基于控制障碍函数的多智能体系统安全控制

李博茜; 胡成; 朱松; 温世平

doi:10.16383/j.aas.c260074

基于控制障碍函数的多智能体系统安全控制

doi: 10.16383/j.aas.c260074 cstr: 32138.14.j.aas.c260074

李博茜^1,,
胡成^2,,
朱松^3,,
温世平^4,

1.
天津科技大学人工智能学院天津 300457
2.
新疆大学数学与系统科学学院乌鲁木齐 830017
3.
中国矿业大学数学学院徐州 221116
4.
深圳理工大学计算机科学与人工智能学院深圳 518055

基金项目: 国家自然科学基金(62506239, 62506048, 62366034)资助

详细信息

作者简介:
李博茜：天津科技大学人工智能学院讲师. 2025年获得澳大利亚悉尼科技大学工程与信息技术学院博士学位. 主要研究方向为多智能体系统控制. E-mail: liboqian@tust.edu.cn

胡成：新疆大学数学与系统科学学院教授. 2012年获得新疆大学数学与系统科学学院博士学位. 主要研究方向为微分方程, 神经网络. E-mail: hucheng@xju.edu.cn

朱松：中国矿业大学数学学院教授. 2010年获得华中科技大学系统工程系博士学位. 主要研究方向为随机系统稳定性, 神经网络. E-mail: songzhu@cumt.edu.cn

温世平：深圳理工大学计算机科学与人工智能学院教授. 2013年获得华中科技大学自动化学院博士学位. 主要研究方向为神经网络, 深度学习. 本文通信作者. E-mail: wenshiping@suat-sz.edu.cn

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出版历程
- 收稿日期: 2026-01-28
- 录用日期: 2026-03-21
- 网络出版日期: 2026-07-02
- 刊出日期: 2026-10-25

Safe Control of Multi-agent Systems via Control Barrier Functions

1.
College of Artificial Intelligence, Tianjin University of Science and Technology, Tianjin 300457
2.
College of Mathematics and System Science, Xinjiang University, Urumqi 830017
3.
School of Mathematics, China University of Mining and Technology, Xuzhou 221116
4.
Faculty of Computer Science and Artificial Intelligence, Shenzhen University of Advanced Technology, Shenzhen 518055

Funds: Supported by National Natural Science Foundation of China (62506239, 62506048, 62366034)

More Information

Author Bio:
LI Bo-Qian　Lecturer at the College of Artificial Intelligence, Tianjin University of Science and Technology. She received her Ph.D. degree from the Faculty of Engineering and Information Technology, University of Technology Sydney, Australia, in 2025. Her main research interest is control of multi-agent systems

HU Cheng　Professor at the College of Mathematics and System Science, Xinjiang University. He received his Ph.D. degree from the College of Mathematics and System Science, Xinjiang University in 2012. His research interests include differential equations and neural networks

ZHU Song　Professor at the School of Mathematics, China University of Mining and Technology. He received his Ph.D. degree from the Department of Systems Engineering, Huazhong University of Science and Technology in 2010. His research interests include stability of stochastic systems and neural networks

WEN Shi-Ping　Professor at the Faculty of Computer Science and Artificial Intelligence, Shenzhen University of Advanced Technology. He received his Ph.D. degree from the School of Automation, Huazhong University of Science and Technology in 2013. His research interests include neural networks and deep learning. Corresponding author of this paper

摘要

摘要: 研究多智能体系统的避碰安全控制问题, 目标是在尽量保持标称控制输入的同时, 确保任意智能体对之间始终保持安全距离. 针对二阶系统中安全约束函数相对度为2、传统控制障碍函数难以直接施加控制约束的问题, 引入高阶控制障碍函数框架构造碰撞避免条件, 并将其转化为最小侵入的二次规划控制器. 进一步, 利用安全约束项的对称性, 将原本耦合的不等式约束分解为各智能体可独立求解的线性约束. 在此基础上, 将所提方法推广至含有不确定项的多智能体系统, 设计鲁棒控制障碍函数及构建可实现的鲁棒控制器, 并证明了系统安全集的前向不变性. 数值仿真结果表明, 所提方法可使得系统保持安全性并维持良好的跟踪性能.
- 多智能体系统 /
- 控制障碍函数 /
- 避碰 /
- 鲁棒性
Abstract: This paper investigates the collision avoidance safety control for multi-agent systems, with the objective of guaranteeing a safe distance between any pair of agents while preserving nominal control input as much as possible. For second-order systems, the safety constraint functions have relative degree two, which makes it difficult to directly impose control constraints using classical control barrier functions. To address this issue, a high-order control barrier function framework is introduced to formulate collision avoidance conditions, which are then incorporated into a minimally invasive quadratic programming controller. Furthermore, by exploiting the symmetry of the safety constraints, the originally coupled inequality constraints are decomposed into linear constraints that can be solved independently by each agent. On this basis, the proposed approach is extended to uncertain multi-agent systems. Robust control barrier functions are designed to construct a realizable controller, and the forward invariance of the system safety set is rigorously proved. Numerical simulation results demonstrate that the proposed method can maintain system security while achieving satisfactory tracking performance.
- multi-agent system /
- control barrier function /
- collision avoidance /
- robustness

HTML全文

图 1 多智能体系统的通信拓扑

Fig. 1 Communication topology of multi-agent system

下载: 全尺寸图片幻灯片

图 2 在控制器(19)的作用下, 智能体对$ (i,\;j) $的一阶CBF$ h_{ij}^0(t) $和二阶CBF$ h_{ij}^1(t) $

Fig. 2 First-order CBF $ h_{ij}^0(t) $ and second-order CBF $ h_{ij}^1(t) $ of agent pair under controller (19)$ (i,\;j) $

下载: 全尺寸图片幻灯片

图 3 编队追踪误差$ \|e_x(t)\| $和速度追踪误差$ \|e_v(t)\| $

Fig. 3 Formation tracking error $ \|e_x(t)\| $ and velocity tracking error $ \|e_v(t)\| $

下载: 全尺寸图片幻灯片

图 4 在控制器(36)的作用下, 智能体对$ (i,\;j) $的一阶CBF$ h_{ij}^0(t) $和二阶CBF$ h_{ij}^1(t) $

Fig. 4 First-order CBF $ h_{ij}^0(t) $ and second-order CBF $ h_{ij}^1(t) $ of agent pair $ (i,\;j) $ under controller (36)

下载: 全尺寸图片幻灯片

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