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distributed optimization for discrete-time multiagent systems with nonconvex control input constraints and switching topologies

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Chinese Physics B 2021年第12期30卷 283-290页

作者： Xiao-Yu Shen Shuai Su Hai-Liang Hou School of Automation Central South UniversityChangsha 410083China National Engineering Research Center of Rail Transportation Operation and Control System Beijing Jiaotong UniversityBeijing 100044China State Key Laboratory of Rail Traffic Control and Safety Beijing Jiaotong UniversityBeijing 100044China

This paper addresses the distributed optimization problem of discrete-time multiagent systems with nonconvex control input constraints and switching *** introduce a novel distributed optimization algorithm with a switching mechanism to guarantee that all agents eventually converge to an optimal solution point,while their control inputs are constrained in their own nonconvex *** is worth noting that the mechanism is performed to tackle the coexistence of the nonconvex constraint operator and the optimization gradient *** on the dynamic transformation technique,the original nonlinear dynamic system is transformed into an equivalent one with a nonlinear error *** utilizing the nonnegative matrix theory,it is shown that the optimization problem can be solved when the union of switching communication graphs is jointly strongly ***,a numerical simulation example is used to demonstrate the acquired theoretical results.

关键词： multiagent systems nonconvex input constraints switching topologies distributed optimization

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distributed optimization and Scaling Design for Solving Sylvester Equations

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Journal of Systems Science & Complexity 2024年第6期37卷 2487-2510页

作者： CHENG Songsong YU Xin ZENG Xianlin LIANG Shu HONG Yiguang Anhui Engineering Laboratory of Human-Robot Integration System and Intelligent Equipment School of Electrical Engineering and AutomationAnhui UniversityHefei 230601China Key Laboratory of Intelligent Control and Decision of Complex Systems School of AutomationBeijing Institute of TechnologyBeijing 100081China Department of Control Science and Engineering Tongji UniversityShanghai 201804China Shanghai Research Institute for Intelligent Autonomous Systems Tongji UniversityShanghai 201210China

This paper develops distributed algorithms for solving Sylvester *** authors transform solving Sylvester equations into a distributed optimization problem,unifying all eight standard distributed matrix *** the authors propose a distributed algorithm to find the least squares solution and achieve an explicit linear convergence *** results are obtained by carefully choosing the step-size of the algorithm,which requires particular information of data and Laplacian *** avoid these centralized quantities,the authors further develop a distributed scaling technique by using local information *** a result,the proposed distributed algorithm along with the distributed scaling design yields a universal method for solving Sylvester equations over a multi-agent network with the constant step-size freely chosen from configurable ***,the authors provide three examples to illustrate the effectiveness of the proposed algorithms.

关键词： distributed optimization least squares solution linear convergence rate step-size interval Sylvester equation

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distributed optimization for Model Predictive Control of Linear-Dynamic Networks

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IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART A-SYSTEMS AND HUMANS 2009年第6期39卷 1331-1338页

作者： Camponogara, Eduardo de Oliveira, Lucas Barcelos Univ Fed Santa Catarina Dept Automat & Syst Engn BR-88040900 Florianopolis SC Brazil

A linear-dynamic network consists of a directed graph in which the nodes represent subsystems and the arcs model dynamic couplings. The local state of each subsystem evolves according to discrete linear dynamics that depend on the local state, local control signals, and control signals of upstream subsystems. Such networks appear in the model predictive control (MPC) of geographically distributed systems such as urban traffic networks and electric power grids. In this correspondence, we propose a decomposition of the quadratic MPC problem into a set of local subproblems that are solved iteratively by a network of agents. A distributed algorithm based on the method of feasible directions is developed for the agents to iterate toward a solution of the subproblems. The local iterations require relatively low effort to arrive at a solution but at the expense of high communication among neighboring agents and with a slower convergence rate.

关键词： distributed optimization linear systems model predictive control (MPC) urban traffic control

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distributed optimization over directed graphs with row stochasticity and constraint regularity

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AUTOMATICA 2019年 102卷 94-104页

作者： Mai, Van Sy Abed, Eyad H. Univ Maryland College Pk MD 20742 USA

This paper deals with an optimization problem over a network of agents, where the cost function is the sum of the individual (possibly nonsmooth) objectives of the agents and the constraint set is the intersection of local constraints. Most existing methods employing subgradient and consensus steps for solving this problem require the weight matrix associated with the network to be column stochastic or even doubly stochastic, conditions that can be hard to arrange in directed networks. Moreover, known convergence analyses for distributed subgradient methods vary depending on whether the problem is unconstrained or constrained, and whether the local constraint sets are identical or nonidentical and compact. The main goals of this paper are: (i) removing the common column stochasticity requirement;(ii) relaxing the compactness assumption, and (iii) providing a unified convergence analysis. Specifically, assuming the communication graph to be fixed and strongly connected and the weight matrix to (only) be row stochastic, a distributed projected subgradient algorithm and a variation of this algorithm are presented to solve the problem for cost functions that are convex and Lipschitz continuous. The key component of the algorithms is to adjust the subgradient of each agent by an estimate of its corresponding entry in the normalized left Perron eigenvector of the weight matrix. These estimates are obtained locally from an augmented consensus iteration using the same row stochastic weight matrix and requiring very limited global information about the network. Moreover, based on a regularity assumption on the local constraint sets, a unified analysis is given that can be applied to both unconstrained and constrained problems and without assuming compactness of the constraint sets or an interior point in their intersection. Further, we also establish an upper bound on the absolute objective error evaluated at each agent's available local estimate under a nonincreasing step s

关键词： distributed optimization Subgradient method Multiagent systems Communication networks Directed graphs

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distributed optimization for a class of uncertain MIMO nonlinear multi-agent systems with arbitrary relative degree

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INFORMATION SCIENCES 2020年 506卷 58-77页

作者： Li, Ranran Yang, Guang-Hong Northeastern Univ Coll Informat Sci & Engn Shenyang 110819 Liaoning Peoples R China Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang 110819 Liaoning Peoples R China

The paper is concerned with the distributed optimization problem (DOP) for a class of uncertain multi-input-multi-output (MIMO) nonlinear multi-agent systems with arbitrary relative degree. The target is to design distributed control laws such that the outputs of the agent systems converge to a consensus value and on which the sum of the local cost functions is minimized. By introducing pseudo gradient technique, internal model technique and adaptive control technique, a novel state based distributed control law is firstly constructed. An incremental type Lyapunov function based approach is presented to show that the proposed DOP is solved by the state based control law without requiring the eigenvalue information of Laplacian matrix. By further introducing distributed high-gain observer technique, an output based distributed control law is constructed and by which the DOP is solved under some mild assumption. The proposed control laws are validated on a group of Euler-Lagrange systems, a group of robot manipulators with flexible joints and a group of Chua circuit systems. The simulation results illustrate the effectiveness of the proposed methods. (C) 2019 Elsevier Inc. All rights reserved.

关键词： distributed optimization Multi-agent system Uncertain nonlinear system Arbitrary relative degree Pseudo gradient

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distributed optimization of Hierarchical Small Cell Networks: A GNEP Framework

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IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS 2017年第2期35卷 249-264页

作者： Wang, Jiaheng Guan, Wei Huang, Yongming Schober, Robert You, Xiaohu Southeast Univ Natl Mobile Commun Res Lab Nanjing 210096 Jiangsu Peoples R China Friedrich Alexander Univ Erlangen Nuremberg Inst Digital Commun D-91058 Erlangen Germany

Deployment of small cell base stations (SBSs) over-laying the coverage area of a macrocell BS (MBS) results in a two-tier hierarchical small cell network. Cross-tier and inter-tier interference not only jeopardize primary macrocell communication but also limit the spectral efficiency of small cell communication. This paper focuses on distributed interference management for downlink small cell networks. We address the optimization of transmit strategies from both the game theoretical and the network utility maximization (NUM) perspectives and show that they can be unified in a generalized Nash equilibrium problem (GNEP) framework. Specifically, the small cell network design is first formulated as a GNEP, where the SBSs and MBS compete for the spectral resources by maximizing their own rates while satisfying global quality of service (QoS) constraints. We analyze the GNEP via variational inequality theory and propose distributed algorithms, which only require the broadcasting of some pricing information, to achieve a generalized Nash equilibrium (GNE). Then, we also consider a nonconvex NUM problem that aims to maximize the sum rate of all BSs subject to global QoS constraints. We establish the connection between the NUM problem and a penalized GNEP and show that its stationary solution can be obtained via a fixed point iteration of the GNE. We propose GNEP-based distributed algorithms that achieve a stationary solution of the NUM problem at the expense of additional signaling overhead and complexity. The convergence of the proposed algorithms is proved and guaranteed for properly chosen algorithm parameters. The proposed GNEP framework can scale from a QoS constrained game to an NUM design for small cell networks by trading off signaling overhead and complexity.

关键词： distributed optimization game theory generalized Nash equilibrium problem network utility maximization small cell network variational inequality

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distributed optimization Based on Graph Filter for Ensuring Invariant Simplification of High-Volume Point Cloud

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IEEE TRANSACTIONS ON CONSUMER ELECTRONICS 2023年第3期69卷 608-621页

作者： Zhou, Xuhong Zeng, Yan Wu, Zhou Liu, Jiepeng Chongqing Univ Sch Civil Engn Chongqing 400045 Peoples R China Chongqing Univ Sch Automat Chongqing 400045 Peoples R China

In many consumer electronic applications, three-dimensional (3D) point cloud data (PCD) is commonly generated in data-driven models. The expensive burden of computation and storage would be brought out, as the point number reaches billions in the large-scale augmented or virtual reality models. Based on the concept of graph signal, a new PCD simplification approach is developed to handle the high-volume PCD and develop a feature-controllable mechanism. In particular, PCD simplification is modeled as an optimization problem with the hybridization of contour and planar feature items. To reduce the complexity of computation, invariant decomposition is proposed, and distributed optimization is developed for the feature controllable PCD simplification. The self-adoption scheme is adopted to improve the convergence rate. Verification experiments and applications on different scenarios demonstrate the effectiveness and feasibility of the proposed simplification approach.

关键词： Point cloud distributed optimization simplification graph signal processing virtual reality

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distributed optimization approaches for emerging power systems operation: A review

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ELECTRIC POWER SYSTEMS RESEARCH 2017年 144卷 127-135页

作者： Wang, Yamin Wang, Shouxiang Wu, Lei Clarkson Univ ECE Dept Potsdam NY 13699 USA Tianjin Univ Minist Educ Key Lab Smart Grid Tianjin 300072 Peoples R China

Independent system operators (ISO) and regional transmission organizations (RTO) adopt centralized optimization approaches for the optimal operation of power systems, which collect all required information and perform centralized operation decisions at the central controller. As the size of power systems expends and more flexible and distributed resources from the demand side are being involved in power systems, such a centralized framework raises computation and communication concerns. distributed optimization, as an alternative approach to solve challenges of the centralized optimization mechanism, has attracted increasing attention recently. This paper reviews existing works on distributed optimization for power systems operation. We first discuss various distributed optimization algorithms that have been studied for power systems operation, followed by a detailed literature review on adopting such distributed algorithms for major power systems operation applications including distributed economic dispatch (ED), distributed AC-optimal power flow (OPF), distributed Unit commitment (UC), and other distributed applications. The advantages and barriers of applying each distributed algorithm in practice are discussed. Since the applications of distributed algorithms in practical cases largely rely on the high performance computing (HPC) platform, the application of HPC techniques on power system operation problems is also reviewed. Future research needs for effectively and efficiently promoting the practical deployment of such distributed optimization approaches in emerging power systems are identified. (C) 2016 Elsevier B.V. All rights reserved.

关键词： distributed optimization distributed economic dispatch distributed optimal power flow distributed unit commitment

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distributed optimization Algorithm for Discrete-Time Heterogeneous Multi-Agent Systems With Nonuniform Stepsizes

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IEEE ACCESS 2019年 7卷 87303-87312页

作者： Mo, Lipo Li, Jingyi Huang, Jian Beijing Technol & Business Univ Sch Math & Stat Beijing 100048 Peoples R China Beihang Univ Sch Math & Syst Sci Beijing 100083 Peoples R China Univ Coll Cork Sch Math Sci Cork T12 XF62 Ireland

This paper is devoted to the distributed optimization problem of heterogeneous multi-agent systems, where the communication topology is jointly strongly connected and the dynamics of each agent is the first-order or second-order integrator. A new distributed algorithm is first designed for each agent based on the local objective function and the local neighbors' information that each agent can access. By a model transformation, the original closed-loop system is converted into a time-varying system and the system matrix of which is a stochastic matrix at any time. Then, by the properties of the stochastic matrix, it is proven that all agents' position states can converge to the optimal solution of a team objective function provided the union communication topology is strongly connected. Finally, the simulation results are provided to verify the effectiveness of the distributed algorithm proposed in this paper.

关键词： distributed optimization multi-agent systems heterogeneous nonuniform stepsizes

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distributed optimization for Two Types of Heterogeneous Multiagent Systems

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021年第3期32卷 1314-1324页

作者： Sun, Chao Ye, Maojiao Hu, Guoqiang Nanyang Technol Univ Sch Elect & Elect Engn Singapore 639798 Singapore Nanjing Univ Sci & Technol Sch Automat Nanjing 210094 Peoples R China

This article studies distributed optimization algorithms for heterogeneous multiagent systems under an undirected and connected communication graph. Two types of heterogeneities are discussed. First, we consider a class of multiagent systems composed of both continuous-time dynamic agents and discrete-time dynamic agents. The agents coordinate with each other to minimize a global objective function that is the sum of their local convex objective functions. A distributed subgradient method is proposed for each agent in the network. It is proved that driven by the proposed updating law, the agents' position states converge to an optimal solution of the optimization problem, provided that the subgradients of the objective functions are bounded, the step size is not summable but square summable, and the sampling period is bounded by some constant. Second, we consider a class of multiagent systems composed of both first-order dynamic agents and second-order dynamic agents. It is proved that the agents' position states converge to the unique optimal solution if the objective functions are strongly convex, continuously differentiable, and the gradients are globally Lipschitz. Numerical examples are given to verify the conclusions.

关键词： optimization Multi-agent systems Vehicle dynamics Power system dynamics Linear programming Heuristic algorithms Sun distributed optimization heterogeneous system hybrid system multiagent system subgradient descent

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