基于滤波控制障碍函数的严格反馈系统安全控制

陈仲秋; 刘勇华; 苏春翌

doi:10.16383/j.aas.c240003

基于滤波控制障碍函数的严格反馈系统安全控制

doi: 10.16383/j.aas.c240003 cstr: 32138.14.j.aas.c240003

陈仲秋^{1, 2, 3,},
刘勇华^{1, 2, 3,},
苏春翌^{1, 2, 3,}

1.
广东工业大学自动化学院广州 510006
2.
粤港智能决策与控制联合实验室广州 510006
3.
广东省智能决策与协同控制重点实验室广州 510006

基金项目: 国家自然科学基金(62173097, U2013601), 广东省基础与应用基础研究基金面上项目(2022A515011239), 广东省特支计划本土创新创业项目(2019BT02X353) 资助

详细信息

作者简介:
陈仲秋：广东工业大学自动化学院博士研究生. 主要研究方向为非线性系统安全分析与控制. E-mail: 1112104010@mail2.gdut.edu.cn

刘勇华：广东工业大学自动化学院副教授. 主要研究方向为非线性控制与智能控制. 本文通信作者. E-mail: yonghua.liu@outlook.com

苏春翌：广东工业大学自动化学院教授. 主要研究方向为控制理论及其在机电系统中的应用. E-mail: chunyi.su@concordia.ca

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出版历程
- 收稿日期: 2024-01-03
- 录用日期: 2024-07-23
- 网络出版日期: 2024-09-02
- 刊出日期: 2024-12-20

Safe Control of Strict-feedback Systems Using Filtered Control Barrier Functions

CHEN Zhong-Qiu^{1, 2, 3
,},
LIU Yong-Hua^{1, 2, 3
,},
SU Chun-Yi^{1, 2, 3
,}

1.
School of Automation, Guangdong University of Technology, Guangzhou 510006
2.
Guangdong-Hong Kong Joint Laboratory of Intelligent Decision and Cooperative Control, Guangzhou 510006
3.
Guangdong Province Key Laboratory of Intelligent Decision and Cooperative Control, Guangzhou 510006

Funds: Supported by National Natural Science Foundation of China (62173097, U2013601), GuangDong Basic and Applied Basic Research Foundation (2022A515011239), and the Local Innovative and Research Team Project of Guangdong Special Support Program (2019BT02X353)

More Information

Author Bio:
CHEN Zhong-Qiu　Ph.D. candidate at the School of Automation, Guangdong University of Technology. Her research interest covers safe analysis and control of nonlinear systems

LIU Yong-Hua　Associate professor at the School of Automation, Guangdong University of Technology. His research interest covers nonlinear control and intelligent control. Corresponding author of this paper

SU Chun-Yi　Professor at the School of Automation, Guangdong University of Technology. His research interest covers control theory and its applications to mechanical systems

摘要

摘要: 针对一类严格反馈系统的安全控制问题, 提出一种基于滤波控制障碍函数(Filtered control barrier functions, FCBF)的优化控制方法. 首先引入一阶低通滤波器, 构建滤波控制障碍函数. 然后结合控制李雅普诺夫函数(Control Lyapunov functions, CLF)及离线优化技术, 提出一种新颖的安全反推控制算法. 与现有文献相比, 所提控制算法通过运用滤波控制障碍函数, 有效克服了安全反推过程中的“计算膨胀”问题. 仿真结果验证了所提控制算法的有效性与正确性.
- 非线性系统 /
- 安全控制 /
- 控制障碍函数 /
- 低通滤波器 /
- 反推设计
Abstract: In this paper, an optimal control approach with filtered control barrier functions (FCBF) is proposed for the safe control problem of class of strict-feedback systems. Initially, a sequence of first-order low-pass filters is first introduced to formulate the FCBF. Subsequently, by integrating control Lyapunov functions (CLF) with an off-line optimization approach, a novel safe backstepping control algorithm is devised. In contrast to existing literature, the proposed control algorithm effectively mitigates the issue of “explosion of complexity” inherent in safety backstepping procedures through the utilization of FCBF. Simulation outcomes corroborate the efficacy and validity of the proposed algorithm.
- Nonlinear systems /
- safe control /
- control barrier functions (CBF) /
- low-pass filter /
- backstepping design

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图 1 不同滤波时间常数条件下系统的安全与跟踪性能

Fig. 1 Safe and tracking performance of the system with various filter time constants

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图 2 基于FCBF与文献[26]控制方法的系统安全与跟踪性能

Fig. 2 Safe and tracking performance of the system under the control schemes in FCBF and in reference [26]

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图 3 基于FCBF与文献[26]控制方法的系统输入$ u $

Fig. 3 System input $ u $under the control schemes in FCBF and in reference [26]

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图 4 不同滤波时间常数条件下系统位置轨迹

Fig. 4 Position trajectories of the system with various filter time constants

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图 5 不同滤波时间常数条件下输入信号$ u_1 $和$ u_2 $

Fig. 5 Input signals $ u_1 $ and $ u_2 $ with various filter time constants

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图 6 基于FCBF与文献[26]控制方法的系统位置轨迹

Fig. 6 Position trajectories of the system under the control schemes in FCBF and in reference [26]

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图 7 基于FCBF与文献[26]控制方法的输入信号$ u_1 $和$ u_2 $

Fig. 7 Input signals $ u_1 $and $ u_2 $under the control schemes in FCBF and in reference [26]

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