arXiv subjects

André M. H. Teixeira

Publications and source records attributed to André M. H. Teixeira.

35 records · Page 2Linked to original sources

arXiv2025

Switching multiplicative watermark design against covert attacks

Active techniques have been introduced to give better detectability performance for cyber-attack diagnosis in cyber-physical systems (CPS). In this paper, switching multiplicative watermarking is considered, whereby we propose an optimal design strategy to define switching filter parameters. Optimality is evaluated exploiting the so-called output-to-output gain of the closed loop system, including some supposed attack dynamics. A worst-case scenario of a matched covert attack is assumed, presuming that an attacker with full knowledge of the closed-loop system injects a stealthy attack of bounded energy. Our algorithm, given watermark filter parameters at some time instant, provides optimal next-step parameters. Analysis of the algorithm is given, demonstrating its features, and demonstrating that through initialization of certain parameters outside of the algorithm, the parameters of the multiplicative watermarking can be randomized. Simulation shows how, by adopting our method for parameter design, the attacker's impact on performance diminishes.

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arXiv2024

Data-Driven and Stealthy Deactivation of Safety Filters

Safety filters ensure that control actions that are executed are always safe, no matter the controller in question. Previous work has proposed a simple and stealthy false-data injection attack for deactivating such safety filters. This attack injects false sensor measurements to bias state estimates toward the interior of a safety region, making the safety filter accept unsafe control actions. The attack does, however, require the adversary to know the dynamics of the system, the safety region used in the safety filter, and the observer gain. In this work we relax these requirements and show how a similar data-injection attack can be performed when the adversary only observes the input and output of the observer that is used by the safety filter, without any a priori knowledge about the system dynamics, safety region, or observer gain. In particular, the adversary uses the observed data to identify a state-space model that describes the observer dynamics, and then approximates a safety region in the identified embedding. We exemplify the data-driven attack on an inverted pendulum, where we show how the attack can make the system leave a safe set, even when a safety filter is supposed to stop this from happening.

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arXiv2024

Scalable and Optimal Security Allocation in Networks against Stealthy Injection Attacks

This paper addresses the security allocation problem in a networked control system under stealthy injection attacks. The networked system is comprised of interconnected subsystems which are represented by nodes in a digraph. An adversary compromises the system by injecting false data into several nodes with the aim of maximally disrupting the performance of the network while remaining stealthy to a defender. To minimize the impact of such stealthy attacks, the defender, with limited knowledge about attack policies and attack resources, allocates several sensors on nodes to impose the stealthiness constraint governing the attack policy. We provide an optimal security allocation algorithm to minimize the expected attack impact on the entire network. Furthermore, under a suitable local control design, the proposed security allocation algorithm can be executed in a scalable way. Finally, the obtained results are validated through several numerical examples.

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arXiv2024

Security Allocation in Networked Control Systems under Stealthy Attacks

This paper considers the problem of security allocation in a networked control system under stealthy attacks. The system is comprised of interconnected subsystems represented by vertices. A malicious adversary selects a single vertex on which to conduct a stealthy data injection attack with the purpose of maximally disrupting a distant target vertex while remaining undetected. Defense resources against the adversary are allocated by a defender on several selected vertices. First, the objectives of the adversary and the defender with uncertain targets are formulated in a probabilistic manner, resulting in an expected worst-case impact of stealthy attacks. Next, we provide a graph-theoretic necessary and sufficient condition under which the cost for the defender and the expected worst-case impact of stealthy attacks are bounded. This condition enables the defender to restrict the admissible actions to dominating sets of the graph representing the network. Then, the security allocation problem is solved through a Stackelberg game-theoretic framework. Finally, the obtained results are validated through a numerical example of a 50-vertex networked control system.

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arXiv2024

Stealthy Deactivation of Safety Filters

Safety filters ensure that only safe control actions are executed. We propose a simple and stealthy false-data injection attack for deactivating such safety filters; in particular, we focus on deactivating safety filters that are based on control-barrier functions. The attack injects false sensor measurements to bias state estimates to the interior of a safety region, which makes the safety filter accept unsafe control actions. To detect such attacks, we also propose a detector that detects biases manufactured by the proposed attack policy, which complements conventional detectors when safety filters are used. The proposed attack policy and detector are illustrated on a double integrator example.

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arXiv2023

Data-Driven Identification of Attack-free Sensors in Networked Control Systems

This paper proposes a data-driven framework to identify the attack-free sensors in a networked control system when some of the sensors are corrupted by an adversary. An operator with access to offline input-output attack-free trajectories of the plant is considered. Then, a data-driven algorithm is proposed to identify the attack-free sensors when the plant is controlled online. We also provide necessary conditions, based on the properties of the plant, under which the algorithm is feasible. An extension of the algorithm is presented to identify the sensors completely online against certain classes of attacks. The efficacy of our algorithm is depicted through numerical examples.

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arXiv2023

Risk-based Security Measure Allocation Against Injection Attacks on Actuators

This article considers the problem of risk-optimal allocation of security measures when the actuators of an uncertain control system are under attack. We consider an adversary injecting false data into the actuator channels. The attack impact is characterized by the maximum performance loss caused by a stealthy adversary with bounded energy. Since the impact is a random variable, due to system uncertainty, we use Conditional Value-at-Risk (CVaR) to characterize the risk associated with the attack. We then consider the problem of allocating the security measures which minimize the risk. We assume that there are only a limited number of security measures available. Under this constraint, we observe that the allocation problem is a mixed-integer optimization problem. Thus we use relaxation techniques to approximate the security allocation problem into a Semi-Definite Program (SDP). We also compare our allocation method $(i)$ across different risk measures: the worst-case measure, the average (nominal) measure, and $(ii)$ across different search algorithms: the exhaustive and the greedy search algorithms. We depict the efficacy of our approach through numerical examples.

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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

A Single-Adversary-Single-Detector Zero-Sum Game in Networked Control Systems

This paper proposes a game-theoretic approach to address the problem of optimal sensor placement for detecting cyber-attacks in 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 target vertex, the detector places a sensor at a single vertex to monitor the system and detect the presence of the adversary. On the other hand, the adversary selects a single vertex through which to conduct a cyber-attack that maximally disrupts the target vertex while remaining undetected by the detector. As our first contribution, for a given pair of attack and monitor vertices and a known target vertex, the game payoff function is defined as the output-to-output gain of the respective system. Then, the paper characterizes the set of feasible actions by the detector that ensures bounded values of the game payoff. Finally, an algebraic sufficient condition is proposed to examine whether a given vertex belongs to the set of feasible monitor vertices. The optimal sensor placement is then determined by computing the mixed-strategy Nash equilibrium of the zero-sum game through linear programming. The approach is illustrated via a numerical example of a 10-vertex networked control system with a given target vertex.

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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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arXiv2016

From Control System Security Indices to Attack Identifiability

In this paper, we investigate detectability and identifiability of attacks on linear dynamical systems that are subjected to external disturbances. We generalize a concept for a security index, which was previously introduced for static systems. The generalized index exactly quantifies the resources necessary for targeted attacks to be undetectable and unidentifiable in the presence of disturbances. This information is useful for both risk assessment and for the design of anomaly detectors. Finally, we show how techniques from the fault detection literature can be used to decouple disturbances and to identify attacks, under certain sparsity constraints.

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