arXiv subjects

Sribalaji C. Anand

Publications and source records attributed to Sribalaji C. Anand.

26 records · Page 2Linked to original sources

arXiv2023

Optimal Detector Placement in Networked Control Systems under Cyber-attacks with Applications to Power Networks

This paper proposes a game-theoretic method to address the problem of optimal detector placement in a networked control system under cyber-attacks. The networked control system is composed of interconnected agents where each agent is regulated by its local controller over unprotected communication, which leaves the system vulnerable to malicious cyber-attacks. To guarantee a given local performance, the defender optimally selects a single agent on which to place a detector at its local controller with the purpose of detecting cyber-attacks. On the other hand, an adversary optimally chooses a single agent on which to conduct a cyber-attack on its input with the aim of maximally worsening the local performance while remaining stealthy to the defender. First, we present a necessary and sufficient condition to ensure that the maximal attack impact on the local performance is bounded, which restricts the possible actions of the defender to a subset of available agents. Then, by considering the maximal attack impact on the local performance as a game payoff, we cast the problem of finding optimal actions of the defender and the adversary as a zero-sum game. Finally, with the possible action sets of the defender and the adversary, an algorithm is devoted to determining the Nash equilibria of the zero-sum game that yield the optimal detector placement. The proposed method is illustrated on an IEEE benchmark for power systems.

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arXiv2022

Privacy and Security in Network Controlled Systems via Dynamic Masking

In this paper, we propose a new architecture to enhance the privacy and security of networked control systems against malicious adversaries. We consider an adversary which first learns the system dynamics (privacy) using system identification techniques, and then performs a data injection attack (security). In particular, we consider an adversary conducting zero-dynamics attacks (ZDA) which maximizes the performance cost of the system whilst staying undetected. However, using the proposed architecture, we show that it is possible to (i) introduce significant bias in the system estimates of the adversary: thus providing privacy of the system parameters, and (ii) efficiently detect attacks when the adversary performs a ZDA using the identified system: thus providing security. Through numerical simulations, we illustrate the efficacy of the proposed architecture.

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arXiv2022

A Zero-Sum Game Framework for Optimal Sensor Placement in Uncertain Networked Control Systems under Cyber-Attacks

This paper proposes a game-theoretic approach to address the problem of optimal sensor placement against an adversary in uncertain networked control systems. The problem is formulated as a zero-sum game with two players, namely a malicious adversary and a detector. Given a protected performance vertex, we consider a detector, with uncertain system knowledge, that selects another vertex on which to place a sensor and monitors its output with the aim of detecting the presence of the adversary. On the other hand, the adversary, also with uncertain system knowledge, chooses a single vertex and conducts a cyber-attack on its input. The purpose of the adversary is to drive the attack vertex as to maximally disrupt the protected performance vertex while remaining undetected by the detector. As our first contribution, the game payoff of the above-defined zero-sum game is formulated in terms of the Value-at-Risk of the adversary's impact. However, this game payoff corresponds to an intractable optimization problem. To tackle the problem, we adopt the scenario approach to approximately compute the game payoff. Then, the optimal monitor selection is determined by analyzing the equilibrium of the zero-sum game. The proposed approach is illustrated via a numerical example of a 10-vertex networked control system.

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arXiv2022

Risk assessment and optimal allocation of security measures under stealthy false data injection attacks

This paper firstly addresses the problem of risk assessment under false data injection attacks on uncertain control systems. We consider an adversary with complete system knowledge, injecting stealthy false data into an uncertain control system. We then use the Value-at-Risk to characterize the risk associated with the attack impact caused by the adversary. The worst-case attack impact is characterized by the recently proposed output-to-output gain. We observe that the risk assessment problem corresponds to an infinite non-convex robust optimization problem. To this end, we use dissipative system theory and the scenario approach to approximate the risk-assessment problem into a convex problem and also provide probabilistic certificates on approximation. Secondly, we consider the problem of security measure allocation. We consider an operator with a constraint on the security budget. Under this constraint, we propose an algorithm to optimally allocate the security measures using the calculated risk such that the resulting Value-at-risk is minimized. Finally, we illustrate the results through a numerical example. The numerical example also illustrates that the security allocation using the Value-at-risk, and the impact on the nominal system may have different outcomes: thereby depicting the benefit of using risk metrics.

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arXiv2022

Risk-averse controller design against data injection attacks on actuators for uncertain control systems

In this paper, we consider the optimal controller design problem against data injection attacks on actuators for an uncertain control system. We consider attacks that aim at maximizing the attack impact while remaining stealthy in the finite horizon. To this end, we use the Conditional Value-at-Risk to characterize the risk associated with the impact of attacks. The worst-case attack impact is characterized using the recently proposed output-to-output $\ell_2$-gain (OOG). We formulate the design problem and observe that it is non-convex and hard to solve. Using the framework of scenario-based optimization and a convex proxy for the OOG, we propose a convex optimization problem that approximately solves the design problem with probabilistic certificates. Finally, we illustrate the results through a numerical example.

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arXiv2022

Risk Assessment of Stealthy Attacks on Uncertain Control Systems

In this article, we address the problem of risk assessment of stealthy attacks on uncertain control systems. Considering data injection attacks that aim at maximizing impact while remaining undetected, we use the recently proposed output-to-output gain to characterize the risk associated with the impact of attacks under a limited system knowledge attacker. The risk is formulated using a well-established risk metric, namely the maximum expected loss. Under this setups, the risk assessment problem corresponds to an untractable infinite non-convex optimization problem. To address this limitation, we adopt the framework of scenario-based optimization to approximate the infinite non-convex optimization problem by a sampled non-convex optimization problem. Then, based on the framework of dissipative system theory and S-procedure, the sampled non-convex risk assessment problem is formulated as an equivalent convex semi-definite program. Additionally, we derive the necessary and sufficient conditions for the risk to be bounded. Finally, we illustrate the results through numerical simulation of a hydro-turbine power system.

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arXiv2021

Design of multiplicative watermarking against covert attacks

This paper addresses the design of an active cyberattack detection architecture based on multiplicative watermarking, allowing for detection of covert attacks. We propose an optimal design problem, relying on the so-called output-to-output l2-gain, which characterizes the maximum gain between the residual output of a detection scheme and some performance output. Although optimal, this control problem is non-convex. Hence, we propose an algorithm to design the watermarking filters by solving the problem suboptimally via LMIs. We show that, against covert attacks, the output-to-output l2-gain is unbounded without watermarking, and we provide a sufficient condition for boundedness in the presence of watermarks.

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arXiv2021

Stealthy Cyber-Attack Design Using Dynamic Programming

This paper addresses the issue of data injection attacks on control systems. We consider attacks which aim at maximizing system disruption while staying undetected in the finite horizon. The maximum possible disruption caused by such attacks is formulated as a non-convex optimization problem whose dual problem is a convex semi-definite program. We show that the duality gap is zero using S-lemma. To determine the optimal attack vector, we formulate a soft-constrained optimization problem using the Lagrangian dual function. The framework of dynamic programming for indefinite cost functions is used to solve the soft-constrained optimization problem and determine the attack vector. Using the Karush-Kuhn-Tucker conditions, we also provide necessary and sufficient conditions under which the obtained attack vector is optimal to the primal problem.

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