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A privacy-preserving resilient algorithm for multi-agent cooperative optimization to defend against both Byzantine and eavesdropping attacks

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EXPERT SYSTEMS WITH APPLICATIONS 2025年 284卷

作者： Xu, Chentao Liu, Qingshan Nanjing Forestry Univ Coll Informat Sci & Technol Nanjing 210094 Peoples R China Southeast Univ Frontiers Sci Ctr Mobile Informat Commun & Secur Sch Math Nanjing 210096 Peoples R China Southeast Univ Sch Cyber Sci & Engn Nanjing 210096 Peoples R China Purple Mt Labs Nanjing 211111 Peoples R China

Multi-agent cooperative optimization offers significant benefits in terms of scalability, adaptivity, and flexibility. However, the distributed nature of multi-agent systems also makes the agents be vulnerable to external attacks. To defend against Byzantine attacks in the network, a resilient algorithm is proposed for multi-agent optimization that takes into account coupled equality constraint, which is seldom considered before in resilient algorithms. Moreover, to defend against both Byzantine and eavesdropping attacks in the network, a privacy-preserving resilient algorithm is proposed, which is innovative as it has rarely been explored before. The theoretical validity of the proposed algorithms is guaranteed through rigorous error and privacy analyses. Finally the effectiveness of the proposed algorithms are validated through simulation and contrast experiments, and the impact of different parameters on the optimization results are compared.

关键词： Multi-agent system Cooperative optimization resilient algorithm Byzantine attack Cryptography Privacy preservation

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resilient algorithm for distributed resource allocation under false data injection attacks

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ASIAN JOURNAL OF CONTROL 2024年第4期26卷 1635-1645页

作者： Chen, Xingzhi Cai, Xin Gao, Bingpeng Nan, Xinyuan Xinjiang Univ Sch Elect Engn Urumqi 830017 Peoples R China

For a first-order nonlinear multi-agent system who is subject to false data injection (FDI) attacks on agents' actuators and sensors, agents execute a distributed resource allocation algorithm according to the compromised control inputs and interactive information such that the multi-agent system is unstable and agents' decisions deviate from the optimal resource allocation. At first, we analyze the robustness of the distributed resource allocation algorithm under the FDI attacks. Then, a resilient distributed algorithm is proposed to solve the distributed resource allocation problem by resisting the adverse effect of the attacks. In detail, the unknown nonlinear term and the false data injected in agents are considered as extended states that can be estimated by extended state observers. The estimation is used in the feedback control to suppress the effect of the FDI attacks. As a result, the designed resilient algorithm ensures that agents' decisions converge to the optimal allocation without requiring any information about the nature of the attacks. An example is given to illustrate the results.

关键词： distributed algorithm false data injection attacks nonlinear dynamics resilient algorithm resource allocation

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resilient Fusion of LMB Densities Based on Medoids

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IEEE SENSORS JOURNAL 2025年第6期25卷 10370-10379页

作者： Zhou, Yao Gao, Lin Li, Gaiyou Wei, Ping Univ Elect Sci & Technol China Sch Informat & Commun Engn Chengdu 611731 Peoples R China

This article deals with the problem of resilient fusion of labeled multi-Bernoulli (LMB) densities, which arises in the situation that the sensor network (SN) undergoes abnormal behaviors like malicious attacks, resulting in the change of transmitted data from each sensor node. Compared to fusion algorithms based on perfect SN conditions, a detection procedure should be deployed before performing fusion so as to exclude abnormal data. To this end, we propose to decompose the LMB densities as the union of Bernoulli components (BCs), and then the medoids of BCs are exploited to form the fused LMB density. Besides, a new density-based spatial clustering of applications with noise (DBSCAN)-based label-matching algorithm is proposed. The performance of the proposed algorithm is verified via simulations.

关键词： Sensors Sensor fusion Clustering algorithms Target tracking Radio frequency Filtering algorithms Noise Matched filters Information theory Filtering theory Labeled multi-Bernoulli (LMB) medoid multiobject fusion random finite set resilient algorithm

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resilient Distributed Optimization algorithm Against Adversarial Attacks

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2020年第10期65卷 4308-4315页

作者： Zhao, Chengcheng He, Jianping Wang, Qing-Guo Zhejiang Univ State Key Lab Ind Control Technol Hangzhou 310027 Peoples R China Shanghai Jiao Tong Univ Dept Automat Shanghai 200240 Peoples R China Univ Johannesburg Fac Engn & Built Environm Inst Intelligent Syst ZA-2006 Johannesburg South Africa

As the cyber-attack is becoming one of the most challenging threats faced by cyber-physical systems, investigating the effect of cyber-attacks on distributed optimization and designing resilient algorithms are of both theoretical merits and practical values. Most existing works are established on the assumption that the maximum tolerable number of attacks, which depends on the network connectivity, is known by all normal agents. All normal agents will use the maximum number of attacks to decide whether the received information will be used for iterations. In this article, we relax this assumption and propose a novel resilient distributed optimization algorithm. The proposed algorithm exploits the trusted agents which cannot be compromised by adversarial attacks and form a connected dominating set in the original graph to constrain effects of adversarial attacks. It is shown that local variables of all normal and trusted agents converge to the same value under the proposed algorithm. Further, the final solution belongs to the convex set of minimizers of the weighted average of local cost functions of all trusted agents. The upper bound of the distance between the final solution and the optimal one has also been provided. Numerical results are presented to demonstrate the effectiveness of the proposed algorithm.

关键词： Cost function Distributed algorithms Security Automation Performance analysis Consensus algorithm Adversarial attacks connected dominating set distributed optimization resilient algorithm trusted agents

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Exploiting non-constant safe memory in resilient algorithms and data structures

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THEORETICAL COMPUTER SCIENCE 2015年 583卷 86-97页

作者： De Stefani, Lorenzo Silvestri, Francesco Univ Padua Dipartimento Ingn Informaz I-35131 Padua Italy

We extend the Faulty RAM model by Finocchi and Italiana (2008) by adding a safe memory of arbitrary size S, and we then derive tradeoffs between the performance of resilient algorithmic techniques and the size of the safe memory. Let delta and alpha denote, respectively, the maximum amount of faults which can happen during the execution of an algorithm and the actual number of occurred faults, with alpha <= delta. We propose a resilient algorithm for sorting n entries which requires O (n log n + alpha(delta/S +log S)) time and uses Theta (S) safe memory words. Our algorithm outperforms previous resilient sorting algorithms which do not exploit the available safe memory and require O (n log n + alpha delta) time. Finally, we exploit our sorting algorithm for deriving a resilient priority queue. Our implementation uses Theta (S) safe memory words and Theta (n) faulty memory words for storing n keys, and requires O (log n + delta/S) amortized time for each insert and deletemin operation. Our resilient priority queue improves the O (log n + delta) amortized time required by the state of the art. (C) 2015 Elsevier B.V. All rights reserved.

关键词： resilient algorithm resilient data structure Memory errors Sorting Priority queue Tradeoffs Fault tolerance

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resilient Online Distributed Optimization algorithm against Byzantine Attacks 13

Resilient Online Distributed Optimization Algorithm against ...

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13th Asian Control Conference (ASCC)

作者： Li, Lili Li, Xi Teng, Fei Dalian Maritime Univ Coll Marine Elect Engn Dalian Peoples R China

ISBN: (纸本)9788993215236

This paper presents a resilient online distributed optimization algorithm against Byzantine attacks. Each agent exchanges local information with neighbors on an unbalanced digraph with the row-stochastic matrix. Firstly, the gradient scaling technique based on consistency estimation is used to learn the left vector of the adjacency matrix asymptotically to overcome the imbalance of gradient weight caused by the row-stochastic matrix and improve the convergence speed and accuracy of the algorithm. Secondly, to effectively solve the problem of node consistency and optimality caused by Byzantine attacks, this paper uses the boundedness of the projection operator to limit state deviation between different nodes and extends the existing offline distributed optimization algorithm against Byzantine attacks to the online form, and regret bounds are derived for each node. Finally, the effectiveness and superiority of the proposed method are demonstrated by the comparison of numerical simulation. The results show that the proposed algorithm against Byzantine attacks extends offline form to the online form, and optimizes its accuracy and convergence speed.

关键词： online distributed optimization Byzantine attacks resilient algorithm row-stochastic matrix gradient scaling

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resilient distributed optimization for cyber-physical systems under adversarial environments: An event-based method

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ISA TRANSACTIONS 2024年 149卷 1-15页

作者： Liao, Zirui Wang, Shaoping Shi, Jian Li, Ming Zhang, Yuwei Sun, Zhiyong Beihang Univ Sch Automat Sci & Elect Engn Beijing 100191 Peoples R China Beihang Univ Ningbo Inst Technol Ningbo 315800 Peoples R China Eindhoven Univ Technol Dept Elect Engn NL-5600 MB Eindhoven Netherlands Beihang Univ Shenyuan Honors Coll Beijing 100191 Peoples R China

This work presents a resilient distributed optimization algorithm based on the event-triggering mechanism for cyber-physical systems (CPSs) to optimize an average of convex cost functions corresponding to multiple agents under adversarial environments. Two attack scenarios, including the f -total (each agent is affected by at most f malicious agents in the whole network) and the f -local (each agent is affected by at most f malicious agents in its in-neighbor set) attacks are considered. Subsequently, the convergence conditions under these two attack scenarios are provided, respectively, both of which guarantee that the state values of benign agents converge to a bounded error range. The optimality conditions are also presented by theoretical analysis, which guarantee that the state values of benign agents converge to a safety interval constructed by local optimal values under certain graph conditions, despite the misbehavior of malicious agents. In addition, four numerical examples are presented to show the effectiveness and superiority of the event-triggering resilient distributed optimization (RDO-E) algorithm. Compared to existing resilient algorithms, the proposed method achieves resilient distributed optimization with higher accuracy and less demanding communication overheads. Finally, by applying the proposed method to the multi-microgrid system, a resilient economic dispatch problem (REDP) is successfully solved, which validates the practical viability of the RDO-E algorithm.

关键词： Cyber-physical system Distributed optimization Event-triggering mechanism resilient algorithm

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resilient fixed-time bipartite consensus of multi-agent systems with nonlinear dynamics and directed graphs

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART I-JOURNAL OF SYSTEMS AND CONTROL ENGINEERING 2022年第9期236卷 1755-1765页

作者： Sharifi, Arman Pourgholi, Mahdi Shahid Beheshti Univ Fac Elect Engn Daneshjoo Blvd Evin Tehran *** Iran

This article is concerned with the bipartite fixed-time consensus problem for a class of multi-agent systems with nonlinear dynamics and directed graphs. To achieve the fixed-time consensus, a discontinuous control protocol is proposed. Compared to the protocols with undirected graphs, the control parameters are designed using a new Laplacian matrix based on an underlying undirected graph. Besides, to apply the method to the multi-agent systems with malicious agents, the proposed controller is combined with the Weighted Mean Subsequence Reduced (WMSR) algorithm which is modified for signed graphs. Finally, some simulations are presented to demonstrate the performance of the proposed method.

关键词： Multi-agent system nonlinear function fixed-time convergence resilient algorithm directed graph

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Accelerated Distributed Optimization algorithm With Malicious Nodes

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IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING 2024年第2期11卷 2238-2248页

作者： Zhang, Shiheng Liu, Zhi-Wei Wen, Guanghui Wang, Yan-Wu Huazhong Univ Sci & Technol Sch Artificial Intelligence & Automat Wuhan 430074 Peoples R China Huazhong Univ Sci & Technol Hubei Key Lab Brain inspired Intelligent Syst Wuhan 430074 Peoples R China Southeast Univ Sch Math Dept Syst Sci Nanjing 210096 Peoples R China

This paper addresses the challenges of slow convergence and vulnerability to attacks in distributed optimization for multi-agent systems. To improve the convergence rate in the presence of malicious nodes, a novel algorithm that combines the Mean-Subsequence-Reduce (MSR) method with gradient tracking is proposed. This algorithm enables the local variables of normal agents to converge to a convex combination of locally optimal solutions. However, using the MSR method in distributed optimization can lead to a time-varying transition matrix and the loss of the double stochasticity of the transition matrix, which presents design and analysis challenges. To mitigate this issue, a decreasing factor is introduced to alleviate the accumulation of errors caused by the single-row stochasticity of the transition matrix. We prove that the proposed algorithm achieves consensus and convergence to the point satisfying the optimality conditions. Numerical examples demonstrate the effectiveness of the proposed algorithm, showing a faster convergence rate than existing methods.

关键词： Optimization Convergence Multi-agent systems Stochastic processes Symmetric matrices Linear programming Transforms optimization methods resilient algorithm malicious nodes acceleration method

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resilient Nash Equilibrium Seeking in Multiagent Games Under False Data Injection Attacks1-7mm0mmPlease verify and confirm the term "Multi-Agent" has been changed to "Multiagent" in the title of the article.

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2023年第1期53卷 275-284页

作者： Cai, Xin Xiao, Feng Wei, Bo North China Elect Power Univ State Key Lab Alternate Elect Power Syst Renewabl Beijing 102206 Peoples R China North China Elect Power Univ Sch Control & Comp Engn Beijing 102206 Peoples R China Xinjiang Univ Sch Elect Engn Urumqi 830047 Peoples R China

This article proposes a resilient distributed Nash equilibrium (NE) seeking algorithm for noncooperative games with multiple double-integrator agents who suffer from false data injection (FDI) attacks. A malicious attacker injects false data into agents' actuators and sensors so that agents' strategies deviate from the NE of the game with the compromised control inputs and interactive information. First, the robustness of the seeking algorithm against the FDI attacks is analyzed. Then, to mitigate the effect of the attacks on agents' strategies, the false data injected in the actuators and sensors are regarded as extended states which can be observed by extended state observers (ESOs). Thus, a resilient NE seeking algorithm is proposed based on ESOs. The resilient algorithm can drive the system to converge to the NE without requiring any information about the nature of the attacks. An explicit criterion is given to ensure the effectiveness of the designed algorithms. An example is given to illustrate the results.

关键词： Games Sensors Actuators Distributed databases Sensor systems Denial-of-service attack Robustness False data injection (FDI) attacks Nash equilibrium (NE) noncooperative games resilient algorithm

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