On minimal tests of sensor veracity for dynamic watermarking-based defense of cyber-physical systems

Abstract

We address the problem of security of cyber-physical systems where some sensors may be malicious. We consider a multiple-input, multiple-output stochastic linear dynamical system controlled over a network of communication and computational nodes which contains (i) a controller that computes the inputs to be applied to the physical plant, (ii) actuators that apply these inputs to the plant, and (iii) sensors which measure the outputs of the plant. Some of these sensors, however, may be malicious. The malicious sensors do not report the true measurements to the controller. Rather, they report false measurements that they fabricate, possibly strategically, so as to achieve any objective that they may have, such as destabilizing the closed-loop system or increasing its running cost. Recently, it was shown that under certain conditions, an approach of “dynamic watermarking” can secure such a stochastic linear dynamical system in the sense that either the presence of malicious sensors in the system is detected, or the malicious sensors are constrained to adding a distortion that can only be of zero power to the noise already entering the system. The first contribution of this paper is to generalize this result to partially observed MIMO systems with both process and observation noises, a model which encompasses some of the previous models for which dynamic watermarking was established to guarantee security. This result, similar to the prior ones, is shown to hold when the controller subjects the reported sequence of measurements to two particular tests of veracity. The second contribution of this paper is in showing, via counterexamples, that both of these tests are needed in order to secure the control system in the sense that if any one of these two tests of sensor veracity is dropped, then the above guarantee does not hold. The proposed approach has several potential applications, including in smart grids, automated transportation, and process control.