In this paper, an auxiliary system method is proposed to address the predefined-time distributed constrained optimization with an event-triggered mechanism, which is applied to target monitoring in multi-robot systems. For multi-robot target monitoring, coupled equality and inequality constraints are handled simultaneously, and a predefined-time event-triggered algorithm with a time-based generator is proposed. Furthermore, the given algorithm eliminates the Zeno behavior by proving that the time interval length between two adjacent triggering instants is greater than a positive constant. Finally, a numerical example with simulations is provided to substantiate the effectiveness of the obtained results.
This paper addresses the exponential synchronization challenges in coupled network systems subjected to impulsive effects and bandwidth-constrained communication channels. We introduce a novel hybrid quantization framework that synergistically integrates logarithmic and dynamic quantization mechanisms to optimize synchronization performance under limited bandwidth conditions. The framework systematically accounts for the dual nature of impulsive effects- manifested as both control inputs and system disturbances- through carefully designed quantization parameters tailored to each scenario. Utilizing Lyapunov stability theory, we establish comprehensive synchronization criteria that characterize system behavior under various impulsive conditions. The theoretical developments are validated through two detailed numerical simulation studies, demonstrating the effectiveness and practical applicability of the proposed hybrid quantization approach.
This paper investigates the problem of fusion estimation by proposing both distributed and centralized fusion filtering algorithms, developed within the framework of the $\beta$-quaternion algebra. The objective is to estimate multidimensional signals in the $\beta$-quaternion domain from sensor observations that may be degraded not only by uncertainty arising from intermittency but also by adversarial actions, including denial-of-service (DoS) and deception attacks, as well as scenarios in which both threats act concurrently. Furthermore, the proposed framework incorporates correlated observation noises, which enhances modeling fidelity under realistic sensing conditions. A key advantage of adopting the $\beta$-quaternion algebra lies in its ability to exploit first-order properness conditions, which enable a reduction of the problem dimensionality to one-fourth that of the corresponding real-valued formulation. This dimensionality reduction leads to a significant decrease in computational complexity without compromising estimation accuracy. Numerical simulation examples are presented to demonstrate the benefits of the proposed approach and to provide a comparative performance assessment achieved by proper $\beta$-quaternion distributed and centralized fusion estimation schemes.
This paper addresses the challenge of achieving consensus in multi-agent systems (MASs) subject to the twofold constraints of denial-of-service (DoS) attacks and limited bandwidth. Here, “limited bandwidth” refers to two distinct constraints arising in separate channels of MASs: the inter-agent communication bandwidth and the bit-rate capacity of the controller-to-actuator channel. We propose a comprehensive solution framework comprising three key components. First, a bandwidth-efficient event-triggered mechanism (ETM) is designed to reduce the frequency of inter-agent information exchange in the inter-agent network, while ensuring positive inter-event intervals to prevent Zeno behavior. Second, a dynamic quantizer with quasi-periodic adjustment is introduced to accommodate the finite bit-rate of the controller-to-actuator channel, prevent saturation, and progressively drive the quantization error to zero. Third, a quantized controller is designed, and sufficient conditions for consensus under DoS attacks are established. The attack conditions mainly constrain the average attack duration, leading to less conservative results than existing methods. The effectiveness of the integrated framework is validated through numerical simulations.
We consider robust distributed estimation over adaptive networks using diffusion strategies in the presence of impulsive measurement noise and noisy inter-node communication links. The underlying diffusion algorithm employs an automatically tuned and adaptive error nonlinearity, enabling robust operation without prior knowledge of the noise statistics. While such robustness effectively mitigates impulsive disturbances in local measurements, the performance of the network can still degrade when the information exchanged among neighboring nodes is corrupted by communication noise. In this work, we analyze the impact of imperfect information exchange on the steady-state performance of robust diffusion adaptation. Closed-form expressions are derived for the network mean-square deviation (MSD) and excess mean-square error (EMSE), explicitly characterizing the contribution of link noise and the role of combination matrix. Based on these results, we develop an optimized combination rule that accounts for both local data statistics and communication noise levels. An adaptive implementation of the proposed rule is further introduced, enabling fully distributed operation with online reliability learning. Simulation results under impulsive noise conditions demonstrate close agreement with the theoretical analysis and show that the proposed adaptive combination strategy significantly improves steady-state performance compared to diffusion schemes with fixed combination weights.
This paper studies the event-triggered distributed zonotopic fusion estimation problem for large-scale interconnected systems under limited communication resources. To reduce unnecessary transmissions, two event-triggered strategies are designed for coupled state estimates and overlapping state estimates, respectively. For non-transmitted overlapping information, different compensation strategies are developed for different communication structures. Then, a zonotopic fusion criterion is designed to integrate overlapping states under the weighted Frobenius norm performance index, and the corresponding analytical solution is derived to ensure the optimality of the fusion results. To manage asynchronously available overlapping state estimates, a sequential fusion criterion is also designed. The batch and sequential criteria are shown to achieve equivalent fused estimates, while the sequential fusion improves computational efficiency. Both criteria satisfy the state inclusion property and achieve better estimation performance than the local estimates. Moreover, the stability conditions that ensure the boundedness of estimators' generator matrices are derived as well. Finally, an interconnected unmanned container truck system is employed to validate the effectiveness of the proposed methods.
A differentially privacy-preserving problem is critical for a class of linear discrete-time multi-agent systems. A state-related dynamic memory event-triggered mechanism (SR-DMETM) is proposed to overcome conservatism in existing fixed METMs and DMETMs. With the SR-DMETM, the memory ratio evolves in response to the agents' states, and triggered behaviors are adaptive. A differentially private weighted average consensus control scheme is then proposed, where the weights of each agent can be arbitrarily selected, and the mean square of its final state converges to the weighted average of initial states. With the proposed control scheme, the convergence, accuracy and differential privacy are analyzed, and it is proven that the control scheme preserves privacy of agents' initial states. Finally, two examples are presented to demonstrate the feasibility of the scheme.
Distributed Nash equilibrium (NE) tracking has attracted increasing attention in noncooperative games with time-varying environments, where players must adapt their strategies using only local information and limited communication. Most existing distributed NE-seeking algorithms are based on integer-order, memoryless gradient dynamics, which often exhibit degraded tracking performance when game parameters evolve over time. To address this limitation, this paper proposes a Distributed Fractional-Order Online Mirror Descent (DFOMD) algorithm for online Nash equilibrium tracking in dynamic games. The proposed algorithm enables each player to update its strategy using only local cost information and neighbor-to-neighbor communication over a connected network. By incorporating Caputo-type fractional-order dynamics into the online mirror descent framework, DFOMD introduces an explicit temporal memory mechanism that enhances adaptability and robustness against equilibrium variations. Under standard convexity and strong monotonicity assumptions, we establish that the proposed algorithm achieves sublinear dynamic regret. Numerical experiments on a time-varying Nash–Cournot game demonstrate that DFOMD exhibits improved tracking performance and reduced oscillations compared with classical integer-order methods.
This paperaddresses the resilient consensus problem of networked systems under hybrid attacks by co-designing the network and control layers. To ensure system stability and enhance robustness, the approach involves constructing hidden nodes and edges, with three critical steps: detection, isolation, and control. Firstly, auxiliary variables are employed as information carriers to estimate neighboring states and detect stealthy attacks, following the mechanism of safe diffusion. Secondly, compromised nodes are isolated (removed) after identification to prevent the propagation of attacks, with an emphasis on the connectivity conditions for achieving resilient consensus under various attack scenarios. Thirdly, a secure control algorithm is developed for unaffected nodes to maintain system consensus post-isolation. Finally, simulations validate the algorithm's effectiveness while demonstrating its advantages due to highly tolerant isolation conditions and robust anti-attack performance. Overall, this study provides a solution for resilient control of networked systems under single or hybrid complex cyber-attacks.
In this paper, we are interested in the role of memory information in achieving privacy-preserving average consensus for the multi-agent systems under state-decomposition mechanism. Firstly, using the linear combination of previous and current iteration states of agents, a memory-based protocol is developed. Then, we separately present the systems' coefficients ranges for achieving average consensus under time-varying and time-invariant settings of weight and memory coefficient. Furthermore, under the time-invariant setting, we determine the coefficients range that accelerates the systems' convergence rate and derives its optimum. Subsequently, we separately analyze the privacy-preserving performance of the systems under different weight and memory coefficient settings. A key finding from our analysis is that the introduction of memory information can weaken the condition of privacy preservation, compared to the memoryless case. Finally, we give some numerical simulations to validate our theoretical results.
In real-world applications, multi-agent systems (MASs) rely on public networks for communication, making them susceptible to various security threats and cyber attacks. However, the problem of achieving exponential consensus in fractional-order MASs has not been sufficiently addressed in the existing literature. This paper investigates the exponential bounded consensus of fractional-order heterogeneous uncertain MASs under denial-of-service (DoS) attacks, addressing critical issues such as agent heterogeneity, fractional dynamics, parameter uncertainties, and communication delays. To realistically capture the dynamic nature of network interruptions, DoS attacks are modeled as switching topologies. By leveraging Lyapunov stability theory, sufficient conditions are established to guarantee bounded consensus in two distinct scenarios of non-impulsive force error systems. The proposed delay-dependent distributed impulsive control protocol ensures exponential bounded consensus and achieves a significantly faster convergence rate compared to existing asymptotic or Mittag-Leffler-based methods. Finally, the theoretical results are validated through numerical and comparative simulations, demonstrating the effectiveness and robustness of the proposed control strategy.
Neural networks can be used to approximate unknown nonlinear terms when designing controllers, and a long-overlooked factor is that the effectiveness of neural network-based controllers critically depends on whether the independent variables of the approximated function remain within a compact set, which has gained increasing attention in recent years. Ignoring this condition in the design and analysis may not only lead to circular arguments at the theoretical level but also cause the controller to fail in practical implementation. Designing an effective neural-network-based distributed tracking scheme for nonlinear multiagent systems is challenging, as it requires restricting the state of each agent to a compact set and rigorously proving the validity of the scheme without circular arguments. In this paper, a novel explicit-compact-set-guaranteed neural-network-based prescribed performance distributed consensus tracking protocol is proposed for a class of heterogeneous multiagent systems. Using the graph theory, the Lyapunov function method, and the ordinary differential equation theory, it is proven that, under the proposed protocol, i) the existence of the explicit compact set for neural network approximation can always be guaranteed; ii) each agent can track the desired signal with a tracking error satisfying the prescribed performance requirement. It is emphasized that the proof process avoids circular arguments. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method.
This paper addresses the task of detecting spatiallyconstrained group anomalies, relevant in fields such as geosciences, environmental monitoring, and medical imaging. Classical approaches include scan statistics and local outlier factor, while modern methods are heavily based on autoencoder structures. In this paper, we propose an end-to-end machine learning (ML)- based unsupervised approach robust to abnormalities outside the anomalous region. We target geospatial data, where each point consists of a multivariate feature vector coupled with a coordinate vector. In this scenario, localized group anomalies are groups of points whose features do not adhere to some concept of normality across the dataset, and that are confined to a region within this dataset. Abnormalities outside this region are not considered part of the anomaly. The proposed methodology uses an ML-based clustering approach that solves a version of the graph mincut problem and the assumption that anomalous and non-anomalous data are clustered at different paces to generate an anomaly score for each point. With the networked graph representation, the proposed methodology can also be used when data points do not have absolute position vectors, but relative distances can be inferred from the datasets (e.g., in social networks a friendship relation indicates closeness between users and locality can be expressed as a group of friends). The proposed algorithm is compared using different metrics against a wide range of well-known state-of-the-art approaches for unsupervised anomaly detection, such as nearest-neighbors and autoencoderbased algorithms, outperforming them in most scenarios. We also provide an analysis of the algorithm applicability with respect to locality properties of the anomaly and the data structure.
This paper presents a distributed filtering framework based on the maximum correntropy criterion for sensor networks under non-Gaussian noise. To improve robustness against impulsive disturbances, the proposed method integrates a Cauchy kernel-based maximum correntropy criterion into the unscented Kalman filtering (UKF). A linear encoding-decoding mechanism is further introduced to address privacy preservation in sensor networks, where artificial noise is added to the encoded signal prior to transmission and removed through a decoding process at the receiver. The resulting distortion is modeled as measurement noise and handled within the filtering scheme. Covariance intersection is employed to fuse local estimates from neighboring nodes, enabling consistent distributed filtering without requiring exact cross-covariance information. The artificial noise variance is analytically bounded to maintain signal concealment below a prescribed signal-to-noise ratio threshold, while rigorous proof of estimator convergence is provided. Simulation results verify that the proposed approach improves both estimation accuracy and transmission confidentiality compared to conventional distributed UKF methods.
In recent years, graph signal processing has emerged as a powerful framework at the intersection of signal processing and graph theory, providing tools for the analysis of signals defined on nodes while accounting for their relationships represented by edges. These tools have been successfully applied to various settings, including statistical hypothesis testing. In particular, non-parametric approaches based on surrogate generation have been proposed for signals on undirected graphs. However, they are yet to be extended to directed graphs. In this work, we first revisit the notion of stationary graph signals on directed graphs. Specifically, and through the eigendecomposition of the graph shift operator, we define directed graph wide-sense stationary signals. Then, we propose a new framework to generate surrogate graph signals that preserve covariance structure under stationarity assumptions. Null distributions of the test metric can then be constructed from these surrogates and serve as a reference for the empirical data. Finally, we provide guiding examples and an application on real data, in which we compare the performance of our framework with existing techniques for undirected graphs or based on naive permutation, demonstrating feasibility and superiority of the proposed approach.
This paper proposes an intermittent dynamic event triggered control (ETC) algorithm for disturbed second-order multi-agent systems (MASs). The proposed control algorithm aims to guarantee practical fixed-time containment under Denial of-Service (DoS) attacks. First, a novel detection algorithm is designed to identify whether the MAS is under connectivity-broken DoS attacks. Subsequently, based on the detection algorithm, an intermittent dynamic event-triggered control algorithm is devised to attain the fixed-time containment for disturbed second-order MASs by considering the connectivity-broken DoS attack periods as rest intervals. By introducing suitable parameters, the control algorithm obtains an upper bound for the convergence time, which is independent of the initial conditions. Then, based on the dynamic ETC algorithm, a self-triggered control (STC) algorithm is proposed to avoid continuous monitoring of neighboring followers and leaders. Furthermore, Zeno phenomenon is avoided in both the dynamic ETC and STC algorithms. Ultimately, the effectiveness of the proposed control algorithms is systematically evaluated through numerical simulations.
This paper investigates cooperative dynamic positioning (CDP) for multiple uncrewed surface vehicles (USVs) under switching-edge deception attacks (SEDAs). The SEDAs can not only disconnect connected links but also fabricate malicious connections where no physical link exists. Existing secure control schemes, which predominantly concentrate on data tampering and disruptions in communication edges, become ineffectual for this new SEDAs. These existing control schemes lack the ability to detect and respond to this attack pattern that manipulates the communication edge. To address SEDAs, an injected edge energy function is used to construct a model that can accurately describe the changes in communication edges during this attack. Then, a detection mechanism is developed to effectively monitor the reliability of communication edges and data. Finally, based on this detection mechanism, the cooperative controller is designed to ensure CDP of multiple USVs. The validity and outperformance of the secure control scheme are confirmed by an example simulation.
This paper investigates the output-constrained containment control problem for heterogeneous uncertain nonlinear multiagent systems with a directed graph. First, a state-feedback adaptive control scheme is proposed using integral barrier Lyapunov functions (iBLFs), which effectively addresses time-invariant output constraints even with unknown control directions. Unlike traditional barrier Lyapunov functions, this approach resolves the issue of an overly restrictive feasible initial output domain relative to the actual constraints. Second, an output-feedback adaptive control scheme is developed by integrating neural network-based state observers with an event-triggered control strategy. Within this scheme, a novel tracking error formulation with adjustable sensitivity to output constraint boundaries is introduced to enhance flexibility. It is proved that the semi-globally uniformly ultimately bounded containment control is achieved. Finally, two simulation cases validate the effectiveness of the proposed control schemes.
This paper develops a novel distributed optimization algorithm which combines the differentially private technique with the Barzilai-Borwein method (DPBB) for unbalanced directed networks. The algorithm protects the gradient data of agents by adding Gaussian noise to a gradient tracking process, achieving (epsilon, delta)-differential privacy with an explicit expression. Then, it analyses the trade-off between convergence accuracy and privacy level. In order to accelerate convergence rate, it incorporates the Barzilai-Borwein method for dynamically adjusting the step size. DPBB is ultimately able to reach the neighborhood of optimal solution in a linearly convergent manner. Two distributed logistic regression examples demonstrate the algorithms' effectiveness for fast convergence speed, low optimal mean square error and high model classification accuracy.
This paper investigates the distributed security fusion estimation (DSFE) issue for time-varying systems in multi-sensor networks, considering the limitations of communication energy and network bandwidth. Combined with the event-triggered mechanism and the improved Round-Robin (R-R) protocol, a dual-layer screening (DLS) mechanism is proposed to meet the energy constraints in the channel. Addressing bandwidth limitations, the local estimator compresses the signal via dimension reduction before forwarding it to the fusion center. Combined with the False Data Injection (FDI) attack, a compensation model that can be directly used for sensor fusion is designed. An optimized sensor fusion algorithm is developed based on the compensation model, targeting minimal estimation errors. The design of optimal fusion coefficients is recast as a convex optimization problem, where derived stability conditions ensure the mean square error remains bounded for the fusion estimator. Theoretical analysis and simulation studies verify that the method achieves substantial improvements in computational performance and resource usage without compromising estimation precision.
