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基于连续时间的二阶多智能体分布式资源分配算法

时侠圣 杨涛 林志赟 王雪松

时侠圣,  杨涛,  林志赟,  王雪松.  基于连续时间的二阶多智能体分布式资源分配算法.  自动化学报,  2021,  47(8): 2050−2060 doi: 10.16383/j.aas.c200968
引用本文: 时侠圣,  杨涛,  林志赟,  王雪松.  基于连续时间的二阶多智能体分布式资源分配算法.  自动化学报,  2021,  47(8): 2050−2060 doi: 10.16383/j.aas.c200968
Shi Xia-Sheng,  Yang Tao,  Lin Zhi-Yun,  Wang Xue-Song.  Distributed resource allocation algorithm for second-order multi-agent systems in continuous-time.  Acta Automatica Sinica,  2021,  47(8): 2050−2060 doi: 10.16383/j.aas.c200968
Citation: Shi Xia-Sheng,  Yang Tao,  Lin Zhi-Yun,  Wang Xue-Song.  Distributed resource allocation algorithm for second-order multi-agent systems in continuous-time.  Acta Automatica Sinica,  2021,  47(8): 2050−2060 doi: 10.16383/j.aas.c200968

基于连续时间的二阶多智能体分布式资源分配算法

doi: 10.16383/j.aas.c200968
基金项目: 国家自然科学基金重大项目(61991403, 61991400), 国家自然科学基金(61976215, 61673344)资助
详细信息
    作者简介:

    时侠圣:中国矿业大学信息与控制工程学院讲师. 主要研究方向为分布式协同优化和网络化系统. E-mail: shixiasheng@cumt.edu.cn

    杨涛:东北大学流程工业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. 本文通信作者. E-mail: yangtao@email.neu.edu.cn

    林志赟:杭州电子科技大学自动化学院人工智能研究院教授. 主要研究方向为多智能体系统, 机器人与无人系统和网络化系统. E-mail: linz@hdu.edu.cn

    王雪松:中国矿业大学信息与控制工程学院教授. 主要研究方向为机器学习, 人工智能, 复杂系统优化及控制. E-mail: wangxuesongcumt@163.com

Distributed Resource Allocation Algorithm for Second-order Multi-agent Systems in Continuous-time

Funds: Supported by Major Program of the National Natural Science Foundation of China (61991403, 61991400), National Natural Science Foundation of China (61976215, 61673344)
More Information
    Author Bio:

    SHI Xia-Sheng Lecturer at the School of Information and Control Engineering, China University of Mining and Technology. His research interest covers distributed cooperative optimization and network system

    YANG Tao Professor at the State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University. His research interest covers industrial artificial intelligence, cyber physical system, distributed collaborative control and optimization. Corresponding author of this paper

    LIN Zhi-Yun Professor at the Intelligence, Automation School, Hangzhou Dianzi University. His research interest covers multi-agent systems, unmanned robotic systems, and network systems

    WANG Xue-Song Professor at the School of Information and Control Engineering, China University of Mining and Technology. His research interest covers machine learning, artificial intelligence, and complex system optimization and control

  • 摘要:

    针对二阶多智能体系统中的分布式资源分配问题, 本文设计两种连续时间算法. 基于KKT (Karush−Kuhn−Tucker, 卡罗需−库恩−塔克)优化条件, 第一种控制算法利用节点局部不等式及其梯度信息来约束节点状态. 与上述梯度方法不同, 第二种控制算法包括一致性梯度下降法和固定时间收敛映射算子, 其中固定时间收敛映射算子确保算法的节点状态在固定时间收敛到局部约束集, 一致性梯度下降法目的是确保节点迭代到资源分配问题最优解. 两种控制算法都对状态无初始值约束, 且控制参数都是常数. 利用凸优化理论和固定时间李雅普诺夫方法, 分别分析了上述控制策略在有向平衡网络条件下的渐近和指数收敛性. 最后通过数值仿真验证了所设计算法在一维和高维资源分配问题的有效性.

  • 图  1  案例1中算法(8)的各发电机曲线图

    Fig.  1  The trajectories of each generator by algorithm (8) in case 1

    图  2  案例1中算法(9)的各发电机曲线图

    Fig.  2  The trajectories of each generator by algorithm (9) in case 1

    图  3  基于案例1数据的算法性能对比

    Fig.  3  The comparison between the existence algorithms and ours based on case 1

    图  4  案例2中算法 (8)的各节点仿真结果轨迹

    Fig.  4  The trajectories of each agent by algorithm (8) in case 2

    图  5  案例2中算法 (9)各节点仿真结果轨迹

    Fig.  5  The trajectories of each agent by algorithm (9) in case 2

    图  6  基于案例2数据的算法性能对比

    Fig.  6  The comparison between the existence algorithms and ours based on case 2

    图  7  案例3中各发电单元的通信链路

    Fig.  7  The communication links of each generator in case 3

    图  8  案例3中算法 (8)的各节点仿真结果轨迹

    Fig.  8  The trajectories of each agent by algorithm (8) in case 3

    图  9  案例3中算法 (9)各节点仿真结果轨迹

    Fig.  9  The trajectories of each agent by algorithm (9) in case 3

    图  10  案例3中算法 (8)和 (9)的收敛速度比较

    Fig.  10  The convergence rate comparison between algorithms (8) and (9) in case 3

    表  1  案例1各节点参数

    Table  1  System parameters in case 1

    Agent $a_{i1}$ $a_{i2}$ $a_{i3}$ 功率约束 $d_i$ $x_i(0)$
    1 2 3 0.5 $[20,40]$ 45 40
    2 1 4 1.5 $[25,35]$ 40 24
    3 0.5 5 3 $[35,50]$ $25$ 35
    4 1.5 2 1 $[25,45]$ 35 45
    5 1 3.5 2.5 $[30,47]$ 30 28
    6 1.5 4.5 2 $[28,42]$ 40 50
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  • 收稿日期:  2020-11-22
  • 录用日期:  2021-03-02
  • 网络出版日期:  2021-03-29
  • 刊出日期:  2021-08-20

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