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.

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.

In this contribution, the properties of sub-stochastic matrices and super-stochastic matrices are applied to solve the bipartite tracking issues of multi-agent systems (MASs) over signed networks, ...

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 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.

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.