Synchronization of small oscillations

Synchronization is studied in an array of identical oscillators undergoing small vibrations. The overall coupling is described by a pair of matrix-weighted Laplacian matrices; one representing the dissipative, the other the restorative connectors. A construction is proposed to combine these two real matrices in a single complex matrix. It is shown that whether the oscillators synchronize in the steady state or not depends on the number of eigenvalues of this complex matrix on the imaginary axis. Certain refinements of this condition for the special cases, where the restorative coupling is either weak or absent, are also presented.Comment: 16 pages, 6 figure

Bearing-Based Network Localization Under Gossip Protocol

This paper proposes a bearing-based network localization algorithm with a randomized gossip protocol. Each sensor node is assumed to be able to obtain the bearing vectors and communicate its position estimates with several neighboring agents. Each update involves two agents, and the update sequence follows a stochastic process. Under the assumption that the network is infinitesimally bearing rigid and contains at least two beacon nodes, we show that the proposed algorithm could successfully estimate the actual positions of the network in probability. The randomized update protocol provides a simple, distributed, and reduces the communication cost of the network. The theoretical result is then supported by a simulation of a 1089-node sensor network.Comment: preprint, 7 pages, 2 figure

Dynamic Event-Triggered Consensus of Multi-agent Systems on Matrix-weighted Networks

This paper examines event-triggered consensus of multi-agent systems on matrix-weighted networks, where the interdependencies among higher-dimensional states of neighboring agents are characterized by matrix-weighted edges in the network. Specifically, a distributed dynamic event-triggered coordination strategy is proposed for this category of generalized networks, in which an auxiliary system is employed for each agent to dynamically adjust the trigger threshold, which plays an essential role in guaranteeing that the triggering time sequence does not exhibit Zeno behavior. Distributed event-triggered control protocols are proposed to guarantee leaderless and leader-follower consensus for multi-agent systems on matrix-weighted networks, respectively. It is shown that that the spectral properties of matrix-valued weights are crucial in event-triggered mechanism design for matrix-weighted networks. Finally, simulation examples are provided to demonstrate the theoretical results

Distributed consensus algorithm for events detection in cyber-physical systems

In the harsh environmental conditions of cyber-physical systems (CPSs), the consensus problem seems to be one of the central topics that affect the performance of consensus-based applications, such as events detection, estimation, tracking, blockchain, etc. In this paper, we investigate the events detection based on consensus problem of CPS by means of compressed sensing (CS) for applications such as attack detection, industrial process monitoring, automatic alert system, and prediction for potentially dangerous events in CPS. The edge devices in a CPS are able to calculate a log-likelihood ratio (LLR) from local observation for one or more events via a consensus approach to iteratively optimize the consensus LLRs for the whole CPS system. The information-exchange topologies are considered as a collection of jointly connected networks and an iterative distributed consensus algorithm is proposed to optimize the LLRs to form a global optimal decision. Each active device in the CPS first detects the local region and obtains a local LLR, which then exchanges with its active neighbors. Compressed data collection is enforced by a reliable cluster partitioning scheme, which conserves sensing energy and prolongs network lifetime. Then the LLR estimations are improved iteratively until a global optimum is reached. The proposed distributed consensus algorithm can converge fast and hence improve the reliability with lower transmission burden and computation costs in CPS. Simulation results demonstrated the effectiveness of the proposed approach