Set‐Theoretic Safety Control With Formal Guarantees for Uncertain Linear Systems Under Sensor Attacks

ABSTRACT Safety control is an essential requirement in industrial systems, such as autonomous driving systems. An effective method for safety control is formal analysis, which mostly depends on the availability of reliable state information. Under adversarial conditions, especially in the presence of sensor attacks, corrupted measurements can lead to erroneous state information, causing state‐based formal methods ineffective. To address this challenge, this paper presents a robust framework with formal guarantee for the safety control of uncertain linear systems subject to sensor attacks. The core of the framework lies in a new notion of unsafe closure together with a set‐valued observer. The new notion defines the critical boundary of a safe set. The set‐valued observer is designed for state estimation and attack detection. Building on these developments, an innovative real‐time separating hyperplane algorithm is presented to synthesize provably safety control. The effectiveness of the approach is validated through extensive simulations in the CARLA environment, showing collision‐free navigation in urban traffic scenarios and reduced occurrences of unsafe states.