集合约束下多智能体系统分布式固定时间优化控制

陈刚; 李志勇

doi:10.16383/j.aas.c190416

集合约束下多智能体系统分布式固定时间优化控制

doi: 10.16383/j.aas.c190416

陈刚^1,,
李志勇^1,

1.
重庆大学自动化学院重庆 400044

基金项目: 国家自然科学基金(61673077)资助

详细信息

作者简介:
陈刚：重庆大学自动化学院教授. 2006年获得浙江大学控制科学与工程博士学位. 主要研究方向为分布式协调控制,分布式优化控制, 多智能体系统. 本文通信作者.E-mail: chengang@cqu.edu.cn

李志勇：重庆大学自动化学院博士研究生. 2018年获得重庆大学控制科学与工程硕士学位. 主要研究方向为分布式优化与控制. E-mail: lizhiyong@cqu.edu.cn

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出版历程
- 收稿日期: 2019-05-29
- 录用日期: 2019-09-02
- 网络出版日期: 2022-08-10
- 刊出日期: 2022-09-16

Distributed Fixed-time Optimization Control for Multi-agent Systems With Set Constraints

CHEN Gang^1
,,
LI Zhi-Yong^1
,

1.
College of Automation, Chongqing University, Chongqing 400044

Funds: Supported by National Natural Science Foundation of China (61673077)

More Information

Author Bio:
CHEN Gang　Professor at the College of Automation, Chongqing University. He received his Ph.D. degree in control science and technology from Zhejiang University in 2006. His research interest covers distributed cooperative control, distributed optimization control, and multi-agent systems. Corresponding author of this paper

LI Zhi-Yong　Ph.D. candidate at the College of Automation, Chongqing University. He received his master degree in control science and engineering from Chongqing University in 2018. His research interest covers distributed optimization and control

摘要

摘要: 本文研究一类具有状态约束的多智能体系统优化控制问题, 提出了一种具有固定时间收敛特性的分布式优化控制算法. 该控制算法由局部投影模块、一致性模块和梯度模块构成, 其中局部投影模块确保智能体的状态在固定时间内收敛到局部约束集合, 基于时变增益的一致性模块实现所有智能体的状态在固定时间内收敛到一致值, 基于时变增益的梯度模块实现智能体的状态在固定时间内收敛到最优解. 利用凸优化理论和固定时间李雅普诺夫理论, 分析了算法的固定时间收敛特性. 算法收敛时间的上界值不依赖系统的初始条件, 因而可以根据任务需求来预先设计收敛时间. 最后通过数值仿真验证了理论结果的有效性.
- 分布式优化 /
- 多智能体系统 /
- 集合约束 /
- 梯度法 /
- 固定时间收敛
Abstract: This paper studies a class of optimization problem with local constraints for multi-agent systems, and a distributed optimization algorithm with fixed-time convergence is proposed. The proposed distributed controller consists of local projection module, consensus module and gradient module. The local projection module is used to ensure that the states converge to the local constraint set in the fixed time; the consensus module with time-varying gain guarantees the fixed-time state consensus; the gradient module with time-varying gain ensures the states converge to the optimal solution in fixed-time. The fixed-time convergence of the proposed algorithm is analyzed by using the convex optimization and the fixed-time Lyapunov theory. Since the upper bound of convergence time for the proposed algorithm does not depend on the initial condition, it possible to predesign the convergence time according to the task requirements. Finally, numerical simulations verify the effectiveness of the theoretical results.
- Distributed optimization /
- multiagent systems /
- set constraints /
- gradient method /
- fixed-time convergence

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图 1 相同局部集合约束下优化问题(2)的仿真结果

Fig. 1 Simulation results for optimization problem (2) with a common constraint set

下载: 全尺寸图片幻灯片

图 2 不同局部集合约束下优化问题(2)的仿真结果

Fig. 2 Simulation results for optimization problem (2) with nonidentical local constraint sets

下载: 全尺寸图片幻灯片

图 3 几种算法在不同初始条件下状态误差范数$\|{\pmb X}-{\pmb X}^*\|_2$ 随时间的变化

Fig. 3 The state errors norm of several algorithms $\|{\pmb X}-{\pmb X}^*\|_2$ with time for various initial conditions

下载: 全尺寸图片幻灯片

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