Kwon, Hyuk Bin, Meriem Ernez, and Jun Ueda. “Time-Varying Affine Transformation-based Perfectly Undetectable Attacks: Eliminating Timing Constraints and Enabling Destination Control” Control Engineering Practice, Vol. 175, October 2026
Abstract
This paper presents a theoretical framework for Time-Varying Affine Transformation-based Perfectly Undetectable Attacks (TV-ATPA) on linear time-invariant (LTI) control systems. The proposed attack methodology employs coordinated multiplicative and additive false data injections targeting both state measurements and control commands through time-varying transformation matrices. The key innovation is the elimination of restrictive timing constraints imposed by initial state matching requirements from previous constant-parameter ATPA approaches, enabling attack deployment at arbitrary times. Unlike constant-parameter ATPA where the additive obserables disturbance is uniquely constrained by initial conditions, TV-ATPA enables free selection of the attack parameter (under one of the options), providing attackers control over the target system’s ultimate destination state. The paper derives mathematical conditions for achieving perfect undetectability while maintaining smooth attack transitions via interpolation functions. The framework is validated through detailed analysis of general LTI state-feedback regulation control systems. Its practicality is also demonstrated through a 2D point-mass trajectory control system simulation and manipulator Jacobian transpose control experiments as illustrative examples. The results show that the attack maintains complete undetectability from the controller’s perspective while significantly altering actual system behavior, representing a practical advancement in attack deployment flexibility, demonstrating that timing constraints can be eliminated and destination control can be achieved while maintaining perfect undetectability through dynamic compensation mechanisms.