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.

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.

In social networks with mixed trust and distrust relationships, polarization is a common class of opinion evolutionary phenomena. Existing studies have generally believed that structural balance on networks is a crucial condition for the emergence of opinion polarization under DeGroot-style interactions. Unlike existing studies, this paper aims to establish a new updating model based on DeGroot-style interactions, thereby relaxing the network structure requirement of achieving opinion polarization to quasi structural balance , which is a more general concept and can include structural balance as a special case. With the assistance of the method of products convergence of infinite super-stochastic matrices, a comprehensive analysis of the model is carried out, and algebraic conditions on the degrees of trust and distrust among agents are established, so as to ensure the realization of opinion polarization on quasi structurally balanced networks. At last, numerical simulations are provided to verify the theoretical results.

Privacy-preserving has been crucial technique of multi-UAV systems, including cooperative detection, cooperative penetration and strike. Unprocessed interactive information poses a serious privacy threat to UAV swarm collaborative tasks. Considering not only privacy-preserving but also bandwidth constraints and the convergence performance of multi-UAV systems, this paper comprehensively proposes an original event-triggered-based finite-time privacy-preserving formation control scheme to resolve these three factors. Firstly, this paper adopted a local, deterministic, time-varying output mapping function for a privacy mask, which encodes the internal states of the UAV prior to its public transmission, and the initial true value of each UAV’s states is kept indecipherable for honest-but-curious UAVs and other malicious eavesdropping attackers. Then, considering the limited communication bandwidth and channels, we employed a distributed event-triggered strategy and deduced the triggering condition for consensus-based formation control, which effectively reduces the excessive consumption of communication and computational resources in contrast to time-triggered strategy. In terms of the convergence performance of the UAVs, finite-time stability theory was introduced to make the system reach the desired formation in finite time and obtain a settling time related to the initial state. Compared with the existing literature, this paper systematically took into account the above three factors for multi-UAV systems and provides a convergence analysis and a privacy analysis in detail. Finally, the effectiveness of the finite-time privacy-preserving protocol based on an event-triggered strategy was demonstrated by numerical simulation examples and comparative experiments. The proposed method achieves the formation control under privacy-preserving, improves the convergence rate and reduces the frequency of controller updates and information transmission.