Quantization Effects on Zero-Dynamics Attacks to Closed-Loop Sampled-Data Control Systems

This paper focuses on cyber-security issues of networked control systems in closed-loop forms from the perspective of quantized sampled-data systems. Quantization of control inputs adds quantization error to the plant input, resulting in certain variation in the plant output. On the other hand, sampling can introduce non-minimum phase zeros in discretized systems. We consider zero-dynamics attacks, which is a class of false data injection attacks utilizing such unstable zeros. Although non-quantized zero-dynamics attacks are undetectable from the plant output side, quantized attacks may be revealed by larger output variation. Our setting is that the attack signal is applied with the same uniform quantizer used for the control input. We evaluate the attack stealthiness in the closed-loop system setting by quantifying the output variation. Specifically, we characterize the cases for static and dynamic quantization in the attack signal, while keeping the control input statically quantized. Then we demonstrate that the attacker can reduce such output variation with a modified approach, by compensating the quantization error of the attack signal inside the attack dynamics. We provide numerical examples to illustrate the effectiveness of the proposed approaches. We show that observing the quantized control input value by a mirroring model can reveal the zero-dynamics attacks.