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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)安全控制問題. 采用KL (Kullback-Leibler)散度描述攻擊的隱蔽性, 并設計動態輸出反饋控制器, 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系; 然后, 通過設計可逆線性變換并構造凸優化問題, 求解安全控制器參數和相應的不變可達集; 最后, 使用彈簧?質量?阻尼系統進行仿真, 驗證了所提控制方法的有效性.
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關鍵詞:
- 信息物理系統 /
- 隱蔽攻擊 /
- 安全控制 /
- KL (Kullback-Leibler)散度 /
- 可達集
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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