The bipartite consensus problem for a group of homogeneous generic linear agents with input saturation under directed interaction topology is examined. It is established that if each agent is asymptotically null controllable with bounded controls and the interaction topology described by a signed digraph is structurally balanced and contains a spanning tree, then the semi-global bipartite consensus can be achieved for the linear multiagent system by a linear feedback controller with the control gain being designed via the low gain feedback technique. The convergence analysis of the proposed control strategy is performed by means of the Lyapunov method which can also specify the convergence rate. At last, the validity of the theoretical findings is demonstrated by two simulation examples.

This paper is concerned with developing a distributed k-means algorithm and a distributed fuzzy c-means algorithm for wireless sensor networks (WSNs) where each node is equipped with sensors. The underlying topology of the WSN is supposed to be strongly connected. The consensus algorithm in multiagent consensus theory is utilized to exchange the measurement information of the sensors in WSN. To obtain a faster convergence speed as well as a higher possibility of having the global optimum, a distributed k-means++ algorithm is first proposed to find the initial centroids before executing the distributed k-means algorithm and the distributed fuzzy c-means algorithm. The proposed distributed k-means algorithm is capable of partitioning the data observed by the nodes into measure-dependent groups which have small in-group and large out-group distances, while the proposed distributed fuzzy c-means algorithm is capable of partitioning the data observed by the nodes into different measure-dependent groups with degrees of membership values ranging from 0 to 1. Simulation results show that the proposed distributed algorithms can achieve almost the same results as that given by the centralized clustering algorithms.

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Summary This article considers distributed optimization problems of complex cyber‐physical networks, whose goal is to minimize a global function consisting of a sum of local functions possessed by each node, when the communication network is suffering L‐local deception attacks. After showing that merely 1‐local deception attacks can arbitrarily affect the outcome of any distributed optimization algorithms without being detected, we propose a resilient consensus‐based distributed optimization algorithm, where the estimation for the optimizer of each node is updated according to its subgradient and its partial neighbors' estimation. Then, we provide the conditions for the proposed algorithm to ensure that all the nodes can make an agreement and converge to the convex hull of the local optimizer of their functions in the presence of L‐local deception attacks. Finally, some simulation examples are presented to demonstrate the effectiveness of the proposed algorithm.

In network systems, a group of nodes may evolve into several subgroups and coordinate with each other in the same subgroup, i.e., reach cluster synchronization, to cope with the unanticipated situations. To this end, the leader-following practical cluster synchronization problem of networks of generic linear systems is studied in this paper. An event-based control algorithm that can largely reduce the amount of communication is first proposed over directed communication topologies. In the proposed algorithm, each node decides itself when to transmit its current state to its neighbors and how to update its controller according to the estimations of the states of it and its neighbors. Then, the Lyapunov method is utilized to perform the convergence analysis. It shows that the practical cluster synchronization can be ensured by choosing appropriate parameters no matter what kind of estimation for the state is applied. Furthermore, the Zeno behavior is also excluded for each node under some mild assumptions. Besides, three kinds of common estimations for the states including zero-order hold model, first-order approximate model, and high-order model-based estimations are, respectively, analyzed from the perspective of the exclusion of Zeno behavior. Finally, the validity of the proposed algorithm is demonstrated, the effects of the concerned parameters are simply presented, and the effects of the three estimations are also compared through several simulations.