Cyber-Physical Security Analysis of Linear Parabolic Partial Differential Equations Under Coordinated Actuator–Sensor Attacks

Abstract Cyber-physical distributed parameter systems (DPS) governed by partial differential equations (PDEs) face unique security challenges due to their spatially distributed dynamics and reliance on sensors placed only at discrete points. While studies on ordinary differential equation (ODE)-modeled systems address the impact of temporal-only cyber-attacks, PDE-modeled systems require additional analysis of spatiotemporal vulnerabilities that can arise from cyber-attacks on sensors and actuators in DPS. Motivated by this need, this article analyzes the effects of coordinated actuator–sensor attacks on a class of DPS, modeled by linear parabolic PDEs—with distributed actuation and boundary measurement. First, we propose a framework for defining adversarial metrics that can capture the effect of attacks in a DPS setting. Subsequently, we derive mathematical conditions under which adversarial objectives can be achieved in terms of the previously defined metrics. Finally, a case study on battery module thermal behavior, based on the proposed adversarial metrics and mathematical conditions, illustrates how cyber-attacks can potentially affect the operation of DPS.