Optimal Design of Stealthy Attacks in Partially Observed Linear Systems: A Likelihood-Based Approach
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866917476470620160 |
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| author | Zhou, Haosheng Hu, Ruimeng |
| author_facet | Zhou, Haosheng Hu, Ruimeng |
| contents | We study the optimal design of stealthy attacks against partially observed linear control systems. We first propose a novel likelihood-based detection mechanism derived from the innovation process, based on which we quantify stealthiness and formulate an attack design problem that trades off performance degradation and detectability. We develop a tractable control-theoretic framework for optimal stealthy attacks under two information structures: deterministic attacks fixed prior to system evolution, and adaptive attacks constructed from available observations. In the adaptive setting, the attacker's partial observation leads to a stochastic control problem with an endogenous information structure. We address this challenge through a hierarchical optimization framework combined with the separation principle, reducing the problem to a Markovian control formulation and yielding semi-explicit optimal attacks. We further establish well-posedness of the resulting systems and illustrate through numerical experiments how information constraints shape the trade-off between attack effectiveness and stealthiness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_05545 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal Design of Stealthy Attacks in Partially Observed Linear Systems: A Likelihood-Based Approach Zhou, Haosheng Hu, Ruimeng Optimization and Control We study the optimal design of stealthy attacks against partially observed linear control systems. We first propose a novel likelihood-based detection mechanism derived from the innovation process, based on which we quantify stealthiness and formulate an attack design problem that trades off performance degradation and detectability. We develop a tractable control-theoretic framework for optimal stealthy attacks under two information structures: deterministic attacks fixed prior to system evolution, and adaptive attacks constructed from available observations. In the adaptive setting, the attacker's partial observation leads to a stochastic control problem with an endogenous information structure. We address this challenge through a hierarchical optimization framework combined with the separation principle, reducing the problem to a Markovian control formulation and yielding semi-explicit optimal attacks. We further establish well-posedness of the resulting systems and illustrate through numerical experiments how information constraints shape the trade-off between attack effectiveness and stealthiness. |
| title | Optimal Design of Stealthy Attacks in Partially Observed Linear Systems: A Likelihood-Based Approach |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2605.05545 |