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distributed optimization for Heterogenous Multi-Agent Systems Under DoS Attacks: Resilient Double-Layer Sampling Filtering Framework

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2025年第8期35卷 3270-3279页

作者： Wu, Han-Yu Liu, Qingshan Park, Ju H. Southeast Univ Sch Cyber Sci Engn Nanjing Peoples R China Yeungnam Univ Dept Elect Engn Kyongsan South Korea Southeast Univ Frontiers Sci Ctr Mobile Informat Commun & Secur Sch Math Nanjing Peoples R China Purple Mt Labs Nanjing Peoples R China

This paper investigates the distributed optimization for heterogenous multi-agent systems (MASs) under zero-topology Denial-of-Service (DoS) attacks, where the attacks are launched within the communication channels. A novel filtering attack framework is proposed based on the periodic sampling and event-triggering mechanism to counteract the impact of the attacks. Under this framework, the consumption of communication resources is reduced, and the minimum lower boundary of triggering time can be obtained to avoid the occurrence of Zeno behavior. Moreover, the relationship between the equilibrium point and optimal solution of heterogenous MASs under DoS attacks is revealed by employing a proportional-integral strategy. Furthermore, constructing an auxiliary system guarantees the output consensus and global exponential convergence of the MAS. Finally, a simulation example is provided to show that the proposed approach has a faster convergence rate and better robust performance against DoS attacks.

关键词： denial-of-service attacks distributed optimization exponential convergence filtering attack framework multi-agent system output consensus

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distributed optimization With Uncertain Communications

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2025年第4期70卷 2746-2753页

作者： Rezaeinia, Pouya Gharesifard, Bahman Linder, Tamas Queens Univ Dept Math & Stat Kingston ON K7L 3N6 Canada Univ Calif Los Angeles Dept Elect & Comp Engn Los Angeles CA 90095 USA

In this article, we consider a distributed optimization problem for the sum of convex functions where the underlying communication network connecting nodes at each time epoch is drawn at random from a collection of directed graphs. We propose a modified version of the subgradient-push algorithm that provably almost surely converges to an optimizer on any such sequence of random directed graphs. We also prove that the convergence rate of our proposed algorithm is upper bounded as O(1/root t), where t is the time horizon.

关键词： Directed graphs Convergence Vectors optimization Communication networks Convex functions Heuristic algorithms Protocols Uncertainty Statistical learning distributed control distributed optimization ergodic chains random networks

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distributed optimization of Cascade Pumping Stations Based on State-based Potential Game

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ENGINEERING LETTERS 2025年第4期33卷 1035-1044页

作者： Zhao, Yikang Xie, Gang Li, Rong Xu, Xinying Taiyuan Univ Technol Coll Elect & Power Engn Taiyuan 030024 Peoples R China Taiyuan Univ Sci & Technol Sch Elect Informat Engn Taiyuan 030024 Peoples R China

To solve the centralized optimization scheduling problem of long-distance water diversion in cascade pumping stations, we propose a fully distributed optimization method based on the state-based potential game (SPG). The primary objective is to minimize the daily electricity operating cost for the cascade pumping stations. Handling the coupled equality constraints of head and water diversion volume is challenging. Inspired by the Lagrangian approach, our SPG framework uses states and state transition functions to manage these constraints effectively. This method uses graph theory and distributed optimization algorithms to achieve stationary Nash equilibrium without requiring central control. The results demonstrate that using a distributed optimization method based on the state-based potential game is feasible and efficient for solving the optimization scheduling problem of cascade pumping stations.

关键词： Cascade pumping stations State-based potential game distributed optimization Stationary Nash equilibrium

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Duality-Based distributed optimization With Communication Delays in Multicluster Networks

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2025年第3期70卷 1867-1874页

作者： Wang, Jianzheng Hu, Guoqiang Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Zhejiang Univ Technol Dept Automat Hangzhou 310023 Peoples R China

In this work, we consider solving a distributed optimization problem in a multiagent network with multiple agent clusters. In each cluster, the agents manage separable cost functions composed of possibly nonsmooth components and aim to achieve an agreement on a common decision of the cluster. The global cost function is considered as the sum of the individual cost functions associated with affine coupling constraints on the clusters' decisions. To solve this problem, the dual problem is formulated by the concept of Fenchel conjugate. Then, an asynchronous distributed dual proximal gradient algorithm is proposed based on a cluster-based partial and mixed consensus protocol, by which the agents are only required to communicate with their neighbors with communication delays. An ergodic convergence result is provided, and the feasibility of the proposed algorithm is verified by solving a social welfare optimization problem in the simulation.

关键词： Agent cluster communication delay distributed optimization distributed optimization dual problem dual problem multiagent network multiagent network multiagent network

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Differentially Private distributed optimization Over Time-Varying Unbalanced Networks With Linear Convergence Rates

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2025年 73卷 1138-1152页

作者： Yang, Zhen He, Wangli Yang, Shaofu East China Univ Sci & Technol State Key Lab Ind Control Technol Shanghai 200237 Peoples R China East China Univ Sci & Technol Minist Educ Key Lab Smart Mfg Energy Chem Proc Shanghai 200237 Peoples R China Huzhou Inst Ind Control Technol Huzhou 313099 Peoples R China Southeast Univ Sch Comp Sci & Engn Nanjing 210096 Peoples R China

This paper addresses the distributed optimization problem with privacy concerns over time-varying unbalanced networks, where agents collaborate to optimize the average of local objective functions while preserving the privacy of sensitive information encoded in local functions. To tackle the problem, the paper proposes a differentially private algorithm by exploiting decaying Laplace noise without requiring bounded gradients. The proposed algorithm is demonstrated to achieve linear convergence to the sub-optimal solution determined by the noise injected to gradient estimations in mean square and ensure $\epsilon$-differential privacy (DP) of local functions under carefully designed noise parameters. The inherent privacy-accuracy trade-off is revealed through both theoretical insights and simulation results. Furthermore, the image classification and deblurring problems are effectively solved with sensitive data being strictly protected through the deployment of the proposed algorithm, demonstrating the convergence and privacy-preserving performance of the algorithm.

关键词： Convergence optimization Privacy Signal processing algorithms Noise Differential privacy Vectors Linear programming Classification algorithms Training distributed optimization differential privacy time-varying unbalanced networks

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Multi/Single-Stage Sliding Manifold Approaches for Prescribed-Time distributed optimization

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2025年第4期70卷 2794-2801页

作者： Zhou, Shuaiyu Wei, Yiheng Cao, Jinde Liu, Yang Southeast Univ Sch Math Nanjing 211189 Peoples R China Ahlia Univ Manama 10878 Bahrain Zhejiang Normal Univ Sch Math Sci Key Lab Intelligent Educ Technol & Applicat Zhejia Jinhua 321004 Peoples R China

The prescribed-time convergence mechanism has garnered significant attention within the fields of optimization and control, primarily attributed to its ability for precise manipulation of target completion times. This article formulates sliding manifolds with prescribed-time stability, based on which two modified zero-gradient-sum (ZGS) algorithms are established. One of the optimization algorithms is developed based on a multistage structural framework and another is based on a single-stage one. Contrary to the necessary customization of multistage structures in the prescribed-time distributed optimization, this study bridges the gap on the single-stage structured prescribed-time ZGS algorithm. Different from the existing multistage algorithms, the proposed optimization algorithms are proven to converge to the optimal solution within a prescribed-time under more mild conditions. Besides, for the first time, a singularity-free prescribed-time distributed optimization algorithm based on time-varying scaling function is proposed. Furthermore, the robustness of the singularity-free algorithm in rejecting external disturbances is also analyzed. The simulation involving a rendezvous formation problem is elaborated to demonstrate the singularity-free prescribed-time convergence and enhanced robustness of the proposed approaches.

关键词： optimization Convergence Heuristic algorithms Periodic structures Manifolds Vectors Robustness Stability analysis Upper bound Protocols distributed optimization prescribed-time stability sliding manifold zero-gradient-sum (ZGS) algorithm

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Differentially Private distributed optimization Over Diagraphs With Application to Image Deblurring

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IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 2025年第1期12卷 634-647页

作者： Yang, Zhen He, Wangli Yuan, Yang East China Univ Sci & Technol Key Lab Smart Mfg Energy Chem Proc Minist Educ Shanghai 200237 Peoples R China

This article investigates the distributed optimization problem over directed graphs, where agents work together to minimize the average of local objective functions. To protect private information from potential eavesdroppers in communication networks, we propose an algorithm that employs decaying Laplace noise, ensuring differential privacy in directed networks. Without assuming bounded gradients, the proposed algorithm can achieve both linear convergence in mean square and epsilon-differential privacy over directed networks. A comprehensive analysis of the tradeoff between privacy and accuracy is also provided. Furthermore, the image deblurring task is formulated as a distributed optimization problem, and visually pleasing results obtained by the deployment of the proposed algorithm verify the theoretical claims.

关键词： Privacy optimization Convergence Directed graphs Differential privacy Linear programming Image restoration directed networks distributed optimization image deblurring

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MUSIC: Accelerated Convergence for distributed optimization With Inexact and Exact Methods

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2025年第3期36卷 4893-4907页

作者： Wu, Mou Liao, Haibin Ding, Zhengtao Xiao, Yonggang Hubei Univ Sci & Technol Sch Comp Sci & Technol Xianning 437100 Peoples R China Hubei Univ Sci & Technol Lab Optoelectron Informat & Intelligent Control Xianning 437100 Peoples R China Wuhan Textile Univ Sch Elect & Elect Engn Wuhan 430200 Peoples R China Univ Manchester Dept Elect & Elect Engn Manchester M13 9PL England

Gradient-type distributed optimization methods have blossomed into one of the most important tools for solving a minimization learning task over a networked agent system. However, only one gradient update per iteration makes it difficult to achieve a substantive acceleration of convergence. In this article, we propose an accelerated framework named multiupdates single-combination (MUSIC) allowing each agent to perform multiple local updates and a single combination in each iteration. More importantly, we equip inexact and exact distributed optimization methods into this framework, thereby developing two new algorithms that exhibit accelerated linear convergence and high communication efficiency. Our rigorous convergence analysis reveals the sources of steady-state errors arising from inexact policies and offers effective solutions. Numerical results based on synthetic and real datasets demonstrate both our theoretical motivations and analysis, as well as performance advantages.

关键词： Convergence acceleration distributed optimization gradient descent machine learning multiple updates

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Discretized distributed optimization Over Dynamic Digraphs

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IEEE TRANSACTIONS ON AUTOMATION SCIENCE AND ENGINEERING 2025年 22卷 2758-2767页

作者： Doostmohammadian, Mohammadreza Jiang, Wei Liaquat, Muwahida Aghasi, Alireza Zarrabi, Houman Semnan Univ Fac Mech Engn Semnan *** Iran Aalto Univ Sch Elect Engn Espoo 02150 Finland Natl Land Survey Finland Finnish Geospatial Res Inst FGI Espoo 02150 Finland Oregon State Univ Dept Elect Engn & Comp Sci Corvallis OR 97331 USA Iran Telecom Res Ctr ITRC Tehran *** Iran

We consider a discrete-time model of continuous-time distributed optimization over dynamic directed-graphs (digraphs) with applications to distributed learning. Our optimization algorithm works over general strongly connected dynamic networks under switching topologies, e.g., in mobile multi-agent systems and volatile networks due to link failures. Compared to many existing lines of work, there is no need for bi-stochastic weight designs on the links. The existing literature mostly needs the link weights to be stochastic using specific weight-design algorithms needed both at the initialization and at all times when the topology of the network changes. This paper eliminates the need for such algorithms and paves the way for distributed optimization over time-varying digraphs. We derive the bound on the gradient-tracking step-size and discrete time-step for convergence and prove dynamic stability using arguments from consensus algorithms, matrix perturbation theory, and Lyapunov theory. This work, particularly, is an improvement over existing stochastic-weight undirected networks in case of link removal or packet drops. This is because the existing literature may need to rerun time-consuming and computationally complex algorithms for stochastic design, while the proposed strategy works as long as the underlying network is weight-symmetric and balanced. The proposed optimization framework finds applications to distributed classification and learning. Note to Practitioners-Inspired by recent advances in cloud-computing and distributed and parallel processing along with embedded low-cost CPUs and wireless communications, this paper considers distributed algorithms for optimization and machine learning over wireless-connected autonomous multi-agent systems (MASs). In contrast to the classical centralized learning methods, which are prone to single-point-of-failure and centralized processing, in cooperative optimization the learning is distributed among a group of data-pro

关键词： distributed optimization matrix perturbation theory consensus constraint dynamic digraphs

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Linear convergence of event-triggered distributed optimization with metric subregularity condition

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ASIAN JOURNAL OF CONTROL 2025年第2期27卷 750-764页

作者： Yu, Xin Cheng, Songsong Qiu, Jianbin Fan, Yuan AnHui Univ Sch Elect Engn & Automat Hefei Peoples R China Harbin Inst Technol Res Inst Intelligent Control & Syst Harbin Peoples R China

This paper designs a continuous-time algorithm with event-triggered communication (ETC) for solving a class of distributed convex optimization problems with a metric subregularity condition. First, we develop an event-triggered continuous-time optimization algorithm to overcome the bandwidth limitation of multi-agent systems. Besides, with the aid of Lyapunov theory, we prove that the distributed event-triggered algorithm converges to the optimum set with an exact linear convergence rate, without the strongly convex condition. Moreover, we provide the discrete version of the continuous-time algorithm and show its exact linear convergence rate. Finally, we give a comparison example to validate the effectiveness of the designed algorithm in communication resource saving.

关键词： distributed optimization event-triggered linear convergence metric subregularity primal-dual

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