Statistical Watermarking for Networked Control Systems

Watermarking can detect sensor attacks in control systems by injecting a private signal into the control, whereby attacks are identified by checking the statistics of the sensor measurements and private signal. However, past approaches assume full state measurements or a centralized controller, which is not found in networked LTI systems with subcontrollers. Since generally the entire system is neither controllable nor observable by a single subcontroller, communication of sensor measurements is required to ensure closed-loop stability. The possibility of attacking the communication channel has not been explicitly considered by previous watermarking schemes, and requires a new design. In this paper, we derive a statistical watermarking test that can detect both sensor and communication attacks. A unique (compared to the non-networked case) aspect of the implementing this test is the state-feedback controller must be designed so that the closed-loop system is controllable by each sub-controller, and we provide two approaches to design such a controller using Heymann's lemma and a multi-input generalization of Heymann's lemma. The usefulness of our approach is demonstrated with a simulation of detecting attacks in a platoon of autonomous vehicles. Our test allows each vehicle to independently detect attacks on both the communication channel between vehicles and on the sensor measurements.