In this note, we discuss finite-time state consensus problems for multi-agent systems and present one framework for constructing effective distributed protocols, which are continuous state feedbacks. By employing the theory of finite-time stability, we investigate both the bidirectional interaction case and the unidirectional interaction case, and prove that if the sum of time intervals, in which the interaction topology is connected, is sufficiently large, the proposed protocols will solve the finite-time consensus problems.

In this paper, we mainly review the topics in consensus and coordination of multi-agent systems, which have received a tremendous surge of interest and progressed rapidly in the past few years. Focusing on different kinds of constraints on the controller and the self-dynamics of each individual agent, as well as the coordination schemes, we categorize the recent results into the following directions: consensus with constraints, event-based consensus, consensus over signed networks, and consensus of heterogeneous agents. We also review some applications of the very well developed consensus algorithms to the topics such as economic dispatch problem in smart grid and k -means clustering algorithms.

The paper studies asynchronous consensus problems of continuous-time multi-agent systems with discontinuous information transmission. The proposed consensus control strategy is implemented based on the state information of each agent's neighbors at some discrete times. The asynchrony means that each agent's update times, at which the agent adjusts its dynamics, are independent of others'. Furthermore, it is assumed that the communication topology among agents is time-dependent and the information transmission is with bounded time-varying delays. If the union of the communication topology across any time interval with some given length contains a spanning tree, the consensus problem is shown to be solvable. The analysis tool developed in this paper is based on nonnegative matrix theory and graph theory. The main contribution of this paper is to provide a valid distributed consensus algorithm that overcomes the difficulties caused by unreliable communication channels, such as intermittent information transmission, switching communication topology, and time-varying communication delays, and therefore has its obvious practical applications. Simulation examples are provided to demonstrate the effectiveness of the theoretical results.

We investigate the cooperation dynamics attributed to the interplay between the evolution of individual strategies and evolution of individual partnerships. We focus on the effect of reputation on an individual’s partner-switching process. We assume that individuals can either change their strategies by imitating their partners or adjust their partnerships based on local information about reputations. We manipulate the partner switching in two ways; that is, individuals can switch from the lowest reputation partners, either to their partners’ partners who have the highest reputation (i.e., ordering in partnership) or to others randomly chosen from the entire population (i.e., randomness in partnership). We show that when individuals are able to alter their behavioral strategies and their social interaction partnerships on the basis of reputation, cooperation can prevail. We find that the larger temptation to defect and the denser the partner network, the more frequently individuals need to shift their partnerships in order for cooperation to thrive. Furthermore, an increasing tendency of switching to partners’ partners is more likely to lead to a higher level of cooperation. We show that when reputation is absent in such partner-switching processes, cooperation is much less favored than that of the reputation involved. Moreover, we investigate the effect of discounting an individual’s reputation on the evolution of cooperation. Our results highlight the importance of the consideration of reputation (indirect reciprocity) on the promotion of cooperation when individuals can adjust their partnerships.

In network science, change is good: Historically, network science focused on static networks, in which nodes are connected by permanent links. However, in networked systems ranging from protein-protein interactions to social networks, links change. Although it might seem that permanent links would make it easier to control a system, Li et al. demonstrate that temporality has advantages in real and simulated networks. Temporal networks can be controlled more efficiently and require less energy than their static counterparts. Science , this issue p. 1042