到控制器,从控制器到执行器间的信息传输,由于其依靠网络传输数据的特性使其控制系统极易遭到安全威胁.本文从物理系统入手,意图保护CPS系统中物理实体的正常运行不受由于恶意攻击造成网络空间入侵带来的干扰.以受到数据包时序攻击的信息物理融合系统为研究对象,将其安全性研究抽象为一个博弈过程,基于非合作博弈的两人零和博弈模型,设计了可变延迟情况下鲁棒输出反馈的极大极小控制器.并且采用参数化的软约束二次型目标函数,在控制器设计时引入干扰衰减因子γ,通过对γ的取值使得二次型目标函数取极小值,从而保证了最差情况下的稳定控制,在满足γ的约束条件下,本文通过粒子群搜索算法得出γ的值.另外,本文还对所设计的极大极小控制器,与线性二次型高斯(Linear quadratic Gaussian, LQG)控制对比分析,用双水箱系统进行了仿真验证,发现在受攻击情况下本文所设计的控制器最终能够实现稳定控制,而LQG却不能.
As a remote control system, the cyber-physical system(CPS) relies mainly on wireless networks to realize the transmission of information from sensors to controllers and from controllers to actuators. Because of this characteristic, the control system of CPS is vulnerable to security threats. Starting with physical devices, the aim of this paper is to protect normal operation of physical entities in CPS system from the interference of network intrusion caused by malicious attacks.Taking the cyber-physical systems suffered packets scheduling attacks into consideration, its secure control was abstracted as a process of two person zero sum game. Based on two person zero sum model of non-cooperative game, the paper designed a min-max controller with a robust output-feedback under time-varying delays. In this paper, a parameterized soft constraint quadratic objective function was adopted. Also, interference attenuation factor γ was introduced in the controller design and the minimum value of the quadratic objective function was determined by the value of γ which guaranteed the stability control under the worst case. Within the constraint of γ, we get the value of γ through particle swarm search algorithm. In addition, the min-max controller is analyzed and compared with the linear quadratic Gaussian(LQG) control, and the simulation was conducted on a two tanks system. The result showed that the min-max controller can stabilize the attacked system, but LQG cannot.
As a remote control system, the cyber-physical system(CPS) relies mainly on wireless networks to realize the transmission of information from sensors to controllers and from controllers to actuators. Because of this characteristic, the control system of CPS is vulnerable to security threats. Starting with physical devices, the aim of this paper is to protect normal operation of physical entities in CPS system from the interference of network intrusion caused by malicious attacks.Taking the cyber-physical systems suffered packets scheduling attacks into consideration, its secure control was abstracted as a process of two person zero sum game. Based on two person zero sum model of non-cooperative game, the paper designed a min-max controller with a robust output-feedback under time-varying delays. In this paper, a parameterized soft constraint quadratic objective function was adopted. Also, interference attenuation factor γ was introduced in the controller design and the minimum value of the quadratic objective function was determined by the value of γ which guaranteed the stability control under the worst case. Within the constraint of γ, we get the value of γ through particle swarm search algorithm. In addition, the min-max controller is analyzed and compared with the linear quadratic Gaussian(LQG) control, and the simulation was conducted on a two tanks system. The result showed that the min-max controller can stabilize the attacked system, but LQG cannot.
引文
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2 Wang Zhong-Jie,Xie Lu-Lu.Cyber-physical systems:a survey.Acta Automatica Sinica,2011,37(10):1157-1166(王中杰,谢璐璐.信息物理融合系统研究综述.自动化学报,2011,37(10):1157-1166)
3 Hespanha J P,Naghshtabrizi P,Xu Y.A survey of recent results in networked control systems.Proceedings of the IEEE,2007,95(1):138-162
4 Cetinkaya A,Ishii H,Hayakawa T.Networked control under random and malicious packet losses.IEEE Transactions on Automatic Control,2017,62(5):2434-2449
5 Fawzi H,Tabuada P,Diggavi S.Secure estimation and control for cyber-physical systems under adversarial attacks.IEEE Transactions on Automatic Control,2014,59(6):1454-1467
6 Jiang Y,Yin S.Recursive total principle component regression based fault detection and its application to vehicular cyber-physical systems.IEEE Transactions on Industrial Infoslatics,2018,14(4):1415-1423
7 Wang E K,Ye Y M,Xu X F,Chow K P.Security issues and challenges for cyber physical system.In:Green Computing and Communications(GreenCom),2010 IEEE/ACM Int l Conference on and Int l Conference on Cyber,Physical and Social Computing(CPSCom).New York,USA:IEEE,2010.733-738
8 Peng Chao-Yu.Research on Security of Model Checkingbased Cyber-Physical Systems[Master thesis],Nanjing University of Posts And Telecommunications,2015(彭超宇.基于模型检验的信息物理融合系统安全性研究[硕士学位论文],南京邮电大学,2015)
9 Ding Chao,Yang Li-Jun,Wu Meng.Security architecture and key technologies for IoT/CPS.ZTE Technology Journal,2011,17(1):11-16(丁超,杨立君,吴蒙.IoT/CPS的安全体系结构及关键技术.中兴通讯技术,2011,17(1):11-16)
10 Amin S,C′ardenas A A,Sastry S S.Safe and secure networked control systems under denial-of-service attacks.In:Proceedings of International Conference on Hybrid Systems:Computation and Control.Heidelberg,Berlin,Germany:Springer,2009.31-45
11 Gupta A,Langbort C,Basar T.Optimal control in the presence of an intelligent jammer with limited actions.In:Proceedings of the Decision and Control(CDC)49th IEEE Conference.New York,USA:IEEE,2010.1096-1101
12 Pang Z H,Liu G P,Dong Z.Secure networked control systems under denial of service attacks.In:Proceedings of the18th IFAC World Congress,Milano,Italy:2011.8908-8913
13 Sinopoli B,Schenato L,Franceschetti M,Poolla K,Jordan M I,Sastry S S.Kalman filtering with inteslittent observations.IEEE Transactions on Automatic Control,2004,49(9):1453-1464
14 Li X,Sun S.Robust H∞,Control for networked systems with random packet dropouts and time delays.Procedia Engineering,2012,29:4192-4197
15 Moon J,Basar T.Control over TCP-like lossy networks:A dynamic game approach.In:Proceedings of the American Control Conference.New York,USA:IEEE,2013.1578-1583
16 Shi Ming-Guang,Chen Wu-Wei.Mixed H2/H∞control based on game theory and its application to the vehicle active suspension system.Control Theory and Applications,2005,22(6):882-888(史明光,陈无畏.基于博弈论的H2/H∞混合控制及其在汽车主动悬架中的应用.控制理论与应用,2005,22(6):882-888)
17 Zhu Chao-Qun,Guo Ge.Optimal control for event-triggered networked control systems.Control and Decision,2014,29(5):802-808(祝超群,郭戈.事件驱动的网络化系统最优控制.控制与决策,2014,29(5):802-808)
18 Li Hai-Tao,Tang Gong-You,Ma Hui.Optimal control for a class of networked control systems with data packet dropout.Control and Decision,2009,24(5):773-776(李海涛,唐功友,马慧.一类具有数据包丢失的网络控制系统的最优控制.控制与决策,2009,24(5):773-776)
19 Shoukry Y,Araujo J,Tabuada P,Srivastava Me,Johansson K H.Minimax control for cyber-physical systems under network packet scheduling attacks.In:Proceedings of the 2nd ACM International Conference on High Confidence Networked Systems.New York,USA:ACM,2013.93-100
20 Basar T,Bernhard P.H∞-optimal Control and Related Minimax Design Problems:a Dynamic Game Approach.Springer Science and Business Media,Birkh¨auser Boston,2008.
21 Zhang Fen.Research The Problem of Differential Games Based on The Optimal Control[Master thesis],Yunnan Normal University,2015.(张芬.基于最优控制的微分博弈问题研究[硕士学位论文],云南师范大学,2015.)
22 Ara′ujo J.Design,Implementation and Validation of Resource-Aware and Resilient Wireless Networked Control Systems[Ph.D.dissertation],KTH Royal Institute of Technology,2014.
23 Garone E,Sinopoli B,Goldsmith A,Casavola A.LQG control for MIMO systems over multiple erasure channels with perfect acknowledgment.IEEE Transactions on Automatic Control,2012,57(2):450-456
24 Changela M,Kumar A.Designing a controller for two tank interacting system.International Journal of Science and Research(IJSR),2015,5(4):589-593
25 Wen Jing-Rong,Wu Mu-Qing,Su Jing-Fang.Cyberphysical System.Acta Automatica Sinica,2012,38(4):507-517(温景容,武穆清,宿景芳.信息物理融合系统.自动化学报,2012,38(4):507-517)
2 Wang Zhong-Jie,Xie Lu-Lu.Cyber-physical systems:a survey.Acta Automatica Sinica,2011,37(10):1157-1166(王中杰,谢璐璐.信息物理融合系统研究综述.自动化学报,2011,37(10):1157-1166)
3 Hespanha J P,Naghshtabrizi P,Xu Y.A survey of recent results in networked control systems.Proceedings of the IEEE,2007,95(1):138-162
4 Cetinkaya A,Ishii H,Hayakawa T.Networked control under random and malicious packet losses.IEEE Transactions on Automatic Control,2017,62(5):2434-2449
5 Fawzi H,Tabuada P,Diggavi S.Secure estimation and control for cyber-physical systems under adversarial attacks.IEEE Transactions on Automatic Control,2014,59(6):1454-1467
6 Jiang Y,Yin S.Recursive total principle component regression based fault detection and its application to vehicular cyber-physical systems.IEEE Transactions on Industrial Infoslatics,2018,14(4):1415-1423
7 Wang E K,Ye Y M,Xu X F,Chow K P.Security issues and challenges for cyber physical system.In:Green Computing and Communications(GreenCom),2010 IEEE/ACM Int l Conference on and Int l Conference on Cyber,Physical and Social Computing(CPSCom).New York,USA:IEEE,2010.733-738
8 Peng Chao-Yu.Research on Security of Model Checkingbased Cyber-Physical Systems[Master thesis],Nanjing University of Posts And Telecommunications,2015(彭超宇.基于模型检验的信息物理融合系统安全性研究[硕士学位论文],南京邮电大学,2015)
9 Ding Chao,Yang Li-Jun,Wu Meng.Security architecture and key technologies for IoT/CPS.ZTE Technology Journal,2011,17(1):11-16(丁超,杨立君,吴蒙.IoT/CPS的安全体系结构及关键技术.中兴通讯技术,2011,17(1):11-16)
10 Amin S,C′ardenas A A,Sastry S S.Safe and secure networked control systems under denial-of-service attacks.In:Proceedings of International Conference on Hybrid Systems:Computation and Control.Heidelberg,Berlin,Germany:Springer,2009.31-45
11 Gupta A,Langbort C,Basar T.Optimal control in the presence of an intelligent jammer with limited actions.In:Proceedings of the Decision and Control(CDC)49th IEEE Conference.New York,USA:IEEE,2010.1096-1101
12 Pang Z H,Liu G P,Dong Z.Secure networked control systems under denial of service attacks.In:Proceedings of the18th IFAC World Congress,Milano,Italy:2011.8908-8913
13 Sinopoli B,Schenato L,Franceschetti M,Poolla K,Jordan M I,Sastry S S.Kalman filtering with inteslittent observations.IEEE Transactions on Automatic Control,2004,49(9):1453-1464
14 Li X,Sun S.Robust H∞,Control for networked systems with random packet dropouts and time delays.Procedia Engineering,2012,29:4192-4197
15 Moon J,Basar T.Control over TCP-like lossy networks:A dynamic game approach.In:Proceedings of the American Control Conference.New York,USA:IEEE,2013.1578-1583
16 Shi Ming-Guang,Chen Wu-Wei.Mixed H2/H∞control based on game theory and its application to the vehicle active suspension system.Control Theory and Applications,2005,22(6):882-888(史明光,陈无畏.基于博弈论的H2/H∞混合控制及其在汽车主动悬架中的应用.控制理论与应用,2005,22(6):882-888)
17 Zhu Chao-Qun,Guo Ge.Optimal control for event-triggered networked control systems.Control and Decision,2014,29(5):802-808(祝超群,郭戈.事件驱动的网络化系统最优控制.控制与决策,2014,29(5):802-808)
18 Li Hai-Tao,Tang Gong-You,Ma Hui.Optimal control for a class of networked control systems with data packet dropout.Control and Decision,2009,24(5):773-776(李海涛,唐功友,马慧.一类具有数据包丢失的网络控制系统的最优控制.控制与决策,2009,24(5):773-776)
19 Shoukry Y,Araujo J,Tabuada P,Srivastava Me,Johansson K H.Minimax control for cyber-physical systems under network packet scheduling attacks.In:Proceedings of the 2nd ACM International Conference on High Confidence Networked Systems.New York,USA:ACM,2013.93-100
20 Basar T,Bernhard P.H∞-optimal Control and Related Minimax Design Problems:a Dynamic Game Approach.Springer Science and Business Media,Birkh¨auser Boston,2008.
21 Zhang Fen.Research The Problem of Differential Games Based on The Optimal Control[Master thesis],Yunnan Normal University,2015.(张芬.基于最优控制的微分博弈问题研究[硕士学位论文],云南师范大学,2015.)
22 Ara′ujo J.Design,Implementation and Validation of Resource-Aware and Resilient Wireless Networked Control Systems[Ph.D.dissertation],KTH Royal Institute of Technology,2014.
23 Garone E,Sinopoli B,Goldsmith A,Casavola A.LQG control for MIMO systems over multiple erasure channels with perfect acknowledgment.IEEE Transactions on Automatic Control,2012,57(2):450-456
24 Changela M,Kumar A.Designing a controller for two tank interacting system.International Journal of Science and Research(IJSR),2015,5(4):589-593
25 Wen Jing-Rong,Wu Mu-Qing,Su Jing-Fang.Cyberphysical System.Acta Automatica Sinica,2012,38(4):507-517(温景容,武穆清,宿景芳.信息物理融合系统.自动化学报,2012,38(4):507-517)