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Distributed average consensus via Noisy and Noncoherent Over-the-Air Aggregation

IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 2025年第1期12卷 64-73页

作者： Yang, Huiwen Chen, Xiaomeng Huang, Lingying Dey, Subhrakanti Shi, Ling Hong Kong Univ Sci & Technol Dept Elect & Comp Engn Hong Kong 00852 Peoples R China Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Uppsala Univ Dept Elect Engn SE-75121 Uppsala Sweden

Over-the-air aggregation has attracted widespread attention for its potential advantages in task-oriented applications, such as distributed sensing, learning, and consensus. In this article, we develop a communication-efficient distributed average consensus protocol by utilizing over-the-air aggregation, which exploits the superposition property of wireless channels rather than combat it. Noisy channels and noncoherent transmission are taken into account, and only half-duplex transceivers are required. We prove that the system can achieve average consensus in mean square and even almost surely under the proposed protocol. Furthermore, we extend the analysis to the scenarios with time-varying topology. Numerical simulation shows the effectiveness of the proposed protocol.

关键词： Wireless networks Multi-agent systems Topology Network topology consensus protocol Transceivers Convergence average consensus multiagent systems noncoherent transmission over-the-air aggregation

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Resilient average consensus With Adversaries via Distributed Detection and Recovery

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2025年第1期70卷 415-430页

作者： Yuan, Liwei Ishii, Hideaki Hunan Univ Coll Elect & Informat Engn Changsha 410082 Peoples R China Univ Tokyo Dept Informat Phys & Comp Tokyo 1138656 Japan

In this article, we study the problem of resilient average consensus (RAC) in multiagent systems where some of the agents are subject to failures or attacks. The objective of RAC is for nonfaulty/normal agents to converge to the average of their initial values despite the erroneous effects from malicious agents. To this end, we propose a successful distributed iterative RAC algorithm for the multiagent networks with general directed topologies. The proposed algorithm has two parts at each iteration: 1) detection and 2) averaging. For the detection part, we propose two distributed algorithms and one of them can detect malicious agents with only the information from direct in-neighbors. For the averaging part, we extend the applicability of an existing averaging algorithm where normal agents can remove the effects from malicious agents so far, after they are detected. Another important feature of our method is that it can handle the case where malicious agents are neighboring and collaborating with each other to mislead the normal ones from averaging. This case cannot be solved by existing detection approaches in related literature. Moreover, our algorithm is efficient in storage usage especially for large-scale networks as each agent only requires the values of neighbors within two hops. Lastly, numerical examples are given to verify the efficacy of the proposed algorithms.

关键词： average consensus directed topologies distributed detection resilient consensus average consensus directed topologies distributed detection resilient consensus

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Mean Squared Error Analysis of Noisy average consensus

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2025年第3期E108A卷 435-441页

作者： Wadayama, Tadashi Nakai-kasai, Ayano Nagoya Inst Technol Dept Comp Sci Nagoya 4668555 Japan

A continuous-time average consensus system is a linear dynamical system defined over a graph, where each node has its own state value that evolves according to a simultaneous linear differential equation. A node is allowed to interact with neighboring nodes. average consensus is a phenomenon that the all the state values converge to the average of the initial state values. In this paper, we assume that a node can communicate with neighboring nodes through an additive white Gaussian noise channel. We first formulate the noisy average consensus system by using a stochastic differential equation (SDE), which allows us to use the Euler-Maruyama method, a numerical technique for solving SDEs. By studying the stochastic behavior of the residual error of the Euler-Maruyama method, we arrive at the covariance evolution equation. The analysis of the residual error leads to a compact formula for mean squared error (MSE), which shows that the sum of the inverse eigenvalues of the Laplacian matrix is the most dominant factor influencing the MSE.

关键词： average consensus stochastic differential equation Euler- Maruyama method MSE

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Optimizing doubly stochastic matrices for average consensus through swarm and evolutionary algorithms

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ANNALS OF MATHEMATICS AND ARTIFICIAL INTELLIGENCE 2025年第1期93卷 151-171页

作者： Syriopoulos, Panos K. Chatzilygeroudis, Konstantinos I. Kalampalikis, Nektarios G. Vrahatis, Michael N. Univ Patras Dept Math Computat Intelligence Lab CILab GR-26110 Patras Greece

Doubly-stochastic matrices play a vital role in modern applications of complex networks such as tracking and decentralized state estimation, coordination and control of autonomous agents. A central theme in all of the above is consensus, that is, nodes reaching agreement about the value of an underlying variable (e.g. the state of the environment). Despite the fact that complex networks have been studied thoroughly, the communication graphs are usually described by symmetric matrices due to their advantageous theoretical properties. We do not yet have methods for optimizing generic doubly-stochastic matrices. In this paper, we propose a novel formulation and framework, EvoDSM, for achieving fast linear distributed averaging by: (a) optimizing the weights of a fixed graph topology, and (b) optimizing for the topology itself. We are concerned with graphs that can be described by positive doubly-stochastic matrices. Our method relies on swarm and evolutionary optimization algorithms and our experimental results and analysis showcase that our method (1) achieves comparable performance with traditional methods for symmetric graphs, (2) is applicable to non-symmetric network structures and edge weights, and (3) is scalable and can operate effectively with moderately large graphs without engineering overhead.

关键词： average consensus Distributed averaging Evolutionary algorithms Sparse matrix identification Particle swarm optimization

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Privacy Preserving average consensus via Integrable Function Based Masking 5th

Privacy Preserving Average Consensus via Integrable Function...

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5th International Conference on Neural Computing for Advanced Applications (NCAA)

作者： Yao, Xinyi Jia, Qiang Jiangsu Univ Sch Math Sci Zhenjiang 212013 Jiangsu Peoples R China

ISBN: (纸本)9789819770069;9789819770076

This work is concerned about the privacy-preserving problem in reaching average consensus of continuous multi-agent systems. Given a network of integrators, some efficient protocols with integrable function based masking scheme are developed, where all agents communicate and then adjust their states by using the masked data so that their initial states are well protected from any external eavesdropper. Moreover, the study is also extended to cases with nonlinear couplings, which is further applied to the privacy-preserving phase synchronization of coupled Kuramoto oscillators. Our design is simple yet efficient for privacy-preservation, and brings more flexibility than some existing works. Numerical examples are presented for the purpose of demonstration and verification.

关键词： Privacy preservation multi-agent system average consensus nonlinear coupling

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Privacy-Preserving average consensus via Pulse-Coupled Oscillators

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2025年

作者： Wang, Zhenqian Miao, Jinxin Li, Hongchao Beihang Univ Sch Automat Sci & Elect Engn Beijing Peoples R China Zhongguancun Lab Beijing Peoples R China Beihang Univ Hangzhou Innovat Inst Hangzhou Peoples R China Hebei Univ Technol Sch Artificial Intelligence Tianjin Peoples R China

average consensus is a cornerstone of distributed systems, facilitating essential functionalities such as distributed information fusion, decision-making, and decentralized control. Achieving average consensus typically relies on explicit exchanges of state and identity information among neighboring nodes. This reliance poses a risk of exposing sensitive information, leading to unpredictable data leakage. Therefore, it is imperative to implement privacy-preserving mechanisms within average consensus protocols. However, existing privacy-preserving approaches primarily focus on protecting the initial states of all nodes, compromising the identity information of the nodes. This vulnerability can be particularly problematic in scenarios where preserving identity information is paramount. In this paper, we propose a novel pulse-coupled oscillator-based privacy-preserving average consensus algorithm. Unlike traditional methods that exchange explicit state information through data packet transmission, our approach utilizes simple, identical, and content-free pulses. This method not only enhances the preservation of identity information but is also well-suited for hostile communication environments, such as during jamming attacks that disrupt data packet transmission. Furthermore, our algorithm does not necessitate synchronized clocks among all nodes, enhancing its suitability for practical applications. Numerical simulations are presented to validate the effectiveness of our theoretical results.

关键词： average consensus privacy-preserving pulse-coupled oscillators

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Privacy-preserving average consensus for second-order discrete-time multi-agent systems

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NEUROCOMPUTING 2025年 639卷

作者： Wang, Jie Huang, Na Chen, Yun Lu, Qiang Hangzhou Dianzi Univ Sch Automat Hangzhou 310018 Peoples R China

This study addresses the privacy-preserving average consensus problem in second-order discrete multi-agent systems under strongly connected and balanced graphs. When both velocity and position states of each agent are measurable, a novel lightweight algorithm is proposed by introducing perturbation signals into the transmitted information. Specifically, the algorithm is divided into two stages. In the initial stage, each agent introduces perturbation signals into its initial position and velocity states during transmission to confound potential attackers. In the subsequent stage, the agents use a standard average consensus algorithm to update their states, ensuring accurate convergence to the average of the initial states. Additionally, further considering the scenario where the velocity state is unavailable for each agent, an improved edge-based perturbation algorithm is introduced. Both algorithms not only effectively prevent the internal honest-but-curious agents from accurately inferring the initial states of other agents, except in the specific case where the curious agent is the sole neighbor of the target agent, but also protect privacy from the external eavesdroppers. Lastly, several numerical examples are conducted to validate the effectiveness of the proposed theoretical approaches.

关键词： Privacy preservation average consensus Second-order multi-agent systems Edge-based perturbations

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average consensus of multi-agent systems with communication time delays and noisy links

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Chinese Physics B 2013年第3期22卷 262-270页

作者：孙永征李望阮炯 School of Sciences China University of Mining and Technology School of Mathematical Sciences Fudan University

In this paper,we consider the average-consensus problem with communication time delays and noisy *** analyze two different cases of coupling topologies：fixed and switching *** utilizing the stability theory of the stochastic differential equations,we analytically show that the average consensus could be achieved almost surely with the perturbation of noise and the communication time delays even if the time delay is *** theoretical results show that multi-agent systems can tolerate relatively large time delays if the noise is weak,and they can tolerate relatively strong noise if the time delays are *** simulation results show that systems with strong noise intensities yield slow convergence.

关键词： average consensus multi-agent systems time delay white noise

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average consensus of Multi-Agent Systems Under Directed Topologies and Binary-Valued Communications

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IEEE ACCESS 2018年 6卷 55995-56006页

作者： Wang, Ting Zhang, Hang Zhao, Yanlong Chinese Acad Sci Key Lab Syst & Control Acad Math & Syst Sci Beijing 100190 Peoples R China Univ Chinese Acad Sci Sch Math Sci Beijing 100190 Peoples R China

This paper is concerned with the average consensus problem of multi-agent systems with binary-valued communications under directed topologies. The information that each agent communicates with others is binary-valued with a fixed threshold and the control is a quantity of transportation from one agent to another, which causes that a decrease of the transmitter's state leads to an increase of the same amount of the receiver's. Due to the limitation of the information obtained, each agent needs to wait for a period of time to collect enough binary-valued information to estimate. Hence, we construct a two-scale control algorithm. At the small-time scale, each agent estimates its neighbors' states based on the accumulation of binary-valued information for a period of time, during which the control is zero. At the large-time scale, each agent designs the control signal based on the estimation, which results in state updating of the multi-agent system. Then, each agent estimates the new states of its neighbors and the process of alternating estimation and control will be repeated. Finally, we prove that the estimation is convergent and give the mean square convergence rate as the reciprocal of the estimation time. More importantly, the multi-agent system is proved to achieve average consensus and the consensus speed is given. Simulation results are given to validate the algorithm.

关键词： Binary-valued communications multi-agent systems average consensus state estimation control design directed topologies

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average consensus for Expressed and Private Opinions

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2024年第8期69卷 5627-5634页

作者： Zhang, Jing Lu, Jianquan Hadjicostis, Christoforos N. Southeast Univ Sch Cyber Sci & Engn Nanjing 210096 Peoples R China Southeast Univ Sch Math Nanjing 210096 Peoples R China Univ Cyprus Dept Elect & Comp Engn CY-1678 Nicosia Cyprus

In this article, we study the problem of privacy-preserving average consensus from a different perspective. Previous research has mainly focused on designing privacy augmentation mechanisms for classical average consensus algorithms, which can lead to overhead (in the form of parameters exchanged between agents or extra privacy operations). Motivated by the framework of expressed and private opinions within social networks, we propose an alternative iterative algorithm to simultaneously update two state variables. One of these variables is used to transmit and interact among the network, while the other variable represents the real state evolution of agents and is not directly visible to other agents. We demonstrate that the algorithm can achieve the same performance as the well-known Laplacian consensus algorithm, but without the overhead of extra privacy protection operations. Furthermore, our algorithm is viable on general strongly connected digraphs, and does not require the topology to be undirected or balanced, nor does it require nodes to know their out-neighbors, thus, greatly weakening the topological requirements. Finally, we validate the effectiveness of the proposed algorithm via numerical simulations.

关键词： Privacy Mathematical models Social networking (online) Directed graphs Perturbation methods Heuristic algorithms Voting average consensus expressed and private opinions (EPOs) privacy preservation social networks

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