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distributed optimization Design for Computation of Algebraic Riccati Inequalities

IEEE TRANSACTIONS ON CYBERNETICS 2022年第3期52卷 1924-1935页

作者： Zeng, Xianlin Chen, Jie Hong, Yiguang Beijing Inst Technol Sch Automat Key Lab Intelligent Control & Decis Complex Syst Beijing 100081 Peoples R China Beijing Inst Technol Minist Educ Key Lab Biomimet Robots & Syst Beijing Adv Innovat Ctr Intelligent Robots & Syst Beijing 100081 Peoples R China Tongji Univ Shanghai Res Inst Intelligent Autonomous Syst Dept Control Sci & Engn Shanghai 200092 Peoples R China Chinese Acad Sci Acad Math & Syst Sci Key Lab Syst & Control Beijing 100190 Peoples R China Univ Chinese Acad Sci Sch Math Sci Beijing 100190 Peoples R China

This article proposes a distributed optimization design to compute continuous-time algebraic Riccati inequalities (ARIs), where the information of matrices is distributed among agents. We propose a design procedure to tackle the nonlinearity, the inequality, and the coupled information structure of ARI;then, we design a distributed algorithm based on an optimization approach and analyze its convergence properties. The proposed algorithm is able to verify whether ARI is feasible in a distributed way and converges to a solution if ARI is feasible for any initial condition.

关键词： Linear matrix inequalities distributed algorithms optimization Heuristic algorithms Dynamical systems Convergence Multi-agent systems distributed algorithm distributed optimization matrix inequality

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distributed optimization of integrated energy communities considering source-load interaction 3

Distributed optimization of integrated energy communities co...

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3rd International Conference on Energy, Power and Electrical Technology, ICEPET 2024

作者： Yang, Bifeng Zeng, Wenhao Bian, Daisen Xuan, Kejie Liu, Shuai Lv, Zhineng Liu, Chunguang State Grid Zhejiang Power Company Shaoxing Power Supply Bureau Shaoxing China North China Electric Power University Yangzhong Intelligent Electric Research Center Yangzhong China

ISBN: (纸本)9798350352658

With the reform of the energy market, the distributed autonomy of each subject of the community integrated energy system becomes more and more obvious, which challenges the computation and communication capability of the traditional centralized model. Considering that flexible loads are connected to the integrated energy community through smart buildings, forming a distributed source-load interaction mode, a distributed optimal scheduling model based on the theory of objective cascade analysis is proposed. Firstly, the integrated energy service provider and smart buildings are considered as different interests, and their respective optimization and autonomy models are established with the goal of minimizing the operation cost. Secondly, an objective cascade analysis is introduced to decouple the operation of different subjects by equating the purchased power to virtual generators and virtual loads. Finally, the validity of the proposed method is verified by an example, which provides a more economical operation scheme for the integrated energy community operation. © 2024 IEEE.

关键词： distributed optimization integrated energy system:integrated energy service provider source-load interaction

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distributed optimization in Distribution Systems: Use Cases, Limitations, and Research Needs

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IEEE TRANSACTIONS ON POWER SYSTEMS 2022年第5期37卷 3469-3481页

作者： Patari, Niloy Venkataramanan, Venkatesh Srivastava, Anurag Molzahn, Daniel K. Li, Na Annaswamy, Anuradha Washington State Univ WSU Pullman WA 99164 USA Natl Renewable Energy Lab Golden CO 80401 USA West Virginia Univ Comp Sci & Elect Engn Dept Morgantown WV 26506 USA Georgia Inst Technol Sch Elect & Comp Engn Atlanta GA 30332 USA Harvard Univ Elect Engn & Appl Math Cambridge MA 02138 USA MIT Dept Mech Engn Act Adapt Control Lab Cambridge MA 02139 USA

Electric distribution grid operations typically rely on both centralized optimization and local non-optimal control techniques. As an alternative, distribution system operational practices can consider distributed optimization techniques that leverage communications among various neighboring agents to achieve optimal operation. With the rapidly increasing integration of distributed energy resources (DERs), distributed optimization algorithms are growing in importance due to their potential advantages in scalability, flexibility, privacy, and robustness relative to centralized optimization. Implementation of distributed optimization offers multiple challenges and also opportunities. This paper provides a comprehensive review of the recent advancements in distributed optimization for electric distribution systems and classifications using key attributes. Problem formulations and distributed optimization algorithms are provided for example use cases, including volt/var control, market clearing process, loss minimization, and conservation voltage reduction. Finally, this paper also presents future research needs for the applicability of distributed optimization algorithms in the distribution system.

关键词： optimization Load flow Mathematical models distributed algorithms Voltage control Couplings Classification algorithms Optimal power flow distributed energy resources active distribution systems distributed optimization

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distributed optimization Design of Iterative Refinement Technique for Algebraic Riccati Equations

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2022年第5期52卷 2833-2847页

作者： Zeng, Xianlin Chen, Jie Hong, Yiguang Beijing Inst Technol Sch Automat Key Lab Intelligent Control & Decis Complex Syst Beijing 100081 Peoples R China Tongji Univ Dept Control Sci & Engn Shanghai 200092 Peoples R China Tongji Univ Shanghai Res Inst Intelligent Autonomous Syst Shanghai 200092 Peoples R China Beijing Inst Technol Minist Educ Beijing Adv Innovat Ctr Intelligent Beijing 100081 Peoples R China

This article focuses on the problem of a distributed computation of continuous-time algebraic Riccati equations (CARE), where information of matrices is split and known by multiple agents. This article proposes a distributed optimization design of the iterative refinement technique (IRM), a well-established centralized method for CARE. By assuming that each agent only knows partial information of CARE, we reformulate IRM for CARE as three classes of distributed optimization subproblems with different formulations and constraints. Then, we propose distributed algorithms for obtained distributed optimization subproblems and prove convergence properties of proposed algorithms. Numerical results show the efficacy of the proposed distributed IRM.

关键词： optimization Riccati equations distributed algorithms Cost function Convergence Optimal control Linear matrix inequalities Continuous-time algebraic Riccati equation (CARE) distributed algorithm distributed optimization iterative refinement method

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distributed optimization of Multiagent Systems Against Unmatched Disturbances: A Hierarchical Integral Control Framework

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2022年第6期52卷 3556-3567页

作者： Guo, Ge Kang, Jian Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang 110819 Peoples R China Northeastern Univ Qinhuangdao Sch Control Engn Qinhuangdao 066004 Hebei Peoples R China Northeastern Univ Coll Informat Sci & Engn Shenyang 110819 Peoples R China

This article investigates a distributed optimization problem of double-integrator multiagent systems with unmatched constant disturbances. Instead of involving an internal model or a disturbance observer to deal with the disturbances as in existing works, a two-layer control framework is presented based on state-integral feedback control (SIFC) and adaptive control techniques. The upper layer uses a virtual system to generate a global optimal consensus trajectory which is shared by the agents via a communication network. The lower layer includes an SIFC controller to guarantee asymptotic tracking of the given trajectory. Also in this layer, a model reference adaptive controller is introduced to enhance the dynamic tracking performance of the SIFC controller. This framework enables distributed optimization with time-triggered communication and mild requirements on the team objective. The method yields an interesting co-design algorithm of the control parameters and the communication intervals, which is proved to be convergent using Lyapunov stability theory. The effectiveness and advantages of the method are illustrated by numerical simulations.

关键词： optimization Multi-agent systems Heuristic algorithms Cost function Trajectory Adaptive control Adaptation models distributed optimization integral control model reference adaptive control (MRAC) multiagent system time-triggered communication unmatched disturbance

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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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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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distributed optimization for Rank-Constrained Semidefinite Programs

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IEEE CONTROL SYSTEMS LETTERS 2022年 7卷 103-108页

作者： Pei, Chaoying You, Sixiong Sun, Chuangchuang Dai, Ran Purdue Univ Sch Aeronaut & Astronaut W Lafayette IN 47907 USA Mississippi State Univ Dept Aerosp Engn Starkville MS 39762 USA

This letter develops a distributed optimization framework for solving the rank-constrained semidefinite programs (RCSPs). Since the rank constraint is non-convex and discontinuous, solving an optimization problem with rank constraints is NP-hard and notoriously time-consuming, especially for large-scale RCSPs. In the proposed approach, by decomposing an unknown matrix into a set of submatrices with much smaller sizes, the rank constraint on the original matrix is equivalently transformed into a set of constraints on the decomposed submatrices. The distributed framework allows parallel computation of subproblems while requiring coordination among them to satisfy the coupled constraints. As the scale of every subproblem solved independently is significantly reduced, the decomposition scheme and the distributed framework can be applied to large-scale RCSPs. Moreover, optimality conditions of the proposed distributed optimization algorithm for RCSPs at the converged point are analyzed. Finally, the efficiency and effectiveness of the proposed method are demonstrated via simulation examples for solving the image denoising problem.

关键词： Matrix decomposition optimization Minimization Linear matrix inequalities Eigenvalues and eigenfunctions Convex functions Signal processing algorithms distributed optimization rank-constrained optimization

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distributed optimization Algorithms for MASs With Network Attacks: From Continuous-Time to Event-Triggered Communication

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IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING 2022年第5期9卷 3332-3344页

作者： Wang, Dandan Fang, Xiao Wan, Yan Zhou, Jialing Wen, Guanghui Southeast Univ Sch Math Dept Syst Sci Nanjing 211189 Peoples R China Univ Texas Arlington Dept Elect Engn Arlington TX 76019 USA Nanjing Univ Sci & Technol Sch Automat Nanjing 210094 Peoples R China

In this paper, the distributed optimization problem for multi-agent systems under the existence of cyber attacks is researched. Each agent has a private local cost function which is assumed to be continuously differentiable and strongly convex with the Lipschitz continuous gradient. The global objective function is the sum of these local cost functions, and the communication topologies among agents are balanced and directed. Unlike most multi-agent systems in the existing literature, the cyber attacks in networks, which may result in the failure of information transmission, are considered. Two novel distributed optimization algorithms with the continuous-time communication are studied for such an optimization problem. In addition, in order to reduce computation and communication consumption efficiently, we further enhance these algorithms with an event-triggered communication mechanism. Under some assumptions and restrictions on attacks, sufficient yet efficient conditions for the convergence of the proposed algorithms are derived. Furthermore, the Zeno-behavior is shown to be excluded for the event-triggered distributed optimization algorithms. Finally, some numerical simulation examples are provided to illustrate and validate the efficiency of the proposed optimization algorithms.

关键词： Topology Cyberattack Cost function Convergence Estimation Symmetric matrices Network topology Network attack distributed optimization event-triggered coupling multi-agent systems Zeno-behavior

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distributed optimization Approach for Solving Continuous-Time Lyapunov Equations With Exponential Rate of Convergence

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IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2022年第3期52卷 1684-1691页

作者： Zeng, Xianlin Chen, Jie Sun, Jian Hong, Yiguang Beijing Inst Technol Sch Automat Beijing 100081 Peoples R China Beijing Inst Technol Beijing Adv Innovat Ctr Intelligent Robots & Syst Beijing 100081 Peoples R China Beijing Inst Technol Key Lab Biomimet Robots & Syst Minist Educ Beijing 100081 Peoples R China Tongji Univ Dept Control Sci & Engn Shanghai 200092 Peoples R China Tongji Univ Shanghai Res Inst Intelligent Autonomous Syst Shanghai 200092 Peoples R China Univ Chinese Acad Sci Acad Math & Syst Sci Chinese Acad Sci Key Lab Syst & Control Beijing 100190 Peoples R China

This article establishes an approach, based on distributed optimization, for solving continuous-time Lyapunov equations (CTLE) over multiagent networks. Each agent in the network knows partial information of the CTLE and has a dynamical system to estimate exact or least-squares solutions. The aim of agents is to find a solution to CTLE by sharing information with connected agents over a network. This article develops distributed algorithms with an exponential rate of convergence for CTLE via the convex optimization design. Finally, this article presents numerical simulations to show the efficacy of the main results.

关键词： optimization distributed algorithms Mathematical model Convergence Standards Multi-agent systems Matrix decomposition Continuous-time Lyapunov equation (CTLE) distributed optimization exponential convergence rate

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