2018/02/28 by Somayeh Salimi, Salimi, Somayeh, Subhrakanti Dey +3
Computer Science · Engineering · #Adversarial Robustness in Machine Learning #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Security in Wireless Sensor Networks #Smart Grid Security and Resilience #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1803.00170
openalex publication_date 2018/02/28 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
In this paper, we investigate the role of a physical watermarking signal in\nquickest detection of a deception attack in a scalar linear control system\nwhere the sensor measurements can be replaced by an arbitrary stationary signal\ngenerated by an attacker. By adding a random watermarking signal to the control\naction, the controller designs a sequential test based on a Cumulative Sum\n(CUSUM) method that accumulates the log-likelihood ratio of the joint\ndistribution of the residue and the watermarking signal (under attack) and the\njoint distribution of the innovations and the watermarking signal under no\nattack. As the average detection delay in such tests is asymptotically (as the\nfalse alarm rate goes to zero) upper bounded by a quantity inversely\nproportional to the Kullback-Leibler divergence(KLD) measure between the two\njoint distributions mentioned above, we analyze the effect of the watermarking\nsignal variance on the above KLD. We also analyze the increase in the LQG\ncontrol cost due to the watermarking signal, and show that there is a tradeoff\nbetween quick detection of attacks and the penalty in the control cost. It is\nshown that by considering a sequential detection test based on the joint\ndistributions of residue/innovations and the watermarking signal, as opposed to\nthe distributions of the residue/innovations only, we can achieve a higher KLD,\nthus resulting in a reduced average detection delay. Numerical results are\nprovided to support our claims.\n