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

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

1.
东北大学流程工业综合自动化国家重点实验室沈阳 110819

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

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出版历程
- 网络出版日期: 2022-10-27

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

1.
State Key laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819

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

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.
- 多智能体网络 /
- 分布式优化 /
- 加权平衡有向图 /
- 耦合不等式约束
Abstract: In this paper, we study a class of distributed optimization problems whose objective is to minimize the value of a nonsmooth global cost function while satisfying the coupling inequality constraint and the local feasible set constraint. First, we extend the original distributed continuous-time projection algorithm with linear algebraic theory analysis to design an algorithm for strongly connected weighted balanced directed communication network topology graphs. Second, under the assumption that the local cost function and the coupled inequality constraint function are non-smooth convex functions, we use the Moreau-Yosida function regularization to make the objective function and the constraint function approximately smooth and differentiable. Then, the Lyapunov function is constructed according to the distributed continuous time projection algorithm of the strongly connected weighted equilibrium directed graph, the equilibrium solution under this algorithm is proved to be the optimal solution of the distributed optimization problem, as well as the convergence analysis of the algorithm is performed. Finally, the effectiveness of the algorithm is verified by numerical simulation.
- Multi-agent networks /
- distributed optimization /
- weight-balanced digraphs /
- coupled inequality constraints

HTML全文

图 1 加权平衡有向交互图.

Fig. 1 Weight-balanced directed interaction graph.

下载: 全尺寸图片幻灯片

图 2 状态$ x_{i} $的轨迹图.

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

下载: 全尺寸图片幻灯片

图 3 状态$ \tau_{i} $的轨迹图.

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

下载: 全尺寸图片幻灯片

图 4 状态$ \mu_{i} $的轨迹图.

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

下载: 全尺寸图片幻灯片

图 5 状态$ s_{i} $的轨迹图.

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

下载: 全尺寸图片幻灯片

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