隱蔽攻擊下信息物理系統的安全輸出反饋控制
doi: 10.16383/j.aas.c220893
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中國礦業(yè)大學(xué)信息與控制工程學(xué)院 徐州 221116
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中國礦業(yè)大學(xué)國家煤加工與潔凈化工程技術(shù)研究中心 徐州 221116
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北京理工大學(xué)自動(dòng)化學(xué)院 北京 100081
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中國礦業(yè)大學(xué)人工智能研究院 徐州 221116
Secure Output-feedback Control for Cyber-physical Systems Under Stealthy Attacks
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School of Information and Control Engineering, China University of Mining and Technology, Xuzhou 221116
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National Engineering Research Center of Coal Preparation and Purification, China University of Mining and Technology, Xuzhou 221116
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School of Automation, Beijing Institute of Technology, Beijing 100081
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Artificial Intelligence Research Institute, China University of Mining and Technology, Xuzhou 221116
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摘要: 研究了受到隱蔽攻擊的信息物理系統(Cyber-physical system, CPS)安全控制問(wèn)題. 采用KL (Kullback-Leibler)散度描述攻擊的隱蔽性, 并設計動(dòng)態(tài)輸出反饋控制器, 使系統可達集始終保持在安全區域內, 其中可達集定義為系統狀態(tài)以一定概率屬于的集合. 首先, 給出隱蔽攻擊下檢測器殘差所在范圍的一個(gè)外橢球近似集; 其次, 根據該近似集和噪聲的范圍給出控制器參數與系統橢球形不變可達集的關(guān)系; 然后, 通過(guò)設計可逆線(xiàn)性變換并構造凸優(yōu)化問(wèn)題, 求解安全控制器參數和相應的不變可達集; 最后, 使用彈簧?質(zhì)量?阻尼系統進(jìn)行仿真, 驗證了所提控制方法的有效性.Abstract: Secure control problem of cyber-physical systems (CPS) under stealthy attacks is studied. The Kullback-Leibler (KL) divergence is adopted to describe the attack's stealthiness. The aim is to design a secure dynamic output-feedback controller such that the reachable set, which is defined as the set that the system's state resides in with a certain probability, resides in a safe set. Firstly, an ellipsoidal outer approximation for the set of residual under stealthy attacks is given. Secondly, based on the approximation and the ranges of noises, the relationship between controller's parameters and the ellipsoidal invariant reachable set is analyzed. Thirdly, a convex optimization problem is constructed by designing an invertible linear transformation. Parameters of the secure controller and the corresponding invariant reachable set are obtained by solving the problem. Finally, a simulation of the spring-mass-damping system is given to verify the effectiveness of the proposed controller.
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圖 1 不同a、b、c值下, 參數$\delta $和橢球形不變可達集體積的關(guān)系
Fig. 1 Relationship between$\delta $and volume of ellipsoidal invariant reachable set with different a, b and c
圖 2 不同a、b、c值下, 參數$\alpha $和橢球形不變可達集體積的關(guān)系
Fig. 2 Relationship between$\alpha $and volume of ellipsoidal invariant reachable set with different a, b and c
圖 3 不同a、b、c值下, 系統狀態(tài)的橢球形不變可達集
Fig. 3 Ellipsoidal invariant reachable sets of system's state with different a, b and c
圖 4 不同a、b、c值下, 參數$\alpha $和$ {\rm{Tr}}(Y)$的關(guān)系
Fig. 4 Relationship between$\alpha $and$ {\rm{Tr}}(Y)$ with different a, b and c
圖 5 未使用控制器和使用控制器式(5)、(6)時(shí),系統狀態(tài)的橢球形不變可達集
Fig. 5 Ellipsoidal invariant reachable set of system's state without controller and with controller (5), (6)
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