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基于有向图的分布式连续时间非光滑耦合约束凸优化分析

刘奕葶 马铭莙 付俊

刘奕葶, 马铭莙, 付俊. 基于有向图的分布式连续时间非光滑耦合约束凸优化分析. 自动化学报, 2022, 45(x): 1001−1010 doi: 10.16383/j.aas.c210808
引用本文: 刘奕葶, 马铭莙, 付俊. 基于有向图的分布式连续时间非光滑耦合约束凸优化分析. 自动化学报, 2022, 45(x): 1001−1010 doi: 10.16383/j.aas.c210808
Liu Yi-Ting, Ma Ming-Jun, Fu Jun. Distributed continuous-time non-smooth convex optimization analysis with coupled constraints over directed graphs. Acta Automatica Sinica, 2022, 45(x): 1001−1010 doi: 10.16383/j.aas.c210808
Citation: Liu Yi-Ting, Ma Ming-Jun, Fu Jun. Distributed continuous-time non-smooth convex optimization analysis with coupled constraints over directed graphs. Acta Automatica Sinica, 2022, 45(x): 1001−1010 doi: 10.16383/j.aas.c210808

基于有向图的分布式连续时间非光滑耦合约束凸优化分析

doi: 10.16383/j.aas.c210808
基金项目: 国家重点研发项目2018AAA0101603
详细信息
    作者简介:

    刘奕葶:东北大学流程工业综合自动化国家重点实验室硕士研究生.主要研究方向为分布式优化、耦合不等式路径约束. E-mail: 13840581163@163.com

    马铭莙:东北大学流程工业综合自动化国家重点实验室博士研究生.主要研究方向为分布式动态优化、切换系统控制. E-mail: mingjun_mmj@163.com

    付俊:东北大学流程工业综合自动化国家重点实验室教授.主要研究方向为动态优化、切换系统、非线性控制. 本文通信作者. E-mail: junfu@mail.neu.edu.cn

Distributed Continuous-Time Non-smooth Convex Optimization Analysis With Coupled Constraints Over Directed Graphs

Funds: Supported by National Key Research and Development Project of China(2018AAA0101603)
More Information
    Author Bio:

    LIU Yi-Ting Master Degree Candidate at the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University. Her research interest includes distributed optimization and coupled inequality path constraint

    MA Ming-jun is currently working toward the Ph.D. degree at the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University. Her research interest covers dynamic optimization of distributed systems and control of switched systems

    FU Jun Professor at the State Key Laboratory of Synthetical Automatic for Process Industries, Northeastern University. His research interest is dynamic optimization, switching system and nonlinear control. Corresponding author of this paper

  • 摘要: 本文研究了一类分布式优化问题, 其目标是在满足耦合不等式约束和局部可行集约束的情况下使非光滑全局代价函数值最小. 首先, 对原有的分布式连续时间投影算法进行拓展, 结合线性代数理论分析, 我们设计一个适用于强连通加权平衡有向通信网络拓扑图的算法. 其次, 在局部代价函数和耦合不等式约束函数是非光滑凸函数的假设条件下, 利用Moreau-Yosida函数正则化使目标函数和约束函数近似光滑可微. 然后, 根据强连通加权平衡有向图的分布式连续时间投影算法构造李雅普诺夫函数, 证明该算法下的平衡解是分布式优化问题最优解, 并对算法进行收敛性分析. 最后, 通过数值仿真验证了算法的有效性.
  • 图  1  加权平衡有向交互图.

    Fig.  1  Weight-balanced directed interaction graph.

    图  2  状态$ x_{i} $的轨迹图.

    Fig.  2  Trajectories graph of state $ x_{i} $.

    图  3  状态$ \tau_{i} $的轨迹图.

    Fig.  3  Trajectories graph of state $ \tau_{i} $.

    图  4  状态$ \mu_{i} $的轨迹图.

    Fig.  4  Trajectories graph of state $ \mu_{i} $.

    图  5  状态$ s_{i} $的轨迹图.

    Fig.  5  Trajectories graph of state $ s_{i} $.

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  • 网络出版日期:  2022-10-27

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