基于固定时间的二阶智能体分布式优化算法

时侠圣; 林志赟

doi:10.13700/j.bh.1001-5965.2022.0060

基于固定时间的二阶智能体分布式优化算法

doi: 10.13700/j.bh.1001-5965.2022.0060

时侠圣¹,
林志赟^2, ,

1.
中国矿业大学信息与控制工程学院，徐州 221116
2.
南方科技大学电子与电气工程系，深圳 518055

基金项目: 中央高校基本科研业务费(2021QN1052)

详细信息

通讯作者:
E-mail：linzy@sustech.edu.cn

中图分类号: TP13
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- 文章访问数: 140
- HTML全文浏览量: 37
- PDF下载量: 22
- 被引次数: 0
出版历程
- 收稿日期: 2022-01-29
- 录用日期: 2022-03-11
- 网络出版日期: 2022-04-02
- 整期出版日期: 2023-11-30

Fixed-time distributed convex algorithm over second-order multi-agent systems under bounded disturbances

SHI Xiasheng¹,
LIN Zhiyun^{2
, ,}

1.
School of Information and Control Engineering，China University of Mining and Technology，Xuzhou 221116，China
2.
Department of Electrical and Electronic Engineering，Southern University of Science and Technology，Shenzhen 518055，China

Funds: Fundamental Research Funds for the Central Universities (2021QN1052)

More Information

Corresponding author: E-mail：linzy@sustech.edu.cn

摘要

摘要:
对有界扰动下二阶多智能系统的分布式凸优化问题进行了研究。分布式优化问题旨在通过智能体间信息交互实现全局成本函数一致最优。基于固定时间理论，提出一种在固定时间内收敛到最优解的算法。为防止智能体泄露局部成本函数的梯度信息，当邻居成本函数二阶导差值有界时，通过平均一致性在固定时间内利用跟踪技术实现平均梯度信息获取。设计一种自适应算法以避免上述全局信息的假设。进一步地，引入符号函数项实现算法对智能体外部有界扰动的自适应抑制。最后给出收敛性证明和仿真案例。
- 有界扰动 /
- 固定时间 /
- 二阶系统 /
- 自适应控制 /
- 分布式优化
Abstract:
In this paper, the convex optimization problem of the distributed second-order multi-agent systems under bounded disturbances has been studied. The distributed optimization problem aims to optimize the global cost function through local information communication. Based on the fixed-time theory, the proposed algorithm converges to the optimal solution within a fixed time. Additionally, the average consensus tracking technique obtains each agent's gradient information at a predetermined period when the second derivative difference of the cost function between surrounding agents is bounded in order to prevent the local information leakage of each agent. Then, an adaptive algorithm is provided to avoid the utilization of global information. Furthermore, the external bounded disturbance is adaptively suppressed by the signal function. Finally, the converge proof and some simulation examples are provided.
- bounded disturbance /
- fixed-time /
- second-order /
- adaptive control /
- distributed optimization

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图 1 算法流程

Figure 1. Algorithm procedure

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图 2 式（8）作用下智能体状态轨迹

Figure 2. Trajectory of agent under Eq.(8)

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图 3 式（8）与已有算法的收敛速度对比

Figure 3. Convergence rate comparison between Eq.(8) and existing algorithms

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图 4 不同控制参数γ下式(8)和文献[18]中算法收敛速度对比

Figure 4. Convergence comparison between Eq.(8) and algorithms in Ref.[18] under different control parameters γ

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图 5 式(6)和式(30)作用下的收敛速度对比

Figure 5. Convergence rate comparison under Eq. (6) and Eq. (30)

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图 6 式(29)作用下智能体状态轨迹

Figure 6. Trajectory of agent under Eq. (29)

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图 7 式（29）作用下的收敛速度

Figure 7. Convergence rate under Eq. (29)

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图 8 式(31)作用下智能体状态轨迹

Figure 8. Trajectory of agent under Eq. (31)

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图 9 式(31)作用下的收敛速度

Figure 9. Convergence rate under Eq. (31)

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