基于ODE-PDE的大规模多智能体系统有限时间编队

满景涛; 曾志刚; 盛银; 来金钢

doi:10.16383/j.aas.c240426

基于ODE-PDE的大规模多智能体系统有限时间编队

doi: 10.16383/j.aas.c240426 cstr: 32138.14.j.aas.c240426

满景涛^{1, 2,},
曾志刚^{1, 2,},
盛银^{1, 2,},
来金钢^{1, 2,}

1.
华中科技大学人工智能与自动化学院武汉 430074
2.
图像信息处理与智能控制教育部重点实验室武汉 430074

基金项目: 国家重点研发计划 (2021ZD0201300), 国家自然科学基金 (U1913602, 61936004, 624B2058), 国家自然科学基金创新群体项目 (61821003), 111计算智能与智能控制项目(B18024), 中央高校基本科研业务费 (2023JYCXJJ010)资助

详细信息

作者简介:
满景涛：华中科技大学人工智能与自动化学院博士研究生.分别于2017年和2021年获得河南科技大学信息工程学院学士和硕士学位.主要研究方向为随机系统、PDE系统和多智能体系统的控制策略设计与稳定性分析. E-mail: mjt546@163.com

曾志刚：华中科技大学人工智能与自动化学院教授. 2003年获华中科技大学系统分析与集成专业博士学位. 主要研究方向为泛函微分方程理论和右不连续微分方程理论, 以及它们在神经网络动力学、忆阻系统和联想记忆中的应用. 本文通信作者. E-mail: zgzeng@hust.edu.cn

盛银：华中科技大学人工智能与自动化学院副教授. 2018年获华中科技大学自动化学院系统分析与集成专业博士学位.主要研究方向为神经网络, 忆阻系统, 模糊逻辑. E-mail: shengyin90@163.com

来金钢：华中科技大学人工智能与自动化学院教授. 主要研究方向为面向微电网、分布式能源系统和信息物理社会系统的类脑智能和群体智能. E-mail: kklai@hust.edu.cn

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出版历程
- 收稿日期: 2024-06-29
- 录用日期: 2024-10-16
- 网络出版日期: 2025-02-11

Finite-time Formation of Large-scale Multi-agent Systems Based on an ODE-PDE Approach

MAN Jing-Tao^{1, 2
,},
ZENG Zhi-Gang^{1, 2
,},
SHENG Yin^{1, 2
,},
LAI Jin-Gang^{1, 2
,}

1.
School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074
2.
Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan 430074

Funds: Supported by National Key Research and Development Program of China (2021ZD0201300), National Natural Science Foundation of China (U1913602, 61936004, 624B2058), Innovation Group Project of the National Natural Science Foundation of China (61821003), the 111 Project on Computational Intelligence and Intelligent Control (B18024), and the Fundamental Research Funds for the Central Universities (2023JYCXJJ010)

More Information

Author Bio:
MAN Jing-Tao　Ph.D. candidate at the School of Artificial Intelligence and Automation, Huazhong University of Science and Technology. He received his bachelor and master degrees at the School of Information Engineering, Henan University of Science and Technology, in 2017 and 2021, respectively. His research interest covers the control design and stability analysis of stochastic systems, PDE systems and multi-agent systems

ZENG Zhi-Gang　Professor at the School of Artificial Intelligence and Automation, Huazhong University of Science and Technology. He received his Ph.D. degree in systems analysis and integration from Huazhong University of Science and Technology in 2003. His research interest covers the theory of functional differential equations and differential equations with discontinuous right-hand sides, and their applications to dynamics of neural networks, memristive systems, and associative memories. Corresponding author of this paper

SHENG Yin　Associate professor at the School of Artificial Intelligence and Automation, Huazhong University of Science and Technology. He received his Ph.D. degree in systems analysis and integration from the School of Automation, Huazhong University of Science and Technology in 2018. His research interest covers neural networks, memristive systems, and fuzzy logic

LAI Jin-Gang　Professor at the School of Artificial Intelligence and Automation, Huazhong University of Science and Technology. His research interest covers brain-inspired intelligence and swarm intelligence for microgirds, distributed renewable energy systems, and cyber-physical-social systems

摘要

摘要: 现有基于偏微分方程(Partial differential equation, PDE)的多智能体系统(Multi-agent system, MAS)编队控制方法要求智能体必须是密集分布的, 为了打破这一限制, 提出一种新的基于常微分−偏微分方程(Ordinary differential equation-partial differential equation, ODE-PDE)的分析方法, 以解决稀疏−密集混合分布的大规模异构MAS编队问题. 首先, 通过设计特定的通信协议, 并基于离散系统部分连续化方法, 将原始大量的异构MAS的ODE动力学模型转化为由一个PDE 和少数几个ODE耦合而成的ODE-PDE 模型. 为了更符合实际复杂场景, 将拓扑权值规定为半马尔科夫切换的, 且稀疏分布和密集分布智能体遵循不一致的切换规则. 其次, 针对无时滞和有时滞两种情形, 设计两种异步边界控制策略, 利用Lyapunov方法得到保证误差系统实际有限时间稳定的充分条件, 并得到停息时间和稳定阈值的计算规则. 最后, 两个广义的数值仿真进一步验证所提方法的有效性.
- 大规模异构多智能体系统 /
- 常微分−偏微分方程 /
- 实际有限时间编队 /
- 半马尔科夫切换拓扑 /
- 异步边界控制
Abstract: The existing formation control methods of multi-agent systems (MASs) based on partial differential equation (PDE) require that agents must be densely distributed. To break this limitation, this paper proposes a novel analysis method based on ordinary differential equation-partial differential equation (ODE-PDE), such that the formation problem of large-scale heterogeneous MASs with sparse and dense mixed distribution could be solved. First, the original numerous heterogeneous ODE dynamics models of MASs are transformed into an ODE-PDE model consisting of a PDE coupled to several ODEs through specific communication protocol design and partial continuum method of discrete systems. To match realistic complex scenes better, the topological weights are designed to be semi-Markov switched, and the switching rules followed by sparsely and densely distributed agents are inconsistent. Second, two asynchronous boundary control strategies are designed for delay-free and time-delayed cases, respectively. The Lyapunov method is used to obtain sufficient conditions to ensure the practically finite-time stability of the error system, and the calculation rules of the settling time and stability threshold are provided. Finally, two generalized numerical simulations further verify the effectiveness of the proposed approach.

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图 1 $\varrho(t)$, $\xi(t)$, $\tilde{\rho}(t)$的模态切换规则

Fig. 1 Mode switching rules of $\varrho(t)$, $\xi(t)$, and $\tilde{\rho}(t)$

下载: 全尺寸图片幻灯片

图 2 无时滞情形下MAS的运行轨迹

Fig. 2 Trajectories of MAS in delay-free case

下载: 全尺寸图片幻灯片

图 3 无时滞情形下单一空间维度上跟踪误差的状态轨迹

Fig. 3 State trajectories of tracking errors along a single spacial dimension in delay-free case

下载: 全尺寸图片幻灯片

图 4 无时滞情形下控制器(11)的状态轨迹

Fig. 4 State trajectories of controller (11) in delay-free case

下载: 全尺寸图片幻灯片

图 5 有时滞情形下MAS的运行轨迹

Fig. 5 Trajectories of MAS in time-delayed case

下载: 全尺寸图片幻灯片

图 6 有时滞情形下单一空间维度上跟踪误差的状态轨迹

Fig. 6 State trajectories of tracking errors along a single spacial dimension in time-delayed case

下载: 全尺寸图片幻灯片

图 7 有时滞情形下控制器(15)的状态轨迹

Fig. 7 State trajectories of controller (15) in time-delayed case

下载: 全尺寸图片幻灯片

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