This paper investigates the leader-following consensus problem for second-order nonlinear multi-UAV systems under both fixed and Markovian switching topologies. A distributed event-triggered control protocol is proposed, which incorporates a unified triggering function that simultaneously handles intra-cluster and inter-cluster state errors. For fixed topology, sufficient conditions are derived to ensure practical fixed-time consensus. For Markovian switching topologies, a rigorous stability-guaranteeing framework is established using Multiple Lyapunov Functions and Average Dwell Time theory, which formally ensures asymptotic consensus under admissible switching signals. The absence of Zeno behavior is rigorously proved by deriving a positive lower bound on inter-event times. Comparative numerical simulations demonstrate that the proposed strategy achieves faster convergence and significantly reduces communication burden compared to conventional methods, validating its effectiveness and superiority in dynamic multi-cluster environments.

This paper investigates the output containment tracking problem in general heterogeneous multi-agent systems facing prescribed performance and intermittent communication. In this case, a novel non-periodic intermittent control framework is introduced to facilitate the intricate nature of the complex network to achieve the containment objective. First, an intermittent communication network is built by introducing a novel intermittent interval condition combining average dwell-time and extreme value theories into the directed graph. Second, a distributed non-periodic intermittent containment control strategy is designed, utilizing an internal system and a modified containment control approach. Subsequently, a distributed prescribed performance hybrid controller is developed to achieve output containment tracking. Additionally, sufficient conditions for the exponential stability are obtained based on the non-periodic intermittent and prescribed performance control methods. This criterion adopts the characterization of the average time interval. The effectiveness of the designed hybrid control strategy is verified by the simulation example, showcasing its advantage to solve the challenges in intermittent communication and prescribed performance.

In numerous applications of multi-agent systems (MASs), e.g., social networks and biological networks, the relationship between agents may shift from competition to cooperation or vice versa. With that in mind, this paper investigates flocking behavior of MASs with evolving cooperation-competition relationships. The relationship between neighboring agents is characterized by a state-dependent nonlinear function: competition is triggered when the state discrepancy between agents exceeds a predefined threshold, whereas cooperation is maintained otherwise. A complete analysis is conducted on flocking behavior using the infinite products of substochastic matrices. As algebraic conditions regarding agent states and cooperative ranges are established to ensure the emergence of flocking behavior, and a lower bound for the convergence rate of flocking behavior is established. Finally, the theoretical results are validated through numerical simulations and an indoor multi-UAV system platform.

Multi-dimensional opinion dynamic models can often be used to describe the mutual influence of agents on different topics expressed in social networks. This paper mainly focuses on the multi-dimensional opinion dynamics on social networks with asynchronous updates, where networks include two types of agents: stubborn agents and non-stubborn agents. In the asynchronous update mechanism, the update time instants of each agent are independent and different from those of other agents, which leads to the complexity and time variance of opinion interaction among agents. This paper comprehensively analyzes the convergence of multi-dimensional opinion dynamic models under asynchronous updates, relying on the techniques of binary relation composition and infinite products of sub-stochastic matrices. The results show that the opinions of stubborn agents gradually influence the opinions of non-stubborn agents, and ultimately completely determine the stable opinions of non-stubborn agents. The theoretical results are validated through numerical simulations.

This paper investigates the distributed localization problem in wireless sensor networks by adopting the barycentric coordinate method based on angle measurement. First, all sensor nodes are divided into two categories: anchor nodes with known locations and non-anchor nodes with unknown locations. On this basis, each non-anchor node calculates its barycentric coordinates relative to its neighbor nodes through angle measurement technology, and constructs an iterative equation for location estimation based on the local information exchange mechanism. Subsequently, corresponding localization algorithms are designed for two typical network deployment scenarios: non-anchor nodes are distributed inside the convex hull of anchor nodes and randomly distributed outside the convex hull. By introducing the convergence analysis method of sub-stochastic matrix multiplication, it is theoretically proved that the proposed distributed iterative localization algorithm can achieve progressive and precise localization of non-anchor nodes in both above two network deployment scenarios. Finally, the effectiveness of the proposed method is verified by numerical simulation experiments. The results show that the method can achieve high localization accuracy in both above two types of sensor network structures.

In nature, populations of organisms (e.g., wolves) exhibit a remarkable ability to coordinate their group actions, such as hunting prey or evading predators, despite the coexistence of cooperative and competitive interactions among individuals. Motivated by this intriguing phenomenon, this article investigates the cooperative consensus tracking control problem of multiagent systems (MASs) over cooperation-competition networks with asynchronous communications. That is, all followers can simultaneously achieve trajectory tracking of the leader agent, even if there exist competitive interactions between the followers and the leader. To portray the cooperation and competition level among agents, a new distance-based weight function is designed, which is more flexible than the fixed weight values in existing research works. Theoretically, the sufficient conditions for achieving consensus tracking control are obtained based on the convergence analysis method of infinite products of super-stochastic matrices. Finally, some numerical simulations are given to verify the effectiveness of the proposed consensus tracking control scheme.

Localization security is crucial to the widespread applications of wireless sensor networks (WSNs) in various fields. This article mainly studies the issue of distributed localization in WSNs subject to deception attacks, in which the attacker randomly compromises communication channels and injects false data, resulting in the codification of data received by sensor nodes. A distributed iterative localization algorithm based on detection-holding strategy is proposed with the help of barycentric coordinate representations. This algorithm detects modified data in communication links through residual detection and communication encryption. It is proved theoretically that the proposed localization algorithm can achieve accurate convergence to the sensors' locations under general random false-data-injection attacks. Finally, the algorithm performance is demonstrated through simulation examples.

This study analyzes the convergence rate of leader–follower multiagent consensus under communication delays by developing a measure standard utilizing products of substochastic matrices. Through the construction of augmented auxiliary digraphs, which combine the binary relations composition, a comprehensive analysis of the leader–follower consensus dynamics is conducted. A mathematical representation of the least convergence rate of the system is established, which is closely related to the network structure, the upper bound of weight factors as well as the size of time delays. Moreover, an upper bound on the finite convergence time of the system with special topological structures, such as chain graph, star graph, and tree graph is given. At last, simulated examples are presented to confirm the theoretical findings.

6G Internet of Things (IoT) is envisioned to provide large-scale network connections and high data transmission rates to satisfy the diverse needs of IoT nodes. The wireless powered communication network (WPCN) is the essential part of the future 6G IoT, which can provide nodes with reliable and efficient data and energy transmission. In complex environments, wireless power transmissions are inefficient due to transmission distance and obstacles. To address these concerns, we propose a novel quality of experience (QoE)-driven framework for aerial intelligent reflective surface (IRS)-assisted WPCN, which exploits the maneuverability of unmanned aerial vehicle (UAV) to improve the network performance. In the framework, we construct a nonlinear satisfaction function to quantify the QoE and design an adaptive reflective units configuration scheme based on the QoE to reduce resource consumption (e.g., energy) while satisfying the QoE requirements. The optimization problem of maximizing average throughput is formulated by jointly optimizing the aerial IRS flight trajectory, node association variable, time slot allocation ratio, and IRS phase. The existence of coupling between optimization variables and the nonconvexity lead to the difficulty of solving the optimization problem directly. To effectively solve the above optimization problem, the block coordinate descent (BCD) algorithm is utilized to decompose the optimization problem into four subproblems to be solved separately. Simulation results demonstrate that the proposed scheme can significantly enhance the throughput compared with other schemes.

Federated learning (FL) is a distributed learning framework that allows clients to build models without disclosing local data. However, in resource-constrained scenarios, it is costly to participate in FL for all clients. Hence, selection strategy should be designed to select the most appropriate client groups. Current selection strategies are mainly cost and accuracy oriented, ignoring the autonomy of clients, which leads to the inability of clients to make autonomous decisions when participating in model training and updating. To realize autonomous selection of clients, we design a novel model accuracy-aware bidirectional client selection (MABCS) algorithm. The MABCS algorithm implements selection from both server and client dimensions. Specifically, the server evaluates the contributions of clients and design an accuracy-aware dynamic incentive mechanism. The client measures participation autonomy based on the reward and cost to decide whether or not to participate in FL. Thus, the client selection problem is modeled as a joint nonconvex optimization problem that maximizes the system revenue by optimizing the selection strategy and resource allocation strategy. The block coordinate descent algorithm is utilized to decouple the selection strategy and resource allocation strategy, and a linear approximation is employed to transform the selection strategy problem into a convex problem. An alternating optimization algorithm is used for the subproblems after the decomposition to obtain a near-optimal solution. Simulation results indicate that the MABCS algorithm exhibits superior convergence performance compared with other benchmark schemes.

This contribution explores the flocking dynamic behavior of multi-agent networks with limited communication resources, where there are both cooperative and antagonistic relationships among agents. Taking into account the shortage of communication resources, a distributed control protocol with edge-asynchronous communications is designed, in which only part of the communication links are awakened at each time instant to perform information transmission. A product approach of super-stochastic matrices is utilized to rigorously check the convergence of the dynamic model. With this method, algebraic conditions on cooperative and antagonistic relationships among agents are established so that the entire multi-agent network emerges with flocking dynamics. At last, theoretical results are tested and verified through computer simulations.

Localization is a key technology to ensure the effective operation of wireless sensor networks in different environments. Due to the prevalence of cyber-attacks in real-world application scenarios, ensuring the accuracy of localization under denial-of-service (DoS) attacks is a growing concern. Existing research focuses on distributed localization ofstatic sensor networksunder DoS attacks. This article aims to extend the study of distributed localization inmobile sensor networkssubject to DoS attacks. Under DoS attacks, communication between sensor nodes can become intermittent, resulting in the time-varying characteristic for communication networks among all sensor nodes, which poses a challenge for successful localization. To overcome this challenge, this article proposes a distributed iterative localization algorithm using relative barycentric coordinates and distance measurements. Based on a hybrid approach composed of graph composition and sub-stochastic matrix, a comprehensive analysis of the convergence, rate and complexity of the localization algorithm is presented. At last, the theoretical results are verified by experimental examples.

Flocking aims to drive a group of agents connecting with each other to interact in a complex way, thereby emerging the behavior of group aggregation. Owing to the prevalence and complexity of cooperation and competition relationships among agents, it is practical and challenging to explore the realization of flocking behavior on multiagent coopetition networks. With that in mind, this article focuses on the study of flocking behavior for Cucker-Smale multiagent model over coopetition networks with communication delays. In this model, the cooperation/competition degree between agents is portrayed as a weight function with respect to communication distance, e.g., the closer (farther) the communication distance, the stronger (weaker) the cooperation/competition degree. With the help of analysis tools consisting of edge composites and substochastic matrices, the algebraic relationships between cooperation and competition degrees are established to ensure the emergence of flocking behavior. Moreover, mathematical expressions are given to show the effect of different communication delays on the agents’ final aggregation upper bound and convergence rate. In the end, the theoretical results are validated through computer simulations.

This article constructs a leader–follower architecture by introducing intermittent-influence opinion leaders to the DeGroot model and analyzes the influence of this type of leaders on the evolution of opinions. Different from the existing studies where the leaders can convey their opinions to the followers uninterruptedly, the leaders in this article can only convey its opinion by broadcasting at some intermittent moments. First, we analyze the relationship between the leaders’ broadcast moments and the consensus opinion of followers and explain that the marginal revenue of the broadcasts is diminishing. Second, we describe the connotation of assimilation and calculate the minimum number of broadcasts required for the leaders to assimilate the followers’ opinions. Finally, aiming to make the consensus opinion of the followers and the leaders’ as close as possible, we give an optimal strategy on how to select followers to broadcast. The correctness of theoretical results is verified by numerical simulations.

This work emphasises the bipartite flocking of leader-follower Cucker-Smale model on cooperation-competition networks under Denial-of-Service (DoS) attacks. The DoS with limited energy is the periodic signal that consists of active periods and asleep periods. It interruptes the information interactions among agents during the activation stages, while it concentrates on storing own energy for the next attack moment during the asleep stages. Meanwhile, the control strategy to defend against DoS attacks is established. The products convergence of infinite sub-stochastic matrices method is employed to implement the bipartite flocking behavior. Based on this method, a algebraic condition which is related to initial states, the topological structure and the weight function is constructed. Moreover, the obtained theoretical results are demonstrated by numerical simulations.

The existing studies for tracking consensus of multiagent systems (MASs) are all restricted to networks with only cooperative relationships among agents. Tracking consensus, however, requires beyond these traditional models due to the ubiquitous competition in many real-world MASs, such as biological systems and social systems. Taking into account this fact, this article aims to extend the dynamics of tracking consensus to signed networks containing both cooperative and competitive relationships among agents. A group of agents with general linear dynamics is considered. The cases of the fixed network as well as switching networks are analyzed, respectively. In the end, some algebraic conditions related to the network structure and the positive/negative edge weight are established to ensure the implementation of tracking consensus. Moreover, the single decoupling system is allowed to be strictly unstable in theory, and the upper bound of the eigenvalue modulus of the system matrix related to the system instability is given.

Signed digraphs with both positive and negative weighted edges are widely applied to explain cooperative and competitive interactions arising from various social, biological, and physical systems. This article formulates and solves the asynchronous tracking control problem of multiagent systems with input uncertainties on switching signed digraphs. In the interaction setting, we assume that the leader moves at a time-varying acceleration that cannot be measured by the followers accurately, and further suppose that each agent receives its neighbors' states information at certain instants determined by its own clock, which is not necessary to be synchronized with those of other agents. Using dynamically changing spanning subdigraphs of signed digraphs to describe graphically asynchronous interactions, the asynchronous tracking problem is equivalently transformed into a convergence problem of products of general substochastic matrices (PGSSM), in which the matrix elements are not necessarily non-negative and the row sums are less than or equal to 1. With the help of the matrix analysis technique and the composition of binary relations, we propose a new and original method to deal with the convergence problem of PGSSM, and further establish a spanning tree condition for asynchronous tracking control. Finally, the validity of the theoretical findings is verified through several numerical examples.

With the popularization of network equipment and the rapid development of information technology, the scale and complexity of wireless sensor networks (WSNs) continue to expand. How to effectively locate link failures has become a challenging problem in WSNs. In this paper, we propose a novel method of locating link failures based on distributed cluster consensus protocol and graph decomposition technique. In our method, the initial data is injected into sensor nodes for distributed interactions, and then link failures can be located by observing and comparing the output data of the nodes. The proposed method is suitable for the situations with both single-link failure and multi-link failures, and has no limitations on the number, distribution and correlation of link failures. Necessary and sufficient conditions are provided to guarantee the accuracy of the proposed method in locating link failures. At last, the effectiveness of the proposed method is verified by both real and simulation experiments.

This article addresses the bipartite tracking consensus for a set of mobile autonomous agents over directed cooperation-competition networks. Here, cooperative and competitive interactions among the agents are described by positive and negative edges of the directed network topology, respectively. Both fixed and switching network topologies are considered. For the case with fixed network topology, the matrix product technique is utilized to derive the convergence result. For the case with switching network topologies, some key results related to the composition of binary relations are the main technical tools of analyzing the error system. In addition, the upper bound for the spectral radius of the system matrix is given to ensure the convergence of the system even if the single uncoupled system is strictly unstable. The applicability of the derived results is verified through two simulation experiments.

This article focuses on the issue of scaled tracking consensus for discrete-time second-order multiagent systems under random packet dropouts, where the cases with a static leader and a dynamic leader are considered, respectively. The scaled tracking consensus means that all agents reach a consensus value determined by the leader but with different scales, and the phenomenon of packet dropout on each communication link is described as a Bernoulli variable independent of other communication links. By virtue of random environment-based scaled consensus algorithms, it is shown how to reconstruct the original system into augmented error systems with random coefficient matrices. With the kind assistance of substochastic matrix and super-stochastic matrix, sufficient conditions for the cases with a static leader and a dynamic leader are derived, respectively. Moreover, computer simulations are performed to demonstrate the dynamics of network agents under random packet dropouts.

This paper proposes a new model and its analysis results for time-varying structurally balanced networks. Through model transformations, the system stability problem is converted into the problem of product convergence of infinite sub-stochastic matrices (PCISM). Further, by constructing a new digraph for each interaction topology, the problem of PCISM can be handled by virtue of the properties of row-stochastic matrices. When all leaders belong to only one of the two subgroups, it is shown that the followers that are in the same subgroup as the leaders gradually enter the convex hull formed by the leaders' states, while the others gradually enter the convex hull formed by the leaders' sign-inverted states. And when both subgroups contain leaders, a sufficient algebraic graph condition is established to ensure that all followers can enter the convex hull consisting of the leaders' states and sign-inverted states together. Moreover, it is also found that the followers keep active after entering the convex hulls. Finally, the bipartite containment performance is verified by a simulation test.

In this contribution, we propose and investigate the containment control issue for general linear multiagent systems (MASs) under the asynchronous setting, where the network topology is not subjected to any structural restrictions and the roles of the leaders and the followers are entirely determined by the network topology. It is assumed that the interaction time instants of each agent, at which this agent interacts with its neighbors, are independent of the other agents' and can be unevenly distributed. An asynchronous distributed algorithm is proposed to implement the control strategy of linear MASs. The non-negative matrix theory and the composition of binary relations are utilized to handle the asynchronous containment control issue. It is shown that the leaders in each closed and strongly connected component of the network topology will reach a common state and the followers will gradually enter the dynamic convex hull constructed by the leaders. Moreover, it is also proved that the system matrix can be strictly unstable, and the upper bound of the system matrix's spectral radius is explicitly stated. Finally, two simulation examples are also provided to verify the efficacy of our theoretical results.

This paper is concerned with the containment control problem for discrete-time high-order multi-agent systems with switching topologies under the asynchronous setting. Based on the distributed asynchronous consensus protocol using only each agent's own information and its neighbors' partial information, the asynchronous high-order containment control problem with switching topologies is transformed into a product problem of infinite time-varying row-stochastic matrices. Then the properties of row-stochastic matrices are explored to derive a sufficient condition involving graph topologies for asynchronous containment control of high-order multi-agent systems. The theoretical results are finally validated through numerical simulations.