非线性系统的安全分析与控制: 障碍函数方法

陈杰; 吕梓亮; 黄鑫源; 洪奕光

doi:10.16383/j.aas.c220888

非线性系统的安全分析与控制: 障碍函数方法

doi: 10.16383/j.aas.c220888

陈杰^{1, 2, 3,},
吕梓亮^{1, 2, 3,},
黄鑫源^{1, 2, 3,},
洪奕光^{1, 2, 3,}

1.
同济大学电子与信息工程学院上海 200092
2.
自主智能无人系统全国重点实验室上海 201210
3.
同济大学上海自主智能无人系统科学中心上海 201210

基金项目: 国家自然科学基金(61903027), 上海市重大专项(2021SHZDZX0100), 上海市科技成果转化和产业化项目(1951113210, 19511132101)资助

详细信息

作者简介:
陈杰：中国工程院院士, 同济大学教授, 北京理工大学自动化学院教授, 自主智能无人系统全国重点实验室教授. 1986年、1996年和2001年分别获得北京理工大学控制理论与应用专业学士学位、硕士学位和博士学位. 主要研究方向为复杂系统智能控制与优化, 多智能体协同控制. E-mail: chenjie@bit.edu.cn

吕梓亮：同济大学电子与信息工程学院博士研究生. 2017年和2020年分别获得广东工业大学学士和硕士学位. 主要研究方向为非线性系统安全分析与控制. E-mail: zlyu@tongji.edu.cn

黄鑫源：同济大学电子与信息工程学院博士研究生. 2019年获得同济大学控制科学与工程专业学士学位. 主要研究方向为安全控制和基于形式化方法的控制. E-mail: xy_huang@tongji.edu.cn

洪奕光：同济大学电子与信息工程学院教授, 自主智能无人系统全国重点实验室教授. 1987年和1990年分别获得北京大学力学系学士和硕士学位, 1993年获得中科院系统所博士学位. 主要研究方向为复杂系统, 控制理论, 人工智能. 本文通信作者. E-mail: yghong@tongji.edu.cn

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出版历程
- 收稿日期: 2022-11-13
- 网络出版日期: 2023-02-06
- 刊出日期: 2023-03-20

Safety Analysis and Safety-critical Control of Nonlinear Systems: Barrier Function Approach

CHEN Jie^{1, 2, 3
,},
LYU Zi-Liang^{1, 2, 3
,},
HUANG Xin-Yuan^{1, 2, 3
,},
HONG Yi-Guang^{1, 2, 3
,}

1.
College of Electronic and Information Engineering, Tongji University, Shanghai 200092
2.
National Key Laboratory of Autonomous Intelligent Unmanned Systems, Shanghai 201210
3.
Shanghai Research Institute for Intelligent Autonomous Systems, Tongji University, Shanghai 201210

Funds: Supported by National Natural Science Foundation of China (61903027), Shanghai Municipal Science and Technology Major Project (2021SHZDZX0100), and Shanghai Municipal Commission of Science and Technology (1951113210, 19511132101)

More Information

Author Bio:
CHEN Jie　Academician of Chinese Academy of Engineering, professor at Tongji University, School of Automation, Beijing Institute of Technology, and National Key Laboratory of Autonomous Intelligent Unmanned Systems. He received his bachelor, master, and Ph.D. degrees in control science and application from Beijing Institute of Technology in 1986, 1996, and 2001, respectively. His research interest covers intelligent control and optimization of complex systems, and cooperative control of multi-agent systems

LYU Zi-Liang　Ph.D. candidate at the College of Electronic and Information Engineering, Tongji University. He received his bachelor and master degrees from Guangdong University of Technology in 2017 and 2020, respectively. His research interest covers safety analysis and safety-critical control of nonlinear systems

HUANG Xin-Yuan　Ph.D. candidate at the College of Electronic and Information Engineering, Tongji University. He received his bachelor degree in control science and engineering from Tongji University in 2019. His research interest covers safety control and formal methods-based control

HONG Yi-Guang　Professor at College of Electronic and Information Engineering, Tongji University and National Key Laboratory of Autonomous Intelligent Unmanned Systems. He received his bachelor and master degrees from Department of Mechanics of Peking University in 1987 and 1990, respectively, and his Ph.D. degree from Institute of Systems Science of Chinese Academy of Sciences in 1993. His research interest covers complex systems, control theory, and artificial intelligence. Corresponding author of this paper

摘要

摘要: 近年来, 非线性系统的安全分析与控制已成为控制领域中的热门研究方向, 而障碍函数则是该方向的一种重要工具. 基于障碍函数的安全分析与控制方法具有计算效率高、鲁棒性强等优点. 本文首先从多个角度介绍了基于障碍函数的非线性系统安全性分析的理论成果, 并进一步综述了障碍函数方法在非线性系统安全控制中的最新进展. 最后, 简要地介绍了当前基于障碍函数的安全分析与控制理论中一系列尚未解决的问题, 并指出了未来可能发展的一些研究方向.
- 安全性分析 /
- 安全控制 /
- 障碍函数 /
- 非线性系统
Abstract: Safety analysis and safety-critical control of nonlinear systems have been important issues in the control society. The barrier function is a promising tool for the safety analysis and safety-critical control of nonlinear systems. This methodology has the advantages of high computation efficiency and strong robustness. In this paper, we first review the theoretical results on barrier function based safety analysis from different viewpoints, and then summarize some recent advances of the barrier function theory in the safety-critical control of nonlinear systems. Finally, we outline a series of open questions in the barrier function theory and point out some possible research directions.
- Safety analysis /
- safety-critical control /
- barrier functions /
- nonlinear systems
注释:

1) ¹ 扩展$ K $类函数是传统$ K $类函数^[2]在安全分析与控制上的推广. 对于任意函数$ \alpha: {\bf{R}}\rightarrow {\bf{R}} $, 我们说它是一个扩展$ K $类函数, 如果该函数在$ {\bf{R}} $上连续、严格递增并满足$ \alpha(0)=0 $; 特别地, 如果$ \alpha(s) $分别随着$s $趋于$ +\infty $和$ -\infty $而趋于$ +\infty $和$ -\infty $, 则该函数是一个扩展$ K_\infty $类函数.

2) ² 这里的相对阶是把$ h(x) $当做某种意义下的输出.

3) ³ 在控制领域, 组合系统有时也被称作互联系统(Interconnected system).

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