Optimal Unobservable Attack Design Against Networked Control Systems

This article investigates the optimal unobservable attack design problem for linear time-invariant networked control systems from the attackers’ perspective. The main purpose of this study is to design the optimal attack strategies to compromise the systems’ observability. To achieve this purpose, the following three types of optimal attack tactics are solved. First, if the attacker can render the system unobservable by attacking <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">arbitrary</i> <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$s$</tex-math></inline-formula> sensors, how to obtain the minimum value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$s$</tex-math></inline-formula>, which is called the minimum number attack problem (MNAP). Second, how to disrupt the observability of the system by using the minimum attack cost? It is termed the minimum-cost attack problem (MCAP). Third, if the attack energy is limited, and the attacker can only attack <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$r$</tex-math></inline-formula> sensors, then how to select proper <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$r$</tex-math></inline-formula> sensors such that the observability degree can be maximally degraded. This problem is named minimum degree attack problem. Next, we first prove that both the MNAP and MCAP are NP-hard problems. In addition, four algorithms, Algorithms 1–4, are constructed to solve the three problems and obtain the optimal unobservable attack strategies, and four simulation examples, Examples 1–4, are proposed to demonstrate the effectiveness of these strategies and the corresponding algorithms.