This paper investigates the differential privacy consensus problem for a class of multiagent systems under dynamic topologies. To meet the requirements of power consumption, a random communication strategy is proposed in which each agent sends data to its neighbors with different probabilities. For analyzing the effect of time-varying topology and coupling strength among agents on system performance, a necessary and sufficient condition for almost sure convergence of differential privacy consensus systems is established. Furthermore, the convergence rate and convergence accuracy of the system are also studied. By formulating the communication costs and topological characteristics as a constrained problem, a convex optimization algorithm for fast convergence of the differential privacy consensus system is proposed. In addition, the differential privacy of the agents is analyzed, and the optimal noise parameters that achieve a trade-off between convergence accuracy and privacy levels are derived. A numerical simulation is presented to demonstrate the effectiveness of the developed approach.

This paper investigates the security issues of average consensus networks under false data injection attacks. Based on the intention of the adversary, the attacks to be analyzed are categorized into two types. The first type aims to rapidly diverge the states of the agents to infinity, while the second type seeks to mislead the states towards the adversary's desired values. A necessary and sufficient condition for Type-I attacks to bypass the anomaly detector is first provided, along with an algorithm for generating false data sequences. Subsequently, for Type-II attacks, the closed-form expression of the optimal attack is derived using dynamic programming. To address these vulnerabilities, a watermarking-based data transmission strategy is proposed by resorting to cryptographic pseudo-random sequences. The influence of watermarking parameters on detection performance across different attack scenarios is analyzed. It is demonstrated that the proposed strategy can effectively assist the anomaly detector in identifying stealthy attacks or mitigate its impact on the consensus networks by adjusting the watermarking parameters. A numerical example is provided to demonstrate the validity of the developed results.

In this paper, we propose a differential-flatness-based controller (DFBC) for precise trajectory tracking of tractor-trailers, particularly during reversing maneuvers, which are challenging due to unstable equilibrium points. The proposed controller leverages the differential flatness property of tractor-trailers, equivalently transforming the nonlinear kinematics into a brunovsky canonical form, allowing the application of linear control theory for control design. Compared to traditional linear quadratic regulator (LQR) controllers, the proposed DFBC method achieves higher precision and robustness in reversing maneuvers. We also showcase the performance of the proposed DFBC method through physical experiments conducted on our self-developed 1/10 scale autonomous tractor-trailer.

This article studies the privacy protection problem in state estimation when using quantized innovation. To protect data privacy and maintain the integrity of privacy guarantees in the presence of remote requantization, a privacy-preserving scheme based on the exponential mechanism (EM) is proposed, in which the innovation is perturbed via a probabilistic mapping confined to the original quantized space. Based on an analysis of the uncertainty introduced by the proposed privacy-preserving mechanism, the necessary and sufficient condition for ensuring the quadratic stability of the remote estimator is derived. Furthermore, a quantitative relationship between the privacy budget and the trace of remote estimation error covariance is established, which reveals the inherent tradeoff between privacy protection and estimation accuracy. Numerical simulations are conducted to validate the feasibility and effectiveness of the proposed methods.

This paper investigates the issue of False Data Injection (FDI) attacks within distributed state estimation. In the network, each sensor transmits its state estimate to neighboring nodes. Based on the detection variables inherent to distributed systems, we construct a covert attack strategy to bypass data detectors and degrade the estimation performance of the system. Furthermore, we propose an enhanced stealthy attack strategy, which aims to prevent interference from the attacks of neighboring edges that otherwise counteract against each other. To improve the detection rate of attacks, a detector with a dynamic coding strategy is designed to secure data transmission. The destructiveness of the stealthy attacks and the effectiveness of the detection mechanism are demonstrated through numerical examples.

In this paper, the problem of optimal deception attacks on remote state estimation is studied, where an interval χ2detector is set up to verify the validity of the data packets received by the remote state estimator. Malicious attackers are not only able to intercept the original measurements transmitted on the wireless network, but also obtain side information about the system states sensed by an extra sensor. First, By fusing these two types of information, an innovation-based deception attack model with combined information is proposed. Then, we present a novel stealthiness constraint and derive the covariance at the final instant of the attack interval to characterize the attack performance. Furthermore, the closed-form optimal deception attack schemes are obtained by utilizing the Lagrange method. Finally, numerical simulations and experiment results confirm the effectiveness of the proposed attack scheme.

This article deals with the observer-based control problem of networked periodic piecewise systems under encoding-decoding frameworks. An encoder with a uniform quantizer, which can compress and encrypt data, is provided to process the measurements from the sensors. The processed data is transmitted over the network to the decoder to recover the original data and then to the remote control station, thereby reducing the communication burden and ensuring data security. Then, by constructing the periodic Lyapunov function with linear interpolation terms, exploiting an effective technique-singular value decomposition-sufficient conditions with linear matrix inequality (LMI) constraints for selecting the observer and controller parameters are derived to achieve the exponentially ultimate boundedness of closed-loop systems. Moreover, to eliminate extra steady-state errors caused by encoding-decoding mechanisms (EDMs), a dynamic quantization factor that can make the asymptotic upper bound tend to zero is designed. Finally, numerical examples are provided to illustrate the effectiveness of the derived theoretical results.

False data injection attacks are widely investigated to exploit the cyber-vulnerability of Cyber-Physical System. However, the existing attack policies only consider the cyber-vulnerability in the one-way communication channel. In this letter, a bidirectional stealthy false data injection attack is proposed to bypass the hostile data detector and degrade the estimation performance in the distributed Kalman filtering system. The stealthiness and the influence of the bidirectional stealthy attack is demonstrated by the theoretical analysis. Furthermore, the alternate transmission protocol is proposed to prevent the bidirectional stealthy attack policy. To remedy the protocol and improve the detection sensitivity, an attack detector with multiple factors is proposed. Besides, the choosing principle of the detection factors is analyzed. Simulation examples are presented to investigate the bidirectional stealthy attack and the developed estimator.

The distributed state estimation problem of a discrete-time linear time-invariant system is considered in the presence of external disturbances and measurement noise. In this scenario, where only the bounding information of the external disturbance and measurement noise is known, an initial design of a distributed interval observer is implemented to provide a set of intervals within which the state of the system locates, subject to certain requirements on relevant matrices. Subsequently, the Internal Positive Representation technique is introduced to eliminate the aforementioned requirements, so that a distributed observer can be accomplished, with the only prerequisite being collectively detectable of the output measurements of the sensor network. Finally, two examples are proposed to illustrate the effectiveness of the theoretical results.

In leader-follower multiagent systems (MASs), seeking an efficient scheme to select a set of agents as leaders is important for realizing the expected cooperative performance. In this article, the problem of minimal leader selection is investigated for impulsive general linear MASs with switching topologies. This study focuses on selecting a set of agents as leaders that receive information from a reference signal directly, while minimizing the number of leaders, subject to consensus tracking performance. First, adopting the average dwell time technique and a time-ratio constraint, an explicit criterion for consensus tracking is derived as prepreparation for leader selection. Second, applying the submodular optimization framework, leader selection metrics are established based on the derived criterion. Third, employing the greedy rule, an efficient leader selection scheme is presented according to the established metrics. The scheme comprises two polynomial-time algorithms that return selected leader sets within a logarithmic bound of the optimum. Finally, the effectiveness of the developed leader selection scheme is verified using an illustrative example.

This work studies the security of consensus-based distributed filtering under the replay attack, which can freely select a part of sensors and modify their measurements into previously recorded ones. We analyze the performance degradation of distributed estimation caused by the replay attack, and utilize the Kullback-Leibler (K-L) divergence to quantify the attack stealthiness. Specifically, for a stable system, we prove that under any replay attack, the estimation error is not only bounded, but also can re-enter the steady state. In that case, we prove that the replay attack is ϵ -stealthy, where ϵ can be calculated based on two Lyapunov equations. On the other hand, for an unstable system, we prove that the trace of estimation error covariance is lower bounded by an exponential function, which indicates that the estimation error may diverge due to the attack. In view of this, we provide a sufficient condition to ensure that any replay attack is detectable. Furthermore, we analyze the case that the adversary starts to attack only if the current measurement is close to a previously recorded one. Finally, we verify the theoretical results via several numerical simulations.

Severe damage caused by transferable adversarial attacks has emerged as a prominent concern in recent years, especially in the smart grid. The security issue of the deep reinforcement learning (DRL)-based dynamic pricing system is directly related to the grid's reliability. Previous works have primarily focused on the attacks' transferability from the perspective of model architecture, whereas the concept of distribution bias offers a novel and relatively underexplored viewpoint. In this work, we propose transferable adversarial attacks with distribution (TAD) targeting the DRL model. The adversary emphasizes destroying the target model with the masqueraded malicious dataset while ensuring stealthiness. Concretely, the masqueraded dataset generated by the attacker is required to have a similar distribution to the original dataset, while perturb some of the critical samples to help the target model misdirect to the nonoptimal policy. To this end, we propose an innovative model named Masquerader, which leverages a variational auto-encoder and incorporates three elaborate loss functions to constrain the distribution and deviation of malicious samples. Extensive experiments in a DRL-based dynamic pricing system indicate that our attack strategy TAD could successfully perturb the target model's output. The aberrant flatness of retail prices and the grid system's reduction in daily profits further validate the attack's transferability and harmfulness.

This study concentrates on the differential private distributed optimization problem with an event-triggered mechanism, whose goals include preserving the privacy of agents’ initial states and local cost functions and improving communication efficiency. A distributed event-triggered mechanism is integrated into the differentially private subgradient-push distributed optimization algorithm and then a new algorithm named as DP-ETSP is designed, where the real-time information propagation among agents is avoided. Additionally, under the proposed event-triggered mechanism, an analysis of mean-square consensus and optimality over time-varying directed networks is made when the added Laplace noises meet some specific decaying conditions. Convergence rate results are further established under a specific stepsize, which are equal to the rate of stochastic gradient-push algorithm without event-triggered communication. Moreover, the differential privacy preservation performance is analyzed and the rule for selecting privacy level is discussed. Finally, the feasibility and effectiveness of DP-ETSP are verified in two simulation cases.

The security problem of state estimation plays a critical role in monitoring and managing operation of cyber-physical systems (CPS). This paper considers the problem of network security under replay attacks and formulates a novel attack detection method. More specifically, we design a model-free reinforcement learning-based replay attack detection framework that can automatically learn and recognize the evolving attacks with more effectiveness. Attackers in some situations are more like intelligent agents with initiative, who can transform their attack strategies purposefully according to the actions of defenders. Thus, we propose a new defense strategy against the interaction between the attacker and the defender which is solved by optimization learning. The proposed analytical procedure concerning reinforcement learning technology can also be extended to the study of other control applications. Finally, the numerical examples are provided to illustrate the effectiveness of the detection method.

This paper studies the confidentiality issue of wireless sensor networks under communication constraints from the perspective of an eavesdropper. The considered communication constraints include both medium access constraint and bandwidth limitation. Specifically, the former results in only one sink node gaining access to the shared network at each time step, while the latter requires data to be quantized by a probabilistic quantizer before being transmitted. The task of the eavesdropper is to develop eavesdropping strategies for the constrained network to infer the state of the system as accurately as possible. Since the data is generally unreadable to unauthorized third parties in terms of secure transmission, an eavesdropper with limited power must decide which sink nodes’ data needs to be decrypted. By analyzing the impact of different decryption strategies on the eavesdropping performance, a deciphering scheduling is proposed, which minimizes the expected estimation error without exceeding the energy budget. Besides, a recursive reset algorithm is put forward based on the properties of the probabilistic quantizer, which reflects that an eavesdropper can infer whether its own estimate is accurate enough from the decoded data. Moreover, a sufficient condition is established in which the eavesdropping performance is improved under the proposed algorithm. A numerical example is provided to demonstrate the validity of the developed approaches.

In this article, the H∞ filter design for discrete-time periodic piecewise systems with missing measurements is studied. First, a Bernoulli process is used to characterize missing measurements. Then, by constructing the continuous Lyapunov function with discrete time-scheduling periodic parameters, under missing measurements, sufficient conditions are obtained to ensure the exponential mean-squared stability and H∞ estimation performance of the periodic piecewise filtering error system (PPFES). Moreover, in the case of complete transmission (no missing case), a nominal H∞ filter with more superior performance is developed by the discontinuous Lyapunov function, which provides a complement for the tradeoff between filter schemes with and without missing measurements. Finally, numerical examples are applied to certify the effectiveness of our method.

This paper studies the defense strategy of remote state estimation under deception attacks. In order to prevent the stealthy attacker from reducing the estimation performance without triggering an alarm, an encoding-decoding mechanism combining linear transformation and artificial noise is proposed. Moreover, the detection performance under three different attack scenarios is analyzed. It is proved that the false data detector can effectively identify the attack or weaken its impact on the system under the proposed strategy, so as to ensure the security of the system. From the perspective of an attacker, an algorithm that can deduce the approximate values of the encoding parameters is also provided, which reveals how the magnitude of the artificial noise affects the accuracy of the attacker’s inference. Finally, a simulation example is presented to verify the effectiveness of the developed approach.

We study the security issue of distributed state estimation under data integrity attacks over wireless sensor networks. We design a detector based on statistical learning to judge the compromised estimate sent from the neighboring sensors. To obtain the best estimation performances, we find an optimal estimator for sensors equipped with the malicious data detector, and find a sufficient condition to ensure the stability of the trace of estimation error covariances (EECs). In addition, we explore the relationship between the steady-state EEC and the parameters of the detector. Finally, by numerical simulations, we show the performances of several typical detectors proposed in the existing works, and verify the influence of the detector parameters on the estimation performances.

In this article, we consider the security problem for the consensus-based distributed state estimation. To resist the malicious attacker who can falsify the data transmitted through the wireless channel, each node equips with an attack defender, which is based on the measurement of its built-in sensor. Under the stealthy attack, which can deceive the defender, we investigate the resilience and convergence of the distributed estimation in two different attack scenarios. For the attack with enough communication resources, we provide a sufficient condition of the optimal attack to quantify the maximum estimation performance degradation. We also analyze the resilience of the worst case distributed estimation caused by the attacker. For the attack with limited resources, the optimal Kalman gain for each node is derived to maximize its estimation performance under the attack. We also give a sufficient condition to guarantee the convergence of the distributed estimation in this case. Finally, numerical simulations are provided to illustrate the effect of the defender on guaranteeing the resilience of sensor networks against attacks.

In the presence of malicious denial-of-service (DoS) attacks, this paper investigates the tracking control of mobile robots. Some explicit characterizations are presented for frequency and duration properties of malicious DoS attacks. A hybrid model is established by considering malicious DoS attacks and event-triggering control. The significance of this paper is to develop a set of event-triggering conditions to ensure the tracking convergence. As well, these conditions can guarantee the existence of uniformly positively minimum interval between any two successive transmissions. Finally, a practical experiment is presented by considering the tracking control of an Amigobot mobile robot over a wireless network with DoS attacks, which verifies the effectiveness of the derived results.

This paper addresses the fixed-time leader-follower consensus problem for second-order multiagent systems without velocity measurement. A new continuous fixed-time distributed observer-based consensus protocol is developed to achieve consensus in a bounded finite time fully independent of initial condition. A rigorous stability proof of the multiagent systems by output feedback control is presented based on the bi-limit homogeneity and the Lyapunov technique. Finally, the efficiency of the proposed methodology is illustrated by numerical simulation.

In this paper, we consider the privacy preserving problem in an agreement network under interception attacks. First, we introduce a consensus protocol with privacy preserving, where each node hides their initial states into a set of random sequences, and then injects the sequences into the process of consensus. Second, we assume that an attacker with limited power can intercept the data transmitted on the edges. Aiming at the case when the privacy preserving protocol fails, we propose an index to measure the degree of network privacy leakage. In the ring and small-world network, we find an optimal attacking strategy for the attacker to maximize the probability of the privacy leakage from the perspective of the attacker. Finally, we verify all the derived theoretical results by simulations.

In this paper, a new filtering problem for sensor networks is investigated. A new type of distributed consensus filters is designed, where each sensor can communicate with the neighboring sensors, and filtering can be performed in a distributed way. In the pinning control approach, only a small fraction of sensors need to measure the target information, with which the whole network can be controlled. Furthermore, pinning observers are designed in the case that the sensor can only observe partial target information. Simulation results are given to verify the designed distributed consensus filters.