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基于Actor-Critic算法的分数阶多自主体系统最优主-从一致性控制

马丽新 刘晨 刘磊

马丽新,刘晨,刘磊. 基于Actor-Critic算法的分数阶多自主体系统最优主-从一致性控制 [J]. 应用数学和力学,2022,43(1):1-11 doi: 10.21656/1000-0887.420124
引用本文: 马丽新,刘晨,刘磊. 基于Actor-Critic算法的分数阶多自主体系统最优主-从一致性控制 [J]. 应用数学和力学,2022,43(1):1-11 doi: 10.21656/1000-0887.420124
MA Lixin, LIU Chen, LIU Lei. Optimal Leader-Following Consensus of Fractional-Order Multi-Agent Systems Based on Actor-Critic Algorithm[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.420124
Citation: MA Lixin, LIU Chen, LIU Lei. Optimal Leader-Following Consensus of Fractional-Order Multi-Agent Systems Based on Actor-Critic Algorithm[J]. Applied Mathematics and Mechanics. doi: 10.21656/1000-0887.420124

基于Actor-Critic算法的分数阶多自主体系统最优主-从一致性控制

doi: 10.21656/1000-0887.420124
基金项目: 国家自然科学基金(面上项目)(61773152);中央高校基本科研业务费(2019B19214)
详细信息
    作者简介:

    马丽新(1997—),女,硕士生(E-mail:1623406486@qq.com)

    刘晨(1993—),男,博士生(E-mail:liuchen_hhu@163.com)

    刘磊(1983—),男,副教授,博士生导师(通讯作者. E-mail:liulei_hust@163.com)

  • 中图分类号: TP273; O232

Optimal Leader-Following Consensus of Fractional-Order Multi-Agent Systems Based on Actor-Critic Algorithm

  • 摘要: 研究了分数阶多自主体系统的最优主-从一致性问题。在考虑控制器周期间歇的前提下,将分数阶微分的一阶近似逼近式、事件触发机制和强化学习中的Actor-Critic算法有机整合,设计了基于周期间歇事件触发策略的强化学习算法结构。最后,通过数值仿真实验证明该算法的可行性和有效性。
  • 图  1  多自主体系统网络拓扑图

    Figure  1.  The net topology of the multi-agent system

    图  2  无控制器作用时各自主体的状态轨迹

    Figure  2.  State trajectories of each agent without controller

    图  3  各自主体的状态轨迹

    Figure  3.  State trajectories of each agent

    图  4  $\|\boldsymbol{e}\left(t\right)\| $及触发阈值变化曲线

    Figure  4.  The error and trigger threshold

    图  5  周期间歇事件触发时刻分布

    Figure  5.  Event-trigger moment distribution of periodic intermittent

    图  6  多自主体系统网络拓扑图

    Figure  6.  The net topology of the multi-agent system

    图  7  无控制器作用时各自主体的状态轨迹

    Figure  7.  State trajectories of each agent without controller

    图  8  各自主体的状态轨迹

    Figure  8.  State trajectories of each agent

    图  9  $ \left|\left|\mathit{e}\left(t\right)\right|\right| $及触发阈值变化曲线

    Figure  9.  The error and trigger threshold

    图  10  事件触发时刻分布

    Figure  10.  Event-trigger moment distribution

    图  11  文献[16]控制器下各自主体的状态轨迹图

    Figure  11.  State trajectories of each agent under ref. [16]

    图  12  $ \left|\left|\mathit{e}\left(t\right)\right|\right| $及触发阈值变化曲线

    Figure  12.  The error $ \left|\left|\mathit{e}\left(t\right)\right|\right| $ and trigger threshold

    图  13  事件触发时刻分布

    Figure  13.  Event-trigger moment distribution

    表  1  网络参数设置

    Table  1.   Values of networks’ parameters

    parametermeaningvalue
    $ {\beta }_{c1} $learning rate of the critic network0.1
    $ {\beta }_{a1} $learning rate of the actor network0.1
    $ {T}_{c,\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}} $threshold for the critic network$ {10^{ - 10}} $
    $ {T}_{a,\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{o}\mathrm{r}} $threshold for the actor network$ {10^{ - 10}} $
    $ {N}_{c1} $number of hidden nodes in the critic network5
    $ {N}_{a1} $number of hidden nodes in the critic network3
    $ {\psi }_{c}\left(\cdot \right) $activation function of the critic network$ \mathrm{tan}\mathrm{h}\left(\cdot \right) $
    $ {\psi }_{a}\left(\cdot \right) $activation function of the critic network$ \mathrm{tan}\mathrm{h}\left(\cdot \right) $
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出版历程
  • 收稿日期:  2021-05-07
  • 录用日期:  2021-05-07
  • 修回日期:  2021-12-03
  • 网络出版日期:  2021-12-17

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