Generalized Optimal Attacks With Unparameterized Patterns on Remote Estimation: Myopic and Non-Myopic Analysis

This paper studies the security issue of malicious attackers degrading remote estimation by injecting false data into sensors in cyber-physical systems. The typical attacks involve initially proposing a parameterized pattern, such as a linear one, then optimizing parameters according to system performance. The parameterized model limits the destructivity because it cannot cover all patterns. To overcome this, we investigate a generalized deception attack model with an unparameterized form. The resulting optimal attack patterns are nonlinear and discontinuous but can be analytically formalized. As a consideration of optimality, we consider two scenarios for attacks: the myopic scenario, focusing on current system time-step performance, and the non-myopic one, considering both pre-given system time-step and steady-state performance. A suboptimal attack with explicit pattern and estimation error is also proposed to reduce computational load. The conditions for the equivalence of different optimal attack models are provided. Moreover, we summarize typical stealthiness constraints and improve the proposed attacks on them. Finally, numerical simulations validate our theoretical results.