Cyber-physical systems (CPS) are increasingly deployed in safety-critical applications, making them prime targets for adversarial attacks. Timely detection and mitigation of such attacks are imperative for the safe operation of CPS. This paper proposes a novel residual generator design method for enhanced detection of bias injection attacks (BIAs) in linear CPS driven by white Gaussian noise. Specifically, we define a flexible attack impact metric based on the weighted norm of the injected bias and a detectability metric based on the Kullback-Leibler divergence. Using these two metrics, we characterize the worst-case BIAs as those that minimize detectability while maintaining a specified minimum impact. For residual generation filter synthesis, we formulate two optimization problems: one for maximizing the detectability of worst-case BIAs at the attack onset and the other at steady state. Since these two problems are inherently conflicting, we employ the epsilon-constraint method to obtain Paretooptimal solutions that balance transient and steady-state detectability. The effectiveness of the proposed filter design method is demonstrated through numerical simulations, with a comparison against two state-of-the-art benchmarks: the Kalman filter and the H-/H-2 filter.

This paper investigates covert wireless communication with a Fusion Center (FC) that aggregates raw energy measurements from multiple Wardens via soft fusion. Extending our prior work on power-threshold randomization, we consider a stronger adversarial model in which FC randomizes both the number of active Wardens W and the detection threshold t, while Alice and a friendly Jammer jointly randomize their transmit powers under an outage constraint at Bob. We derive a closed-form expression for FC's optimal soft-fusion threshold and show that it is independent of the number of active Wardens. Thus, strategic uncertainty in the sensing infrastructure provides no meaningful detection advantage for FC under soft fusion. We further establish a robustness theorem showing that, even under arbitrary FC randomization over (W,t), Alice and Jammer can maintain outage-feasible communication at Bob while preserving covertness with high probability, provided their power ranges are sufficiently large. This reveals a structural limitation of soft fusion. A game-theoretic formulation characterizes the Nash equilibrium mixed strategies of both sides, accounting for deployment costs and detection-pressure parameters. Analytical and numerical results show that: 1) soft fusion is largely insensitive to the number of Wardens; 2) even semi-strategic finite-support geometric randomization of W performs comparably to the full game-theoretic equilibrium; and 3) the covertness-reliability tradeoff remains nearly invariant across a wide range of FC deployment costs and strategy parameters. These findings exemplify a Red Queen effect, in which FC incurs increasing operational costs for only marginal gains in detection performance, and highlight the need for alternative detection architectures.

This paper considers observer-based detection of sensor bias injection attacks (BIAs) on linear cyber-physical systems with single output driven by white Gaussian noise. Despite their simplicity, BIAs pose a severe risk to systems with integrators, which we refer to as integrator vulnerability. Specifically, the residual generated by any linear observer is indistinguishable under attack and normal operation at steady state, making BIAs detectable only during transients. To address this, we propose a principled method based on Kullback-Leibler divergence to design a residual generator that significantly increases the signal-to-noise ratio against BIAs. For systems without integrator vulnerability, our method also enables a trade-off between transient and steady-state detectability. The effectiveness of the proposed method is demonstrated through numerical comparisons with three state-of-the-art residual generators.

In this paper, we consider the solution of encrypted linear regression using Homomorphic Encryption. We propose a method in which each mathematical operation is performed over encrypted real numbers. This method allows the computation of linear regression in an encrypted environment without the need to modify the original dataset and does not require additional techniques for the calculation of matrix multiplications. The proposed method consists of an iterative method based on a modified Goldschmidt sequence. Numerical results on both synthetic and real data show that the method converges with minimal accuracy loss due to encryption noise, indicating that our approach is well-suited for homomorphically encrypted linear regression.

We consider a sampled-data control system where a wireless sensor transmits its measurements to a controller over a communication channel. We assume that the sensor has a harvesting element to extract energy from the environment and store it in a rechargeable battery for future use. The harvested energy is modelled as a first-order Markovian stochastic process conditioned on a scenario parameter describing the harvesting environment. The overall model can then be represented as a Markov decision process, and a suitable transmission policy providing both good control performance and efficient energy consumption is designed using reinforcement learning approaches. Finally, supervisory control is used to switch between trained transmission policies depending on the current scenario. Also, we provide a tool for estimating an unknown scenario parameter based on measurements of harvested energy, as well as detecting the time instants of scenario changes. The above problem is solved based on Bayesian filtering and smoothing.

We consider estimation under scenarios where the signals of interest exhibit change of characteristics over time. In particular, we consider the continual learning problem where different tasks, e.g., data with different distributions, arrive sequentially and the aim is to perform well on the newly arrived task without performance degradation on the previously seen tasks. In contrast to the continual learning literature focusing on the centralized setting, we investigate the problem from a distributed estimation perspective. We consider the well-established distributed learning algorithm COCOA, which distributes the model parameters and the corresponding features over the network. We provide exact analytical characterization for the generalization error of COCOA under continual learning for linear regression in a range of scenarios, where overparameterization is of particular interest. These analytical results characterize how the generalization error depends on the network structure, the task similarity and the number of tasks, and show how these dependencies are intertwined. In particular, our results show that the generalization error can be significantly reduced by adjusting the network size, where the most favorable network size depends on task similarity and the number of tasks. We present numerical results verifying the theoretical analysis and illustrate the continual learning performance of COCOA with a digit classification task.

We address the problem of event-triggered networked control of nonlinear systems under simultaneous deception and Denial-of-Service (DoS) attacks. By DoS attacks, we refer to disruptions in the communication channel that prevent sensor measurements from reaching the controller. When the system undergoes a deception attack, the controller receives a modified output, deviating from the sensor’s original measurement. We implement the input delay approach and the Lyapunov-Krasovskii technique to obtain sufficient conditions, expressed in terms of linear matrix inequalities (LMIs), that characterize the duration of the DoS interruptions under which input-to-state stability (ISS) of the closed-loop system is preserved. Furthermore, we explore scenarios involving simultaneous attacks, where the DoS is modeled as a stochastic Bernoulli process. The closed-loop system is then considered as a stochastic impulsive system. In a similar manner, we derive conditions to ensure mean-square ISS for this case. A numerical example illustrates the efficiency of the results.

This paper considers constant bias injection attacks on the glucose sensor deployed in an artificial pancreas system. The main challenge with such apparently simple attacks is that they are detectable for only a limited duration if the system is linear and has an integrator. More formally put, such attacks are steady-state stealthy. To address this issue, we propose a method to design a bias-sensitive Kalman filter based on the Kullback-Leibler divergence metric. The resulting filter outperforms the nominal Kalman filter for attack detection as illustrated by numerical simulations on a realistic model. Copyright (c) 2024 The Authors.

In this article, we address the problem of risk assessment of stealthy attacks on uncertain control systems. Considering the data injection attacks that aim at maximizing the 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 setup, the risk assessment problem corresponds to an untractable infinite nonconvex optimization problem. To address this limitation, we adopt the framework of scenario-based optimization to approximate the infinite nonconvex optimization problem by a sampled nonconvex optimization problem. Then, based on the framework of dissipative system theory and S-procedure, the sampled nonconvex risk assessment problem is formulated as an equivalent convex semidefinite 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.

We focus on the continual learning problem where the tasks arrive sequentially and the aim is to perform well on the newly arrived task without performance degradation on the previously seen tasks. In contrast to the continual learning literature focusing on the centralized setting, we investigate the distributed estimation framework. We consider the well-established distributed learning algorithm COCOA. We derive closed form expressions for the iterations for the overparametrized case. We illustrate the convergence and the error performance of the algorithm based on the over/under-parameterization of the problem. Our results show that depending on the problem dimensions and data generation assumptions, COCOA can perform continual learning over a sequence of tasks, i.e., it can learn a new task without forgetting previously learned tasks, with access only to one task at a time.

The idea of covert communication is to conceal the presence of a transmission from an illegitimate receiver, known as a warden. This paper tackles the problem of finite blocklength covert communication in the presence of multiple colluding wardens. The system consists of Alice, who aims to covertly transmit to Bob with the help of a cooperative jammer (henceforth known as Jammer), and a Fusion Center (FC) in charge of combining the wardens' information and deciding on the presence of Alice's transmission accordingly. In our proposed approach, we utilize a two-player zero-sum game to model the interaction between Alice and Jammer jointly as one player and FC as the second player. In this game, Alice and Jammer cooperatively randomize over a range of transmitting and jamming powers to confuse FC. In contrast, FC randomly changes the detection threshold to confuse Alice. The main focus of the paper is to study the impact of employing multiple wardens on the trade-off between the probability of error at FC and the outage probability at Bob. We derive a pay-off function that can be efficiently computed using linear programming to find the optimal distributions of transmitting and jamming powers as well as thresholds used by FC. The benefit of using a cooperative jammer in neutralizing the advantage of employing multiple wardens is shown by analytical results and numerical simulations.

Adding a physical watermarking signal to the control input of a networked control system increases the detection probability of data deception attacks at the expense of increased control cost. This paper proposes a parsimonious policy to limit the average number of watermarking events when the attack is not present, which in turn reduces the control cost. We model the system as a stochastic optimal control problem and apply dynamic programming to minimize the average detection delay (ADD) for fixed upper bounds on false alarm rate (FAR) and an average number of watermarking events (ANW) before the attack. Under practical circumstances, the optimal solution results in a two threshold policy on the posterior probability of attack, derived from the Shiryaev statistics for sequential change detection and assuming the change point is a random variable. We derive asymptotically approximate analytical expressions of ADD and FAR, applying the non-linear renewal theory for non-independent and identically distributed data. The derived expressions reveal that ADD reduces with the increase in the Kullback–Leibler divergence (KLD) between the post- and pre-attack distributions of the test statistics. Therefore, we further design the optimal watermarking that maximizes the KLD for a fixed increase in the control cost. The relationship between the ANW and the increase in control cost is also derived. Simulation studies are performed to illustrate and validate the theoretical results.

Recent successes of massively overparameterized models have inspired a new line of work investigating the underlying conditions that enable overparameterized models to generalize well. This paper considers a framework where the possibly overparametrized model includes fake features, i.e., features that are present in the model but not in the data. We present a non-asymptotic high-probability bound on the generalization error of the ridge regression problem under the model misspecification of having fake features. Our high-probability results provide insights into the interplay between the implicit regularization provided by the fake features and the explicit regularization provided by the ridge parameter. Numerical results illustrate the trade-off between the number of fake features and how the optimal ridge parameter may heavily depend on the number of fake features.

In this paper, we propose and analyze an attack detection scheme for securing the physical layer of a networked control system against attacks where the adversary replaces the true observations with stationary false data. An independent and identically distributed watermarking signal is added to the optimal linear quadratic Gaussian (LQG) control inputs, and a cumulative sum (CUSUM) test is carried out using the joint distribution of the innovation signal and the watermarking signal for quickest attack detection. We derive the expressions of the supremum of the average detection delay (SADD) for a multi-input and multi-output (MIMO) system under the optimal and sub-optimal CUSUM tests. The SADD is asymptotically inversely proportional to the expected Kullback-Leibler divergence (KLD) under certain conditions. The expressions for the MIMO case are simplified for multi-input and single-output systems and explored further to distil design insights. We provide insights into the design of an optimal watermarking signal to maximize KLD for a given fixed increase in LQG control cost when there is no attack. Furthermore, we investigate how the attacker and the control system designer can accomplish their respective objectives by changing the relative power of the attack signal and the watermarking signal. Simulations and numerical studies are carried out to validate the theoretical results.

One of the most studied forms of attacks on the cyber-physical systems is the replay attack. The statistical similarities of the replay signal and the true observations make the replay attack difficult to detect. In this paper, we have addressed the problem of replay attack detection by adding watermarking to the control inputs and then performed resilient detection using cumulative sum (CUSUM) test on the joint statistics of the innovation signal and the watermarking signal. We derive the expression of the Kullback-Liebler divergence (KLD) between the two joint distributions before and after the replay attack, which is asymptotically inversely proportional to the detection delay. We perform structural analysis of the derived KLD expression and suggest a technique to improve the KLD for the systems with relative degree greater than one. A scheme to find the optimal watermarking signal variance for a fixed increase in the control cost to maximize the KLD under the CUSUM test is presented. We provide various numerical simulation results to support our theory. The proposed method is also compared with a state-of-the-art method.

We consider estimation under model misspecification where there is a model mismatch between the underlying system, which generates the data, and the model used during estimation. We propose a model misspecification framework which enables a joint treatment of the model misspecification types of having fake features as well as incorrect covariance assumptions on the unknowns and the noise. We present a decomposition of the output error into components that relate to different subsets of the model parameters corresponding to underlying, fake and missing features. Here, fake features are features which are included in the model but are not present in the underlying system. Under this framework, we characterize the estimation performance and reveal trade-offs between the number of samples, number of fake features, and the possibly incorrect noise level assumption. In contrast to existing work focusing on incorrect covariance assumptions or missing features, fake features is a central component of our framework. Our results show that fake features can significantly improve the estimation performance, even though they are not correlated with the features in the underlying system. In particular, we show that the estimation error can be decreased by including more fake features in the model, even to the point where the model is overparametrized, i.e., the model contains more unknowns than observations.

B A. Baddabedalah M. Baglietto E. W. Bai G. J. Balas M. J. Balas F. Balduzzi J. Ball B. Bamieh A. Barabanov N. Barabanov J. Barbot B. Barmish G. Barret Y. Bar-Shalom P. Bartlett R. R. Barton G. K. Basak A. E. Bashirov S. Battilotti P. Bauer D. Bayard N. G. Bean C. Beck O. Beldiman G. Belforte A. Bemporad A. Bentsman J. Bentsman A. Benzaouia P. Bernhard D. Bernstein J. Bernussou S. Bhat S. Bhatnagar S. Bhattacharyya A. Bicchi J. Birge M. Bisiacco M. Blachuta F. Blanchini A. Bloch V. Blondel P. Bolzern D. Bonvin V. Borkar F. Borrelli N. K. Bose E.-K. Boukas O. J. Boxma R. Braatz M. S. Branicky M. Brdys T. Brinsmead P. M. T. Broersen B. Brogliato A. Budhiraja F. Bullo I. Burkov T. Burton

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-atrisk, and the impact on the nominal system may have different outcomes: thereby depicting the benefit of using risk metrics.

We consider estimation under model misspecification where there is a model mismatch between the underlying system, which generates the data, and the model used during estimation. We propose a model misspecification framework which enables a joint treatment of the model misspecification types of having fake and missing features, as well as incorrect covariance assumptions on the unknowns and the noise. Here, features which are included in the model but are not present in the underlying system, and features which are not included in the model but are present in the underlying system, are referred to as fake and missing features, respectively. Under this framework, we characterize the estimation performance and reveal trade-offs between the missing and fake features and the possibly incorrect noise level assumption. In contrast to existing work focusing on incorrect covariance assumptions or missing features, fake features is a central component of our framework. Our results show that fake features can significantly improve the estimation performance, even though they are not correlated with the features in the underlying system. In particular, we show that the estimation error can be decreased by including more fake features in the model, even to the point where the model is overparametrized, i.e., the model contains more unknowns than observations.

The problem of event-triggered sampled-data control of nonlinear systems with sector-bounded nonlinearities is considered. We assume that sensors transmit their measurements to the controller over a communication channel, where the success of transmissions is defined by an i.i.d. Bernoulli process. For the analysis of the closed-loop system stability, we use the Lyapunov–Krasovskii technique. As a result, we obtain stability conditions in terms of linear matrix inequalities (LMIs), which can be used to design the appropriate triggering parameters. A global strictly positive minimum inter-event time is guaranteed to exist by design with the proposed triggering condition. A numerical example demonstrates the efficiency of the event-triggered approach in reducing the number of transmissions compared to periodic sampling, where the period is the enforced minimum time in the event-triggering condition.