Visible to the public @PAD: Adversarial Training of Power Systems Against Denial of Service Attacks

In this work, we study the vulnerabilities of protection systems that can detect cyber-attacks in power grid systems. We show that machine learning-based discriminators are not resilient against Denial-of-Service (DoS) attacks. In particular, we demonstrate that an adversarial actor can launch DoS attacks on specific sensors, render their measurements useless and cause the attack detector to classify a more sophisticated cyber-attack as a normal event. As a result of this, the system operator may fail to take action against attack-related faults leading to a decrease in the operation performance. To realize a DoS attack, we present an optimization problem to determine which sensors to attack within a given budget such that the existing classifier can be deceived. For linear classifiers, this optimization problem can be formulated as a mixed-integer linear programming problem.

In this paper, we extend this optimization problem to find attacks for more complex classifiers such as neural networks. We demonstrate that a neural network, in particular, with RELU activation functions, can be represented as a set of logic formulas using Disjunctive Normal Form, and the optimization problem can be used to efficiently compute a DoS attack. In addition, we propose a defense model that improves the resilience of neural networks against DoS through adversarial training. Finally, we evaluate the efficiency of the approach using a dataset for classification in power systems.

Ali Irmak Ozdagli is a graduate student in the Department of Electrical Engineering and Computer Science at Vanderbilt University. His research focuses on security and resilience of cyber-physical systems. Contact him at


Carlos Barreto is a postdoctoral scholar at Vanderbilt University. His research interests include security and resiliency of cyber-physical systems, risk analysis, and game theoretic analysis of security problems. He received the Ph.D. in computer science from the University of Texas at Dallas. He is member of the IEEE. Contact him at


Xenofon Koutsoukos is a professor with the department of electrical engineering and computer science and a senior research scientist with the Institute for Software Integrated Systems, Vanderbilt University. His research work is in the area of cyber-physical systems with emphasis on security and resilience, control, diagnosis and fault tolerance, formal methods, and adaptive resource management. He received the Ph.D. degree in electrical engineering from the University of Notre Dame. He is a Fellow of the IEEE. Contact him at

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@PAD: Adversarial Training of Power Systems Against Denial of Service Attacks
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