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基于事件触发的分布式优化算法

杨涛 徐磊 易新蕾 张圣军 陈蕊娟 李渝哲

杨涛, 徐磊, 易新蕾, 张圣军, 陈蕊娟, 李渝哲. 基于事件触发的分布式优化算法. 自动化学报, 2021, 47(x): 1−11 doi: 10.16383/j.aas.c200838
引用本文: 杨涛, 徐磊, 易新蕾, 张圣军, 陈蕊娟, 李渝哲. 基于事件触发的分布式优化算法. 自动化学报, 2021, 47(x): 1−11 doi: 10.16383/j.aas.c200838
Yang Tao, Xu Lei, Yi Xin-Lei, Zhang Sheng-Jun, Chen Rui-Juan, Li Yu-Zhe. Event-triggered distributed optimization algorithms. Acta Automatica Sinica, 2021, 47(x): 1−11 doi: 10.16383/j.aas.c200838
Citation: Yang Tao, Xu Lei, Yi Xin-Lei, Zhang Sheng-Jun, Chen Rui-Juan, Li Yu-Zhe. Event-triggered distributed optimization algorithms. Acta Automatica Sinica, 2021, 47(x): 1−11 doi: 10.16383/j.aas.c200838

基于事件触发的分布式优化算法

doi: 10.16383/j.aas.c200838
基金项目: 国家自然科学基金委重大项目资助, 批准号(61991400), (61991403), (61991404)&(61890924)
详细信息
    作者简介:

    杨涛:东北大学流程工业综合自动化国家重点实验室教授. 主要研究方向为工业人工智能、信息物理系统、分布式协同控制和优化. E-mail: yangtao@mail.neu.edu.cn

    徐磊: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控制及优化、网络化系统和马尔可夫跳变系统. E-mail: 2010345@stu.neu.edu.cn

    易新蕾:瑞典皇家理工学院电气工程与计算机科学学院博士后. 主要研究方向为在线优化、分布式优化和事件驱动控制. E-mail: xinleiy@kth.se

    张圣军:北德州大学电气工程专业博士研究生. 主要研究方向为分布式优化, 统计学习和稀疏主成分分析. E-mail: ShengjunZhang@my.unt.edu

    陈蕊娟:华中科技大学人工智能与自动化学院博士研究生. 主要研究兴趣包括基于动力系统的优化算法的设计和理论分析. E-mail: ruijuancheni@hust.edu.cn

    李渝哲:东北大学流程工业综合自动化国家重点实验室教授. 主要研究方向为网络化系统, 信息物理系统, 人工智能与信息安全. 本文通信作者. E-mail: yuzheli@mail.neu.edu.cn

Event-triggered Distributed Optimization Algorithms

Funds: Supported by Major Program of National Natural Science Foundation of China (61991400), (61991403), (61991404)&(61890924)
More Information
    Author Bio:

    YANG Tao Professor at the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University. His research interests include industrial artificial intelligence, cyber physical system, distributed collaborative control and optimization

    XU Lei Ph. D. candidate State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University. His research interests include distributed control and optimization, network system, and Markovian jump systems

    YI Xin-Lei Postdoc at the School of Electrical Engineering and Computer Science, KTH Royal Institute of Technology, Sweden. His research interests include online optimization, distributed optimization, and event-triggered control

    ZHANG Sheng-Jun Ph. D. candidate at the Department of Electrical Engineering, University of North Texas. His current research interests include distributed optimization, statistical learning, and Sparse PCA

    CHEN Rui-Juan Ph. D. candidate at the School of Artificial Intelligence and Automation, Huazhong University of Science and Technology. Her research interests include the design and theoretical analysis of optimization algorithm based on dynamic system

    LI Yu-Zhe Professor at the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University. His research interests include network system, cyber physical system, artificial intelligence and information security. Corresponding author of this paper

  • 摘要: 本文研究了一类分布式优化问题, 其目标是通过局部信息交换使由局部成本函数之和构成的全局成本函数最小. 针对无向连通图, 我们提出了两种基于比例积分策略的分布式优化算法. 在局部成本函数可微且凸的条件下, 证明了所提算法渐近收敛到全局最小值点. 更进一步, 在局部成本函数具有局部Lipschitz梯度和全局成本函数关于全局最小值点是有限强凸的条件下, 证明了所提算法的指数收敛性. 此外, 为了避免智能体之间的连续通信和减少通信负担, 将所提的两种分布式优化算法与事件触发通信相结合, 提出了两种基于事件触发的分布式优化算法. 证明了提出的事件触发优化算法不存在Zeno行为, 并且在相应条件下保持了与连续通信下分布式优化算法一样的收敛性. 最后, 通过数值仿真验证了上述理论结果.
  • 图  1  不同算法中$\sum\nolimits_{i = 1}^{50}\|x_{i}(t)-x^{*}\|^{2}$的演化.

    Fig.  1  The state evolution of $\sum\nolimits_{i = 1}^{50}\|x_{i}(t)-x^{*}\|^{2}$ in various algorithms.

    图  2  算法(4)中智能体6, 16, 26, 36, 46的状态演化.

    Fig.  2  State evolutions of agents 6, 16, 26, 36, 46 of algorithm (4).

    图  3  算法(6)中智能体6, 16, 26, 36, 46的状态演化.

    Fig.  3  State evolutions of agents 6, 16, 26, 36, 46 of algorithm (6).

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  • 收稿日期:  2020-10-10
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