Rumors on social media platforms have a significant negative impact on society, making rumor detection increasingly critical. However, most existing methods focus on identifying rumors only after they have already spread widely and negative impacts have occurred. Therefore, identifying rumors in the early stages is necessary. Early rumor detection is typically characterized by limited spread and small sample sizes, making it impractical to rely on large datasets or rumor propagation structures. To overcome these characteristics, a multimodal meta learning method based on few-shot learning (FSL) for early rumor detection is proposed. A multimodal feature extraction layer is designed to extract data features of various modalities, while a multimodal hidden information extraction layer is constructed to uncover deep information from these features. Furthermore, a multimodal fusion output layer is developed to combine and process the multimodal information, leading to rumor classification. A meta-learning algorithm is introduced to address the challenge of small sample sizes, utilizing fast and multistep update methods to enhance the adaptability and stability of model. Comparative experiments conducted on two publicly available datasets confirm that our proposed method demonstrates strong performance in early rumor detection.

For the frequency regulation and power allocation problem for ac microgrids, the multiple constraints of load frequency restrictions, nodal active power injections, and power-flow balance that guarantee transient stability are as crucial as the final consistent steady-state results. This article investigates a class of droop-controlled ac microgrids with the abovementioned constraints, and it presents sufficient and necessary conditions to improve system robustness and reliability under load fluctuations. By integrating the Kuramoto oscillator model into the primary control law, cyber-physical coupling dynamics for ac microgrids are established. A novel communication-network-based secondary distributed control approach is presented, which considers physical nodes with different characteristics of power generation and load units. By using invariant theory and nonquadratic Lyapunov techniques, the bounded input-output stability of microgrids can be guaranteed under certain conditions, which is especially pertinent in active power allocation. The theoretical results are verified through numerical case studies of both public and self-built power test systems, demonstrating the obvious improvement in robustness and reliability against variable power generation and load demand.

The cross-regional interconnections of the power system complicates the network topology behind it, which undoubtedly brings great computational challenges to the related simulation analysis. To address this issue, this article introduces an innovative framework for power grid topology renormalization based on the Louvain community detection algorithm. This framework aims to coarse-graining the original power grid into a smaller-scale network, thereby significantly simplifying its topology while preserving key properties. To validate the feasibility and effectiveness of this approach, we conducted extensive simulation experiments on a class of synthetic power grids and six real-world power grid datasets. The results demonstrate that the proposed method can nearly perfectly retain the critical structural characteristics and power flow properties of the original power grid during the renormalization process. From a practical application perspective, our findings provide a powerful tool for understanding and predicting the structural evolution and dynamical behavior of large-scale power grids.

This essay investigates the bipartite consensus over matrix-weighted hybrid multiagents signed networks using an event-triggered control method, which reduces unnecessary control updates and saves resources. Under the designed event-triggered hybrid control algorithm, using variable transformation, Gauge transformation, stability theory, and inequality techniques, the hybrid bipartite consensus criteria which are related to the matrix-weight of each edge of the signed networks, coupling gains, discrete interval, and some of the parameters of the event-triggered law are established. Furthermore, Zeno-behavior is excluded. Finally, the obtained results are illustrated via a simulation example.

This paper introduces a novel hierarchical control approach for feature matching, real-time tracking and inter-UAV collision avoidance in multiple unmanned aerial vehicle-unmanned ground vehicle (multi-UAV-UGV) collaborative tracking. Our approach divides into three layers: optimal feature matching, tracking control by reinforcement learning (RL), and collision avoidance using control barrier functions (CBFs). First, a distance cost matrix is cleverly constructed based on the feature matching capabilities of UAVs and UGVs to determine the optimal matching configuration. It allows UAVs to perform the tracking task while minimizing travel distance. Second, a RL-based tracker is developed to achieve precise real-time tracking without depending on UAV dynamic models. The tracker is trained in a single UAV-UGV environment, which reduces policy convergence difficulty by simplifying state space and interactions compared with training in complex multi-UAV-UGV scenarios. Third, a collision avoidance mechanism based on CBFs is introduced to transform RL commands into collision-free actions by solving a quadratic programming (QP) problem. Extensive simulations and real-world experiments demonstrate the effectiveness of the proposed approach.

In this paper, we investigate leader-follower consensus (LFC) of multiple Euler-Lagrange systems (MELSs) under the case that followers can only measure partial output information of leader system, and the communication network among followers is switching and jointly connected. Firstly, in order to accurately estimate complete state information of the leader system in real time, we propose a distributed reduced-order observer, which is valid over a jointly connected switching network. Then, by applying this distributed reduced-order observer, we further design an observer-based controller for multiple Euler-Lagrange systems (MELSs) to reach leader-follower consensus (LFC). Distinct with the existing controllers for LFC of MELSs, this controller is robust for bounded external disturbances, and independent of the structure and features of Euler-Lagrange (EL) system. At last, a simulation example is given to confirm the effectiveness of the proposed distributed reduced-order observer and robust controller.Note to Practitioners—Many practical engineering applications (such as spacecrafts, mobile robot manipulators) can be modeled as multiple uncertain Euler-Lagrange systems, where each agent suffers external input disturbances, and only a portion of followers can measure partial components of leader’s output. However, most relevant works assumed that the dynamic information of each agent is completely known, agents do not suffer external input disturbances, and all follower agents can measure full-dimensional output of leader. How to achieve LFC for such MELSs has become a main focus of control researches. Thus, this paper proposes an adaptive distributed reduced-order observer-based consensus algorithm for such MELSs, whose communication network is switching and jointly connected. Finally, the effectiveness of the proposed algorithm is illustrated by a simulation example.

In this paper, we focus on the problem of distributed state estimation for a target system driven by continuous-time linear time-invariant (LTI) system with unknown inputs, where the communication channels are disturbed by stochastic noise and subjected to impulsive sequential attacks. In multi-agent systems (MASs), agents usually move along relatively smooth paths, but occasionally take evasive actions or make sudden turns. This pattern of motion results in relatively small communication disturbances most of the time, but large communication disturbances can occasionally occur. First, this communication disturbances are modeled as a hybrid form: stochastic noise and impulsive sequential attacks, where stochastic noise stands for relatively small communication disturbances most of the time, and impulsive sequential attacks stand for occasionally large communication disturbances. Then, a practical/bounded distributed unknown input observer (DUIO) under stochastic noise and impulsive sequential attack is proposed. Furthermore, the sufficient conditions for the realization of the practical/bounded DUIO in the sense of mean square convergence are presented by graph theory and stochastic analysis. The error bound that depends on the coupling gain, stochastic noise intensity, and average impulsive interval is provided. Finally, the validity of the designed practical/bounded DUIO is confirmed by numerical simulations. Note to Practitioners—Information exchange among agents is a critical for achieving coordination in MASs. Most existing works usually assume that the communication is ideal, i.e., each agent is able to accurately obtain information from its neighbors or is only disturbed by stochastic noise. However, agents generally move along relatively smooth paths but may occasionally execute evasive maneuvers or abrupt turns in MASs. This motion pattern usually results in relatively small communication disturbances, though in certain instances, significant disruptions may occur. How to effectively deal with the impact of such non-ideal communication environments on system performance and ensure that agents can still maintain stable cooperation in complex dynamic environments has become one of the critical topics in the field of control. Specifically, this problem involves several challenges: First, the random and non-Gaussian characteristics of communication disturbances render traditional filtering and estimation methods difficult to apply directly; Second, the burstiness and uncertainty of impulsive noise can lead to severe fluctuations in system states, thereby affecting coordination among agents. In light of this, this paper models such communication disturbances as stochastic impulsive noise and proposes a practical/bounded DUIO under stochastic impulsive noise.

This paper addresses the edge-consensus problem in a directed nodal network, where each edge is described by uncertain fractional-order dynamics subject to positivity constraints. To solve the issues of positivity and consensus in uncertain fractional-order networked systems (UFONSs) with the order 0q≤ 1, a distributed control protocol by virtue of state feedback is designed. Some sufficient criteria are established to ensure positive edge-consensus of UFONSs. Subsequently, to handle scenarios with unmeasurable states in practical systems, an observer-based control protocol is proposed to achieve positive edge-consensus for UFONSs. Furthermore, by leveraging the fractional-order stability theory and the properties of positive systems, some sufficient positive edge-consensus conditions that depend only on the number of edges and nodes are formulated instead of the global information of the network. Finally, two simulation examples are shown to verify the feasibility of the proposed protocols.

This article explores the average controllability of composite networks generated by factor networks via Cartesian product from energy control perspective, which can be characterized by the controllability Gramian-based metrics. The considered factors are directed weighted networks with diagonalizable / non-diagonalizbable Laplacian dynamics. It is shown that the average controllability of a composite network is determined by the spectral properties of its factors without calculating its own high-dimensional matrix, which reveals how the energy-related controllability of a Cartesian product network (CPN) can be derived from its factors’ features. This will reduce the computational complexity and provide insights to study the energy control of other graph product networks.

Distributed secondary control has shown great advantages in achieving voltage restoration for dc microgrids. However, the negative impedance characteristic of constant power loads (CPLs) increases the challenges of stability analysis for dc microgrids with CPLs. Most previous researches suppose that the system is stable, or just obtain the stability conditions, which are related with global information. To solve these problems, we propose an adaptive secondary control method to achieve voltage restoration and current sharing without the direct feedback of bus voltage. Each generator can estimate the bus voltage at the previous sampling instant according to local current information and system model of dc microgrids. To obtain the distributed stability conditions, two distributed algorithms are proposed to estimate the sum of currents of the generators and the global load information. One of the distributed estimation algorithms is embedded with a multirate sampling strategy to obtain the sum of currents. The other estimation algorithm is based on the least-squares method to obtain the global load information. White noise is added to the transmitted information of the distributed algorithms to protect the privacy information. Theoretical analysis shows that the proposed methods not only can regulate the bus voltage with privacy preservation but also provide the distributed stability conditions of dc microgrids with CPLs. Finally, several simulation results are given to verify the effectiveness of the proposed methods.

This article studies the controllability of a new composite network generated by two smaller scale factor networks via the Corona product with Laplacian dynamics. First, the eigenvalues and corresponding eigenvectors of a new composite network-the -duplication Corona product network-are derived by some properties of its factor networks. Second, a necessary and sufficient algebra-based criterion for the controllability of such network is established based on the Popov-Belevitch-Hautus (PBH) test. Furthermore, the weights on edges between the different factor networks are considered. Finally, several examples are presented to demonstrate the effectiveness of our results applied to the unmanned aerial vehicle (UAV) formation.

In this article, the coordination control problem of discrete-time multiagent systems (MASs) affected by uncertainties, namely unknown initial states and external disturbances, is considered. Inspired by the interval observer constructed by the single system, the definition of distributed interval observer for discrete-time MASs is given, in which the control protocol of each agent obtained by solving a modified algebraic Riccati equation depends on the bounded information of the interval observer connected to itself and its neighbors. By the cooperativity theory and Lyapunov stability theory, it is established that the distributed interval observer can not only access some information about MASs at any instant, that is, the upper and lower bounds of each component of the agent state, but also realize the cooperative behavior of MASs under some essential conditions involving network synchronization and the unstable eigenvalue of the system matrix. In addition, with the help of a new time-varying transformation matrix, the new interval observer is constructed to eliminate the non-negative constraint. Finally, two numerical simulations are provided to confirm the validity of the derived results.

This article focuses on the event-based fully distributed state estimation problem under noisy environment and directed graphs. In a networked system, agents cooperatively estimate the target system state disturbed by process noise. However, due to the existence of measurement noise, each agent can only access partial and disturbed measurement output information. Meanwhile, given the limitations of resources in the networked system and the difficulty of acquiring global information, the event-based robust adaptive distributed observer is proposed. Specifically, by introducing robust adaptive coupling gains, a fully distributed design is achieved, eliminating the dependence on global information. Through the design of event-triggered mechanism, an event-based communication manner is implemented to reduce communication and energy resource consumption. Moreover, in view of the heterogeneity of the undetectable subspace and the differences in parameter design among agents, this article introduces a coordinate transformation and constructs a new Lyapunov function to further analyze the stability of the estimation error. Then, theoretical analysis shows that during cooperative estimation under directed graphs, the norm of estimation error can asymptotically converge to a compact set without Zeno behavior. Finally, a simulation example is provided to verify the effectiveness of the proposed event-based robust adaptive distributed observer.

This paper investigates the controllability of Cartesian product networks consisting of smaller factor networks via Cartesian product of graphs, reveals the controllability relationship between the Cartesian product network and its factor networks, and presents a theoretic analysis framework for a Cartesian product network by the eigenvalue-eigenvector pairs of factor networks. A sufficient and necessary condition for the controllability of Cartesian product networks is established based on the PBH test conjoining with the properties of Kronecker products, which is an important theoretical analysis tool to analyze the controllability of product networks. This work will help us to understand the cooperative mechanisms of the system controllability, network topology and nodal dynamics, and provide a theory and technical guidance to build a more reasonable large-scale network model and design an effective control scheme for a real networked system.

This paper proposes a new dual-design framework to investigate the consensus tracking problem of general switched heterogeneous nonlinear multi-agent systems (MASs) with an uncertain target. A distributed observer that only uses the neighbors’ information is constructed to estimate the target signal by designing a time-varying positive-define matrix function and mode-dependent observer gain matrices. After that, a distributed tracking algorithm is developed to solve the three consensus issues among the observer states, tracker states, and target states at the same time by utilizing the neighbors’ observer states and designing additional mode-dependent feedback gain matrices. The distinct merit of the research is that the designed Lyapunov function is strict monotone decreasing at switching instants, discovering the positive effect of the switching on the consensus. As an application, heterogeneous switched Chua’s circuits are provided to demonstrate the distributed observers and tracking algorithms.

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.

Real-world networks have properties such as complex interactions and large-scale structures, which pose significant computational challenges when analyzing their structural and dynamical behavior. Network reduction algorithms, such as renormalization group and subgraph extraction, have emerged as potential solutions to address these challenges. These algorithms aim to reveal critical properties hidden within the original network, such as self-similarity and scale invariance. However, existing reduction procedures often rely on specific assumptions or have high computational complexity, which severely limits their practicality. To overcome these limitations, this article proposes a subgraph extraction strategy based on edge-reinforced random walks to achieve network reduction. In comparison with traditional renormalization procedures, our method offers lower computational complexity while effectively preserving most of the crucial structural properties of real networks. Specifically, the proposed method selects nodes with higher degree values in the network as candidate starting nodes for the random walk and then obtains smaller scale subgraphs of the original network through a random walk method that depends on the edge weights. Extensive experiments on synthetic and real networks show that the critical properties of most networks exhibit strong self-similarity behavior under the presented subgraph extraction method.

The exchange of information is a crucial factor in achieving consensus among agents. However, in real-world scenarios, nonideal information sharing is prevalent due to complex environmental conditions. Consider the information distortions (data) and stochastic information flow (media) during state transmission both caused by physical constraints, a novel model of transmission-constrained consensus over random networks is proposed in this work. The transmission constraints are represented by heterogeneous functions that reflect the impact of environmental interference in multiagent systems or social networks. A directed random graph is applied to model the stochastic information flow where every edge is connected probabilistically. Using stochastic stability theory and the martingale convergence theorem, it is demonstrated that the agent states will converge to a consensus value with probability 1, despite information distortions and randomness in information flow. Numerical simulations are presented to validate the effectiveness of the proposed model.

This article investigates the leader-follower consensus problem of multiple Euler-Lagrange (EL) systems, where each agent suffers uncertain external disturbances, and the communication links among agents experience faults. Besides, we consider a more general case that only a portion of followers can measure partial components of leader's output and access the dynamic information of leader. The main idea of solving the consensus problem in this article is proceeded in two steps. First, we design an adaptive distributed observer to estimate the full state information of leader in real time with resilience to communication link faults. Second, based on the proposed distributed observer, we propose a proportional-integral (PI) control protocol for each agent to track the trajectory of leader, which is model-independent and robust to uncertain external disturbances. Distinct from the existing leader-follower consensus protocols of multiple EL systems, the proposed distributed observer-based PI consensus protocol in this article is model-independent, which is irrelevant to the structures or features of EL system model. Finally, we present a simulation example to show the resilience of the above adaptive distributed observer and the robustness of the distributed observer-based consensus protocol.

In this article, we study the matrix-weighted consensus issues for second-order discrete-time multiagent systems on directed network topology. Under the designed matrix-weighted consensus algorithm, based on the eigenvalues of the Laplacian matrix, coupling gains, and discrete interval, we build some consensus conditions for reaching discrete-time consensus and deduce some simplified and straightforward consensus conditions for undirected network topology. Besides, for a given network topology, we theoretically analyze the influence of the coupling gains and discrete intervals on the consensus conditions of the network dynamics. Finally, we offer several simulation examples to validate the obtained results.

This article mainly considers the output synchronization (OS) problem of multiple weighted and adaptive output coupled reaction-diffusion neural networks (RDNNs) without and with coupling delays in finite time. Without coupling delays, an adaptive control law and an output feedback controller are, respectively, proposed to ensure that the multiple weighted and output coupled RDNNs are output synchronized and output synchronized in finite time. With coupling delays, an adaptive coupling weights control scheme and a novel feedback controller are put forward to make the multiple weighted RDNNs with output couplings achieve OS in finite time. Moreover, the finite-time OS is considered in the presence of external disturbances. By the Lyapunov approach, several finite-time OS and OS criteria are given. Finally, two simulation examples are presented to justify the effectiveness of the proposed adaptive control laws and controllers.

In this article, we introduce adaptive robust observers for the estimation of comprehensive state variables and model parameters of a leader system. In particular, we suppose that the communication network among followers suffers communication link faults (CLFs), and the leader contains uncertainty, which means no follower knows the model parameters of leader system. Then, by applying the proposed observers, we elaborate on the design of a robust model-independent controller tailored for the leader-follower consensus problem (LFCP) of multiple Euler-Lagrange systems (MELSs). In contrast to the controllers currently employed for the LFCP in MELSs, the controller developed herein exhibits robustness against bounded external disturbances. Besides, the controller does not rely on the specific structure or characteristics of the Euler-Lagrange (EL) system model. At last, we provide simulation examples to demonstrate the validity of the proposed observers and the robust controller in the context of the LFCP for MELSs.

The event-triggered distributed average tracking (ETDAT) problem for heterogeneous multiagent systems (MASs) with uncertain dynamics is investigated in this article. The ETDAT algorithms aim to build control laws for heterogeneous agents to follow the average states of multiple time-varying input signals in event-triggered communication networks. The uncertain dynamics of agents and the event-triggered communication mechanisms make the design of distributed average tracking (DAT) protocols difficult. To achieve ETDAT for heterogeneous MASs with uncertain dynamics, we designed two kinds of ETDAT protocols. First, on the basis of model reference adaptive control (MRAC) technology and sampling measurements, we present a class of static-gain ETDAT algorithms. In comparison to conventional DAT, the proposed ETDAT algorithms not only solve the DAT problem of heterogeneous MASs but also greatly reduce the cost of network communication. Second, dynamic-gain ETDAT algorithms based on self-adaptive principles are presented to minimize network global information needs. The above two algorithms adopt boundary layer approximation methods and dynamic event-triggered strategies, which can further reduce the chattering phenomenon and event-triggered frequency. Finally, the theoretical findings are shown with several examples.

The geometric renormalization (GR) group of complex networks based on hidden metric space provides a powerful framework for studying the self-similarity of networks. Recent studies have shown that this framework can significantly reduce the size and complexity of the initial system. In this sense, the smaller-scale replica can be used as an alternative or guidance to the original large-scale network. In this article, we extend the GR framework to the weighted network and prove that this framework can sustain the self-similarity of synthetic weighted networks and real-world weighted networks. Furthermore, we assign the corresponding weights to all edges of reconstructed human connectomes at five different resolutions, and the results show that topological features of these networks exhibit self-similar behaviors. Remarkably, our results also suggest that the GR transform group can generate a series of low-resolution replica networks that are similar to the initial highest-resolution human connectome networks, which greatly promotes the network science, neuroscience, and physics understanding of brain mechanisms, and is of great significance to the research of brain science. Finally, a typical spin-like model is used to further verify the rationality of this framework.

As we all know, heterogeneity is a very important feature of multiagent systems (MASs). In this article, we examine the consensus control problems of matrix-weighted hybrid MASs, which contain discrete-time and continuous-time dynamic agents. Under fixed and switched undirected networks, three consensus algorithms are proposed for matrix-weighted hybrid MASs. In the three consensus algorithms, the sampled data control method is utilized in the continuous-time subsystem to analyze the convergence of different dynamic agents in the matrix-weighted interaction mode. For the symmetric matrix-weighted fixed and switched multiagent networks, when the sampling period meets certain conditions, the consensus criteria are established via the matrix theory, Lyapunov stability theory, and analysis theory. Moreover, asymmetric matrix-weighted fixed multiagent networks which can be applied to some scenarios with scaled and rotated updates constraints are considered, and consensus criteria are also obtained when the sampling period meets certain conditions. Finally, a few simulation examples are supplied to validate the correctness of the obtained theoretical results.

This article considers the robust consensus problem of the general linear multiagent system (MAS) subject to both heterogeneous additive stable disturbances and input saturation. Distributed low gain feedback-based dynamic output feedback control protocols are proposed, which do not need the controller interaction. Algebraic Riccati equation and unified$H_{\infty }$controller design method are employed to design the output feedback control protocols. It is established that under the assumption that each agent is asymptotically null controllable with bounded controls, semiglobal robust consensus can always be reached under the proposed controller. Furthermore, the design method specialized for leader-following consensus is addressed, under the assumption that the Laplacian matrix is diagonalizable, one can design the control protocol only with the number of follower agents. Finally, several simulations are provided to show the effectiveness of our results.

In this article, the exponential synchronization control issue of reaction-diffusion neural networks (RDNNs) is mainly resolved by the sampling-based event-triggered scheme under Dirichlet boundary conditions. Based on the sampled state information, the event-triggered control protocol is updated only when the triggering condition is met, which effectively reduces the communication burden and saves energy. In addition, the proposed control algorithm is combined with sampled-data control, which can effectively avoid the Zeno phenomenon. By thinking of the proper Lyapunov-Krasovskii functional and using some momentous inequalities, a sufficient condition is obtained for RDNNs to achieve exponential synchronization. Finally, some simulation results are shown to demonstrate the validity of the algorithm.

The leader-following exponential output consensus (LFEOC) problem of nonlinear fractional-order MASs (FOMASs) with unknown mismatched disturbances and event-triggered control (ETC) input is investigated. First, a finite-time higher-order sliding observer is constructed for the estimation of the unknown matched and mismatched disturbances of each agent. Second, a distributed integral sliding-mode (ISM) surface is established to realize exponential stabilization of FOMASs, and a distributed event-based active anti-disturbance consensus protocol is designed to compensate the effects of unmatched uncertainties on the output and save energy. Third, it is proved that the output of all agents can be driven to achieve exponential consensus without Zeno behavior, and the corresponding event-triggered conditions are presented. Finally, the efficacy of conclusions is verified by the examples.

A necessary and sufficient algebraic condition is obtained for the controllability of a composite signed network consisting of two factor networks by Cartesian product, which reveals how the controllability of the higher-dimensional Cartesian product network is affected by the controllability of its smaller-scale low-dimensional factor networks. Furthermore, the structural balance of the Cartesian product network can be judged by the structural balance of its factor networks, which can greatly reduce amount of calculation to some extent. And the agents’ state evolution trajectories of Cartesian product networks can also be predicted by those of their factor networks. Moreover, the controllability of general signed networks is considered. Algorithms and numerical examples are exhibited to demonstrate the validity of our methods.

The exponential consensus issue is investigated for leader-following multiagent systems (MASs) based on nonlinear parabolic partial differential equations (PDEs) on a directed graph via intermittent boundary control (IBC) methods. On the one hand, when the system’s state is accessible, an IBC protocol is designed based on the transfer information generated by the agent’s communication with its neighbors and the information coupling at the boundary$x= l$, and the sufficient conditions for exponential consensus of leader-following MASs are obtained. On the other hand, when the system’s state is not available completely, the agent’s state is estimated by the proposed observer, and the observer’s coupling information and the boundary coupling information of the agent are adopted to design an IBC protocol to solve the leader-following consensus issue. Finally, two numerical simulations are supplied to account for the obtained theoretical results.

This article studies the observer-based non-negative scaled edge-consensus (NNSEC) problems for continuous-time and discrete-time networked systems, and then these problems are extended to the cases with input saturation. Specifically, two observer-based algorithms are proposed by using only the outputs of neighboring edges, and the mathematical expressions of the control gain matrix and observer gain matrix in the two algorithms are derived. Based on the$H_{\infty }$control theory and low-gain feedback technique, the observer gain matrix and control gain matrix can be obtained to achieve the NNSEC of continuous-time cases, and for discrete-time cases, the NNSEC can be achieved if the control gain matrix and observer gain matrix are nonpositive. Finally, four examples are proposed to verify the effectiveness of the main results.

This work studies the scaled consensus problems of exponentially unstable networked systems with time-varying input delays. First, a distributed consensus algorithm is designed under the truncated predictor feedback technique. Then, a delay bound is evaluated by utilizing the Lyapunov function-based method. Moreover, the consensus can be guaranteed when the upper bound of the time-varying input delay is no more than the delay bound. Furthermore, the relation between the delay bound and the network synchronizability is established. In other words, better network synchronizability implies a bigger delay bound. Finally, in the simulation examples, the feasibility of the theoretical results is verified, and the actual delay bounds are evaluated.

This article investigates the consensus control problem for second-order multiagent systems with switched dynamics, consisting of a continuous-time subsystem and a discrete-time subsystem. Under a fixed directed topology, two linear control protocols are proposed for achieving consensus. One is that two subsystems use different control inputs, where the continuous-time system uses continuous-time control, and the discrete-time system uses discrete-time control. In order to reach consensus for this kind of control protocol, some necessary and sufficient conditions are derived. The other is to use the same control algorithm for the two subsystems, which is a sampled-data control input. Similar consensus conditions are also obtained. Finally, a few simulation examples are given to verify the theoretical results.

For scenarios to pass through narrow and irregular channels, we develop a pragmatic distributed flexible formation protocol for multiple unmanned surface vessel systems (Multi-USVs). Therein, for path tracking with two leaders USVs, we propose a model predictive trajectory tracking scheme. Specifically, we design a scanning-formation controller with a trajectory state estimator for the followers to follow the leaders in order to efficiently fulfill the passing-through mission. Asymptotic stability conditions are derived to guarantee the feasibility of the developed multi-USV controller. Finally, both numerical simulations and experiments are conducted to show the effectiveness of the proposed multi-USV control strategies.

This article proposes a Q -learning (QL)-based algorithm for global consensus of saturated discrete-time multiagent systems (DTMASs) via output feedback. According to the low-gain feedback (LGF) theory, control inputs of the saturated DTMASs can avoid the saturation by utilizing the control policies with LGF matrices, which were computed from the modified algebraic Riccati equation (MARE) by requiring the information of system dynamics in most previous works. However, in this article, we first find the lower bound on the real part of Laplacian matrices' nonzero eigenvalues of directed network topologies. Then, we define a test control input and propose a Q -function to derive a QL Bellman equation, which plays an essential part of the QL algorithm. Subsequently, different from the previous works, the output-feedback gain (OFG) matrix of this article can be obtained by limited iterations of the QL algorithm without requiring the information of agent dynamics and network topologies of the saturated DTMASs. Furthermore, the saturated DTMASs can achieve global consensus rather than the semiglobal consensus of the previous results. Finally, the effectiveness of the QL algorithm is confirmed via two simulations.

The second-order scalar-weighted consensus problem of multiagent systems has been well explored. However, in some practical antagonistic interaction networks, the interdependencies of multidimensional states of the agents must be described by matrix coupling. In order to highlight the influence of matrix coupling in the antagonistic interaction network, we investigate the second-order matrix-weighted bipartite consensus problem on undirected structurally balanced signed networks. Under the proposed bipartite consensus protocol, an algebraic condition is obtained for achieving second-order bipartite consensus via utilizing matrix-valued Gauge transformation and stability theory. Then, using the obtained criteria, a more direct algebraic graph condition is given for reaching bipartite consensus. Besides, because of the existence of negative (positive) semidefinite connections, the matrix-weighted network may have clustering phenomena, which means that matrix weights play a critical role in achieving consensus. An algebraic graph condition for admitting cluster bipartite consensus is provided. By designing matrix weights in practical scenarios, the required number of clusters can be obtained. Finally, the theoretical results are verified by five simulation examples.

In this article, we investigate the distributed adaptive consensus problem of parabolic partial differential equation (PDE) agents by output feedback on undirected communication networks, in which two cases of no leader and leader-follower with a leader are taken into account. For the leaderless case, a novel distributed adaptive protocol, namely, the vertex-based protocol, is designed to achieve consensus by taking advantage of the relative output information of itself and its neighbors for any given undirected connected communication graph. For the case of leader-follower, a distributed continuous adaptive controller is put forward to converge the tracking error to a bounded domain by using the Lyapunov function, graph theory, and PDE theory. Furthermore, a corollary that the tracking error tends to zero by replacing the continuous controller with the discontinuous controller is given. Finally, the relevant simulation results are further demonstrated to demonstrate the theoretical results obtained.

Based on the fact that the traditional probability distribution entropy describing a local feature of the system cannot effectively capture the global topology variations of the network, some indicators constructed by the network adjacency matrix and Laplacian matrix come into being. Specifically, these measures are based on the eigenvalues of the scaled Laplace matrix, the eigenvalues of the network communicability matrix, and the spectral entropy based on information diffusion that has been proposed recently, respectively. In this article, we systematically study the dependence of these measures on the topological structure of the network. We prove from various aspects that spectral entropy has a better ability to identify the global topology than the traditional distribution entropy. Furthermore, the indicator based on the eigenvalues of the network communicability matrix achieves good results in some aspects while, overall, the spectral entropy is able to identify network topology variations from a global perspective.

In this article, we consider the problem of distributed adaptive leader-follower coordination of partial differential systems (i.e., reaction-diffusion neural networks, RDNNs) with directed communication topology in the case of multiple leaders. Different from the dynamical networks with ordinary differential dynamics, the design of adaptive protocols is more difficult due to the existence of spatial variables and nonlinear terms in the model. Under directed networks, a novel adaptive control protocol is proposed to solve the containment control problem of RDNNs. By constructing proper Lyapunov functional and adopting some important prior knowledge, the stability of containment for coupled RDNNs is theoretically proved. Furthermore, a corollary about the leader-follower synchronization with a leader for coupled RDNNs with directed communication topology is given. In the end, two numerical examples are provided to illustrate the obtained theoretical results.

This article is concerned with observer-based non-negative edge-consensus (OBNNEC) problems of networked discrete-time systems with or without actuator saturation. An algorithm which only uses actual outputs of neighboring edges is proposed by means of an$H_{\infty }$control method and modified algebraic Riccati equation (MARE)-based technique. The observer matrix and feedback matrix are constructed by solving the MARE and linear matrix inequality (LMI), respectively. Then, sufficient conditions for guaranteeing bounded inputs and non-negative edge states are derived. In addition, the low-gain characteristic of the MARE-based method is instrumental in guaranteeing non-negative edge states and deriving the feasible observer matrix and feedback matrix. Finally, two examples are shown to demonstrate the obtained theoretical results.

This article concerns the robust consensus problem of continuous-time linear multiagent systems (MASs) with uncertainty and discrete-time measurement information, where the output measurement information is in the data-sampled form. Distributed output-feedback protocol with or without controller interaction is proposed for each agent. Specifically, the output-feedback protocol runs in continuous time with an output error correction term mixed with the discrete-time measurement information. The concrete algorithm is given for the construction of the feedback matrices. Then, by using the delay-input approach, sufficient conditions are provided for the robust consensus of this kind of MASs interacting over networks described by the directed graphs. Finally, numerical simulations are given to illustrate the theoretical results.

In this article, we refocus on the distributed observer construction of a continuous-time linear time-invariant (LTI) system, which is called the target system, by using a network of observers to measure the output of the target system. Each observer can access only a part of the component information of the output of the target system, but the consensus-based communication among them can make it possible for each observer to estimate the full state vector of the target system asymptotically. The main objective of this article is to simplify the distributed reduced-order observer design for the LTI system on the basis of the consensus communication pattern. For observers interacting on a directed graph, we first address the problem of the distributed reduced-order observer design for the detectable target system and provide sufficient conditions involving the topology information to guarantee the existence of the distributed reduced-order observer. Then, the dependence on the topology information in the sufficient conditions will be eliminated by using the adaptive strategy and so that a completely distributed reduced-order observer can be designed for the target system. Finally, some numerical simulations are proposed to verify the theoretical results.

The issue of bipartite time-varying formation (BTVF) tracking for linear multiagent systems (MASs) with a leader of unknown input on signed digraphs is investigated. An adaptive nonsmooth protocol is taken in this article that utilizes only the local output feedback information among neighbors and, thus, can avoid employing the eigenvalue information of the Laplacian matrix of the graph. It is proven that if the interaction network of agents containing a spanning tree is structurally balanced, the BTVF tracking can be achieved with a leader of the bounded input via the proposed scheme. This leader-following BTVF includes two time-varying subformations, whose relationship is antagonistic. A convergence analysis of the proposed protocol for MASs is reflected by the Lyapunov method. Finally, the validly numerical simulations are illustrated to show the performance of the proposed schemes.

This article mainly solves the consensus issue of parabolic partial differential equation (PDE) agents with switching topology by output feedback. A novel edge-based adaptive control protocol is designed to reach consensus under the condition that the switching graphs are always connected at any switching instants. Different from the existing adaptive protocol associated with partial differential dynamics, the proposed adaptive observer-type law relies on the relative output information rather than relative state information. A proper Lyapunov functional is constructed and some important lemmas are used, then a sufficient condition is obtained for the consensus of parabolic PDE agents on switching graphs. Besides, a corollary about the distributed adaptive consensus of parabolic PDE agents on fixed undirected communication networks is given. Finally, the theoretical results are demonstrated by two numerical simulations.

This article is devoted to investigating finite-time synchronization (FTS) for coupled neural networks (CNNs) with time-varying delays and Markovian jumping topologies by using an intermittent quantized controller. Due to the intermittent property, it is very hard to surmount the effects of time delays and ascertain the settling time. A new lemma with novel finite-time stability inequality is developed first. Then, by constructing a new Lyapunov functional and utilizing linear programming (LP) method, several sufficient conditions are obtained to assure that the Markovian CNNs achieve synchronization with an isolated node in a settling time that relies on the initial values of considered systems, the width of control and rest intervals, and the time delays. The control gains are designed by solving the LP. Moreover, an optimal algorithm is given to enhance the accuracy in estimating the settling time. Finally, a numerical example is provided to show the merits and correctness of the theoretical analysis.

In this article, the problems of inverse-optimal consensus control (IOCC) for single-integral dynamics in Caputo continuous-time and Grunwald–Letnikov (G-L) discrete-time fractional-order multiagent systems (FOMASs) are investigated. For continuous-time FOMASs, by virtue of the variational method, the optimal solution under the constraint of the global performance index function is presented, and then the optimal state-feedback gain matrix (OSFGM) is derived through the Laplace transform and the inverse transform of fractional order. For discrete-time FOMASs, the OSFGM based on the algebraic Riccati equation (ARE) is computed, then it is shown that the OSFGM is a (asymmetric) Laplace matrix which has a zero eigenvalue and the corresponding network structure is a complete graph. Moreover, we rigorously prove that consensus can be achieved under the optimal state-feedback gain matrices. Finally, two simulation examples are shown to check the validity of the proposed theorems.

The containment control problem in fractional-order multiagent systems over a directed graph is studied in this article. Two distributed control protocols with or without time delays are designed by utilizing the sampled position and velocity data. Then, based on the knowledge of the matrix theory and Laplace transform, some necessary and sufficient conditions to reach containment are derived. For the protocol with time delays, similar sufficient and necessary conditions are obtained. Finally, some simulation examples are designed to verify that the theorems are correct.

A consensus control issue is studied for general second-order multiagent systems via Q-learning method in this article. A novel second-order type with discrete-time dynamics is investigated to solve the corresponding consensus issues. Under fixed directed topology, in order to achieve general second-order consensus for the systems, a model-free Q-learning method is proposed, which can derive the coupling gains matrix without any information from the system dynamics. Moreover, applying the obtained coupling gains matrix, this general second-order multiagent systems can achieve consensus. Then, for undirected graphs, a similar corollary is obtained for this system to achieve general second-order consensus by means of the Q-learning method. Finally, the correctness of the new method is confirmed by several simulation examples.

This article studies the consensus control problem of second-order multiagent systems with switching dynamics, which consist of a continuous-time and a discrete-time subsystem. A novel control protocol is proposed for fixed digraphs by using the same control strategy for two subsystems so that the controller can keep the control strategy unchanged when systems switch. Moreover, this control strategy uses only sampled position data at the current sampling time and the previous sampling time to deal with this possible situation when speed information is difficult to be measured, which is also robustness and low cost. Some necessary and sufficient conditions to achieve consensus are derived about the network topology, structure and sampling period. At last, a few simulation examples are given.

In this article, we propose two model-free algorithms using state or output feedback for saturated discrete-time multiagent systems (SDTMASs) to attain global containment control. In most previous works, the control input can avoid saturation by utilizing the low gain feedback (LGF) method whereas requiring the knowledge of agent dynamics, and SDTMASs just can attain semi-global containment control. Distinct with the previous works, first, based on the$Q$-learning (QL) technique, this article defines a$Q$-function and deduces the corresponding QL Bellman equation, which is the most important part of the QL algorithm. Then, in order to solve the QL Bellman equation, we propose two iterative model-free algorithms using state and output feedback, and the LGF matrix can be acquired from that solution directly. Furthermore, under the state and output feedback control protocols with the feedback matrices obtained from the proposed model-free algorithms, the SDTMASs can achieve global containment control instead of semi-global containment control. Finally, we present some simulations to confirm the validity of the proposed algorithms.

In this article, we study the consensus issues of multiagent systems (MASs) without any information of the system model by using the reinforcement learning (RL) method and event-based control strategy. First, we design an adaptive event-based consensus control protocol using the local sampled state information so that the consensus errors of all agents are uniformly ultimately bounded. The validity of the above event-triggered adaptive control protocol is confirmed by excluding the Zeno behavior within finite time. Then, based on the RL approach, we present a model-free algorithm to get the feedback gain matrix, and accomplish constructing the adaptive event-triggered control strategy without the knowledge of model information. Distinct with the existing related works, this RL-based event-triggered adaptive control algorithm only relies on the local sampled state information, irrelevant to any model information or global network information. Finally, we provide some examples to demonstrate the validity of the above adaptive event-based consensus algorithm.

This article considers the stabilization issue of switched discrete-time positive systems (SDPSs) with delay by using asynchronous control. Combining transition probability (TP) with mode-dependent average dwell time (MDADT), called TP-based MDADT switching, the SDPSs are more practical than classical models with average dwell-time (ADT) switching. With the aid of a co-positive Lyapunov–Krasovskii functional (CLKF), sufficient conditions ensuring the exponential stability almost surely (ES a.s.) of the SDPSs without control is studied, where the mode is not necessary to be stable. After that, a mode-dependent controller with switching delay is designed to stabilize the SDPSs in the case that there are unstable subsystems. An algorithm is provided to design the control gains. It is discovered that the mode in the closed-loop SDPSs is not required to be stable on synchronous and asynchronous switching intervals. Numerical simulations verify the merits of the new results.

This article studies the flocking problem of multiagent systems (MASs) with a dynamic virtual leader (VL) for the linear systems subject to time-varying uncertainties and external disturbance problems. We assume that the agents follow a leader with a bounded acceleration, which information is sensed only by the informed agents. We assign an adaptive estimator to each uninformed agent to estimate the velocity of the leader. By deriving a lemma and using a standard adaptive law, we design a continuous adaptive controller for solving the problem under the mentioned challenges, which is also fully distributed. The designed flocking control ensures that the velocity of followers asymptotically is converged to that of the VL. Also, the agents’ network remains connected, and no collision occurs among agents. Finally, we present a simulation that illustrates the validity of the results.

In this paper, the robust coordination control of multi-agent systems (MASs) with uncertainties is considered, where the uncertainties include the external disturbances and the measurement noises as well as the unknown initial states. Motivated by the interval observer of single-agent systems, a distributed interval observer is designed for MASs communicating through a directed network which contains a directed spanning tree by using only the bounding information on the uncertainties and the output information, to implement the interval-valued state estimation on the absolute state of each agent. It also finds that the robust coordination control is a by-part of the distributed interval observer design of this kind of MASs. Moreover, a time-invariant transformation is used to perfect the distributed interval observer design. Finally, numerical simulations are proposed to verify the theoretical results.

This paper develops two novel containment control protocols for networked fractional-order systems with sampled position data. In the first scenario, time delay is not considered and the protocol is about the last and causal past sampled position data, while in the second scenario, time delay is considered and the protocol is about the last and time delay sampled position data. Successively, some necessary and sufficient criteria are derived for two classes of protocols. It is interesting to find that containment control of networked fractional-order systems cannot be reached under the developed control protocols without the help of the causal past sampled position data or time delay. Lastly, the effectiveness of theoretical results is verified through a simulation example.

In the absence of assuming that all agents know the system matrix of the external system, for heterogeneous linear multiagent systems (MASs), this article resolves the cooperative regulation problem in the presence of communication constraints. Based on the mild assumption on the digraph, two novel adaptive protocols are presented to solve the cooperative output regulation problem (ORP) via state feedback and measurement output feedback subject to snatchy and asynchronous information exchange between agents, unknown time-varying delays, and probable information losses. Finally, some simulations are offered to demonstrate the validity of our results about the problem.

This article studies the consensus of hybrid second-order multiagent systems (MASs), where the hybrid MAS is constituted by the continuous-time second-order (CTSO) and discrete-time second-order (DTSO) dynamic agents. First, a hybrid consensus algorithm is proposed, where a sample-data control is considered in the CTSO subsystems. Under the proposed hybrid consensus algorithm, the convergence of the hybrid second-order MAS matrix is analyzed. Second, a sufficient and necessary condition is proposed, which indicates that the controller parameters, such as coupling gains and the sampling interval, and eigenvalues of network topology have a significant impact on the system consensus. Finally, several simulation examples are presented to prove the validity of the results.

This paper studies the consensus in fractional-order multiagent systems over directed graph via sampled-data control method. A distributed control protocol using the sampled position and velocity data is designed. By virtue of the Mittag-Leffler function, Laplace transform, and matrix theory, some necessary and sufficient conditions associated with the sampling period, the fractional order, the coupling strengths, and the network structure to obtain consensus of the systems are obtained. Then, some detailed discussions are presented about how to select the sampling period and how to design the coupling strengths to attain the consensus of the systems, respectively. Lastly, some numerical simulation results are illustrated to reflect the availability of the theoretical analysis.

In this article, by using the linear graph theory, modified algebraic Riccati equation (MARE)-based method and duality principle, two interaction protocols are proposed to achieve the scaled edge-consensus of networked discrete-time systems with unmeasurable edge-sates. Meanwhile, drawing support from MARE-based low-gain feedback technique and positive system theory, sufficient conditions are derived to ensure the bounded control inputs and positive edge-states. Moreover, feedback matrices and observer matrices are, respectively, constructed by utilizing the solutions of MARE and modified algebraic dual Riccati equation (MADRE). Remarkably, the theoretical results only use the edge number and vertex number of network rather than the global information of network. Finally, five examples are shown to demonstrate the feasibility of the interaction protocols.

This article investigates the observer-based non-negative scaled edge-consensus problems of a continues-time networked system with or without input saturation, in which the proposed algorithm only uses the neighboring edges’ outputs. First, the original networked model and preliminary algorithm are simplified by using the line graph theory and constructing a new variable. Then the specific mathematical formulations of feedback matrix and observer matrix are both derived by combining$H_{\infty }$control theory and low-gain feedback technique. Next, sufficient conditions which can guarantee the non-negative edge states and bounded control inputs are obtained. Moreover, the advantages of low-gain feedback technique for guaranteeing the non-negative edge states and designing the algorithm are developed. Finally, three cases are used to verify the validity of the theorems.

This article refocuses on the global coordination of networked systems with input saturation and external disturbances. With the help of a novel backstepping approach, a multihop relay control algorithm subject to a group of modified heterogenous saturation functions is constructed, in which the number of the hop is equal to the order of the networked system. It is proved that these modified heterogenous saturation functions can develop a global unsaturated control algorithm for each agent. Then, some sufficient and necessary conditions are provided for the global consensus of the connected networked systems with input saturation in the absence of external disturbances. In the presence of the input saturation and external disturbances, a sufficient condition irrelevant to the interactive network topology information is proposed for the global swarm of connected networked systems. Finally, numerical simulations are provided to verify the theoretical results.

This paper investigates the positive edge consensus problems for undirected networks, where each edge is modeled by a continuous-time positive system with sector input nonlinearities. Based on a given nodal network, the corresponding edge network is presented, and some relationships between the given nodal network and its edge network are given. The observer-based protocol for non-negative consensus is proposed. Rigorous theoretical analysis which considers both the input nonlinearities and the positivity constraint is introduced to achieve a global consensus result. Simultaneous stabilization problems are constructed for edge-based non-negative consensus using the maximum and the minimum nonzero eigenvalues of the edge Laplacian matrix. Furthermore, the robustness of the positive edge consensus to parameter perturbation is illustrated. Sufficient non-negative consensus conditions related to the bounds of system matrices are given, and the non-negative edge consensus conditions for star nodal networks are also given only using the vertex number. Iterative linear matrix inequalities (LMIs)/LMI algorithm is presented to obtain the feedback matrix and the observer matrix. The given theoretical results are finally illustrated by some simulations.

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 paper, the controllability problem is addressed for a two-time-scale discrete-time system with multiple agents. First, the system is described by a singularly perturbed difference equation expressed on fast timescale. Then, to eliminate the singular perturbation parameter, by using the iterative method and approximate approach, the two-time-scale system is separated into slow and fast subsystems. Subsequently, some sufficient and/or necessary conditions of controllability for the systems are derived by using matrix theory. Moreover, under three special network topologies, the necessary criteria for controllability are proposed via graph theory. Finally, we give a simulation example to illustrate the effectiveness of the proposed theoretical results.

In this paper, a second-order consensus for multiagent systems with a directed communication topology is studied. A novel consensus strategy is first proposed, where a periodic intermittent control strategy only with casual sampled position data is used, which not only decreases the operating time and the update rates of conditioners for every individual but also responds effectively to the case of missing velocity information. A necessary and sufficient consensus condition based on the coupling gains, the sampling period, the communication width, and the spectrum of the Laplacian matrix is established to reach the consensus, and the right intervals of the sampling period are given. Furthermore, a delay-induced consensus protocol is designed, and a necessary and sufficient condition is also given, by which the sampling period and the communication width can easily be chosen to achieve the consensus. At last, some simulation examples are given to verify the correctness of the theoretical results.

The observer-based edge-consensus problem of networked continuous-time dynamical systems with edge state non-negative constraint and actuator saturation is considered in this paper. Based on line graph theory, low-gain output-feedback technique and algebraic Riccati equation (ARE)-based method, two edge-consensus algorithms are designed to achieve the observer-based edge consensus, in which the specific mathematical expressions of the two algorithms are obtained. Meanwhile, sufficient conditions are obtained to meet the bounded inputs and the non-negative edge states by combining with the ARE-based low-gain output-feedback technique and the positive system theory. Moreover, the feedback-gain and observer-gain matrices which must meet the sufficient conditions at the same time are existed and easy to obtain. Finally, two simulation cases are introduced to show the effectiveness of the theoretical results.

In this article, an event-triggered method is proposed to solve the consensus of the second-order hybrid multiagent systems (MASs), which contain discrete-time and continuous-time individuals. First, we give a selection criteria of the coupling gains, the eigenvalues of communication topology, and the event-triggered sampling interval to guarantee the hybrid consensus, which have an impact on system stability, due to the interaction and co-existence of discrete-time and continuous-time individuals. Second, the hybrid second-order consensus under the event-triggered strategy is proven, where the agents communicate with their neighbors and update their controllers only at the triggered instants. Finally, we give some simulation examples to prove the validity of the main results.

In this article, we take the coordination control problem of linear time-invariant networked systems with uncertain additive disturbance and uncertain initial states into consideration. A distributed interval observer is first constructed for uncertain networked systems in which the control algorithm of each agent involves only the upper bound information and the lower bound information of the interval observer associated with itself and its neighbors, respectively. With the help of the cooperativity theory, it is proved that the interval observer can estimate the piecewise state for each agent and the interval-observer-based control algorithm can drive the uncertain system to achieve coordination behavior. Then, time-varying coordinate transformation is introduced to construct a novel interval observer which can eliminate the cooperativity premise on the system matrices and bound the states of all agents in real time. It is shown that the novel interval-observer-based control algorithm can guide the uncertain system to reach coordinated behavior. Finally, the numerical simulations are provided to verify the theoretical results.

In this paper, the scaled consensus of multiagent systems (MASs) with second-order nonlinear dynamics and time-varying delays is investigated, where agents are supposed to aperiodically communicate with each other under a directed graph at some disconnected time intervals. Different from the existing works, we consider the case where time-varying delays exist in both nonlinear dynamics and communication networks. First, to address this problem, we propose a novel scaled consensus protocol. Second, using Lyapunov theory and graph theory, it is proved that under mild conditions, MASs with second-order nonlinear dynamics exponentially reach scaled consensus. Moreover, we extend our results to the case of leader-following scaled consensus. Finally, the simulation examples are included to verify the effectiveness of the theoretical results.

In this article, the consensus problem for the delayed fractional-order multiagent system (FOMAS) under directed graph is addressed by intermittent sampled-data control. First, an intermittent sampled-data control protocol with input time delay is proposed. By virtue of Laplace transform and stability theory, some necessary and sufficient conditions depending on the order, input time delay, sampling period, communication width, coupling strengths, and network structure are presented for the delayed FOMASs to reach consensus. Moreover, due to the relationship about the input time delay, communication width, and sampling period, four cases are carefully discussed to find that the sampling period has bounds for a given network with known input time delay and communication width to obtain consensus. Finally, some simulation examples are shown to verify the theoretical results.

This paper presents a secure chaotic communication scheme using observer-based synchronization of chaotic systems. A class of chaotic systems satisfying incremental quadratic constraints are considered as the transmitter. The original message is encrypted in the noise-like output of the system. A circle criterion-based observer is designed for the system as the receiver by using the linear matrix inequalities technique. The message is recovered at the receiver end from the estimation error of the observer. To design the observer, a general algorithm to calculate incremental multiplier matrices for nonlinearities in chaotic systems is presented. Moreover, the proposed observer-based chaotic secure communication scheme is feasible for many common chaotic systems with ellipsoidal bounds. The simulation results show the good performance of the proposed communication scheme through an example of image transmission.

This paper investigates the joint effect of quantization, sampled data, and general Markovian interaction links on consensus networks with a leader under directed graphs. The diversity of edges formed by all the followers and the leader is also considered. Each agent in the network possesses continuous-time general linear dynamics. Each agent's state is measured only at sampling time instants, which is encoded before transmission. Subsequently, the encoded state is transmitted through noiseless digital communication links with Markovian switching rates. For this problem, a sufficient condition is derived to guarantee the convergence of the encoded states, based on which a necessary and sufficient condition is obtained to achieve consensus tracking in the mean-square sense. In addition, two sufficient conditions on coupling gain, one of which is fully distributed, are provided by proposing an optimal linear quadratic regulator-based gain matrix to ensure consensus tracking and then, the analysis of consensus region is presented. Finally, a numerical example is presented for illustrating the effectiveness of the theoretical results.

The semi-global output consensus problem for multiagent systems depicted by discrete-time dynamics subject to external disturbances and input saturation over switching networks is investigated in this paper. Assume that only a small part of subsystems have directly received the output of the exosystem. The distributed consensus algorithms are proposed by adopting the low-gain state feedback and the modified algebraic Riccati equation. Then, the outputs of all subsystems can reach synchronization asymptotically with those of the exosystem by using the proposed consensus protocols on some preconditions. Both the connected switching networks and the jointly connected switching networks are considered for the semi-global output consensus problem, respectively. Some numerical simulation results are shown to validate the theoretical analysis.

The time-varying formation problem for multiagent systems (MASs) with stochastic sampling and multiple leaders is studied in this paper, in which communication delays are taken into account. All the agents are divided into the set of the follower group and the set of the leader group. Under the proposed stochastic sampling mechanism for time-varying formation of the MASs with communication delays, the followers are driven to achieve time-varying formation where the center of the formation is the convex combination of the states of the leaders. In the theoretical analysis, sufficient conditions for the MASs achieving time-varying formation in mean square under stochastic sampling with multiple leaders and communication delays are derived. Moreover, some corollaries are also given in this paper. Finally, the theoretical analysis is verified by a given simulation example.

This paper studies the consensus problem for directed positive multiagent systems with nonlinear control input. The directed topology is supposed to be strongly connected. For the case of sector input nonlinearities, the non-negative global consensus conditions are presented by using a novel analysis method which directly considers the nonlinear input, and the feedback matrices are obtained with convex optimization method by solving the quadratic matrix inequalities subject to nonnegative constraints. For the case of saturation-type sector input nonlinearities, the global consensus and local consensus results are analyzed, respectively. With the properties of Metzler matrix, the non-negative consensus results are further extended to the strongly connected and balanced positive multiagent systems subject to (saturation-type) sector input nonlinearities and parameter uncertainties. The results are simplified, and the feedback matrices can be given by solving iterative linear matrix inequality with non-negative constraints. Two simulation examples and a practical electrical circuit model are finally carried out to verify the proposed control schemes.

In this paper, the problem of non-negative edge consensus of undirected networked linear time-invariant systems is addressed by associating each edge of the network with a state variable, for which a distributed algorithm is constructed. Sufficient conditions referring only to the number of edges are derived for non-negative edge consensus of the networked systems. Subsequently, the linear programming method and a low-gain feedback technique are introduced to simplify the design of the feedback gain matrix for achieving the non-negative edge consensus. It is found that the low-gain feedback technique has a good effect on the non-negative edge consensus of the networked systems subject to input saturation. Numerical simulations are presented to verify the effectiveness of the theoretical results.

This paper addresses the robust semiglobal coordinated control of multiple-input multiple-output multiagent systems with input saturation together with dead zone and input additive disturbance. Observer-based coordinated control protocol is constructed, by combining the parameterized low-and-high-gain feedback technique and the high-gain observer design approach. It is shown that, under some mild assumptions on agents' intrinsic dynamics, the robust semiglobal consensus or robust semiglobal swarm can be approached for undirected connected multiagent systems. Then, specific guidelines on the selection of the low-gain parameter, the high-gain parameter, and the high-gain observer gain have been provided. At last, numerical simulations are presented to illustrate the theoretical results.

This paper focuses on addressing the consensus problem of edges for both undirected and directed nodal networks whose edges are described by nominal or uncertain positive linear systems. The definition of line graph is given, and the similar properties and connections between the two types of graphs are established. Based on the rigorous theoretical analysis, distributed positive consensus algorithms are proposed, and the main results are given without utilizing the global interaction information. Subsequently, sufficient conditions for consensus with positivity constraint are given via the vertex number and the edge number of the original nodal network. Furthermore, according to the properties of Metzler matrix, we also solve the consensus problem for multiple edges which are modeled by uncertain positive systems. Some simulation studies are finally presented to verify the feasibility and effectiveness of the proposed results.

This paper establishes several bounds on the algebraic connectivity and spectral radius of graphs. Before deriving these bounds, a directed graph with a leader node is first investigated, for which some bounds on the spectral radius and the smallest real part of all the eigenvalues of M = L + D are obtained using the properties of M-matrix and non-negative matrix under a mild assumption, where L is the Laplacian matrix of the graph and D = diag{d1, d2, ..., dN} with di > 0 if node i can access the information of the leader node and 0 otherwise. Subsequently, by virtue of the results on directed graphs, the bounds on the algebraic connectivity and spectral radius of an undirected connected graph are provided. Besides establishing these bounds, another important feature is that all these bounds are distributed in the sense of only knowing the information of edge weights' bounds and the number of nodes in a graph, without using any information of inherent structures of the graph. Therefore, these bounds can be in some sense applied to agent networks for reducing the conservatism where control gains in control protocols depend on the eigenvalues of matrices M or L, which are global information. Also some examples are provided for corroborating the feasibility of the theoretical results.

This paper studies the multi-input and multi-output discrete-time nonnegative edge synchronization of networked systems based on neighbors' output information. The communication relationship among the edges of networked systems is modeled by well-known line graph. Two observer-based edge synchronization algorithms are designed, for which some necessary and sufficient synchronization conditions are derived. Moreover, some computable sufficient synchronization conditions are obtained, in which the feedback matrix and the observer matrix are computed by solving the linear programming problems. We finally design several simulation examples to demonstrate the validity of the given nonnegative edge synchronization algorithms.

This paper is concerned with the finite-time synchronization issue of nonlinear coupled neural networks by designing a new switching pinning controller. For the fixed network topology and control strength, the newly designed controller could optimize the synchronization time by regulating a parameter α (0 ≤ α < 1). The control law presented in this paper covers both continuous controllers and discontinuous ones, which were studied separately in the past. Some criteria are discussed in detail on how to shorten the synchronization time for the strongly connected networks. Finally, the results are generalized to any network topologies containing a directed spanning tree, and one numerical example is given to demonstrate the effectiveness of the theoretical results.

In this brief, we investigate pinning control for cluster synchronization of undirected complex dynamical networks using a decentralized adaptive strategy. Unlike most existing pinning-control algorithms with or without an adaptive strategy, which require global information of the underlying network such as the eigenvalues of the coupling matrix of the whole network or a centralized adaptive control scheme, we propose a novel decentralized adaptive pinning-control scheme for cluster synchronization of undirected networks using a local adaptive strategy on both coupling strengths and feedback gains. By introducing this local adaptive strategy on each node, we show that the network can synchronize using weak coupling strengths and small feedback gains. Finally, we present some simulations to verify and illustrate the theoretical results.

In this paper, we propose a decentralized adaptive pinning control scheme for synchronization of undirected networks using a local adaptive strategy to determine both coupling strengths and feedback gains. By applying this local adaptive strategy, we show that the network can achieve synchronization with small coupling strengths and feedback gains. We provide some simulations to verify and illustrate the theoretical results.