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

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

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 safety analysis and safety-critical control of nonlinear systems

LIU Yong-Hua　Associate professor at the School of Automation, Guangdong University of Technology. His research interest covers nonlinear 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, 提出了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, 提出了一种新颖的安全反推控制算法. 相比于现有文献, 本文所提控制方案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. 仿真结果验证了文中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 scheme 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 methodology.
- 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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参考文献(37)

[1]	Clarke E M, Grumberg O, Peleg D. Model Checking. Cambridge: MIT Press, 1999.
[2]	Tomlin C, Pappas G J, Sastry S. Conflict resolution for airtraffic management: A study in multiagent hybrid systems. IEEE Transactions on Automatic Control, 1998, 43(4): 509−521 doi: 10.1109/9.664154
[3]	Gao Y, Johansson K H, Xie L. Computing probabilistic controlled invariant sets. IEEE Transactions on Automatic Control, 2021, 66(7): 3138−3151 doi: 10.1109/TAC.2020.3018438
[4]	Sun J, Yang J, Zeng Z. Safety-critical control with control barrier function based on disturbance observer. IEEE Transactions on Automatic Control, 2024, 69(7): 4750−4756 doi: 10.1109/TAC.2024.3352707
[5]	Cohen M H, Belta C. Safe exploration in model-based reinforcement learning using control barrier functions. Automatica, 2023, 147: Article No. 110684 doi: 10.1016/j.automatica.2022.110684
[6]	陈杰, 吕梓亮, 黄鑫源, 洪奕光. 非线性系统的安全分析与控制: 障碍函数方法. 自动化学报, 2023, 49(3): 567−579 Chen Jie, Lyu Zi-Liang, Huang Xin-Yuan, Hong Yi-Guang. Safety analysis and safety-critical control of nonlinear systems: Barrier function approach. Acta Automatica Sinica, 2023, 49(3): 567−579
[7]	Artstein Z. Stabilization with relaxed controls. Nonlinear Analysis: Theory, Methods and Applications, 1983, 7(11): 1163−1173
[8]	Sontag E D. A ‘universal’ construction of Artstein's theorem on nonlinear stabilization. Systems and Control Letters, 1989, 13(2): 117−123 doi: 10.1016/0167-6911(89)90028-5
[9]	Wieland P, Allgöwer F. Constructive safety using control barrier functions. IFAC Proceedings Volumes, 2007, 40(12): 462−467 doi: 10.3182/20070822-3-ZA-2920.00076
[10]	Ames A D, Grizzle J W, Tabuada P. Control barrier function based quadratic programs with application to adaptive cruise control. In: Proceedings of the 53rd IEEE Conference on Decision and Control (CDC). Los Angeles, USA: IEEE, 2014. 6271−6278
[11]	Xu X, Tabuada P, Grizzle J W, Ames A D. Robustness of control barrier functions for safety-critical control. IFAC-PapersOnLine, 2015, 48(27): 54−61 doi: 10.1016/j.ifacol.2015.11.152
[12]	Ames A D, Xu X, Grizzle J W, Tabuada P. Control barrier function based quadratic programs for safety critical systems. IEEE Transactions on Automatic Control, 2017, 62(8): 3861−3876 doi: 10.1109/TAC.2016.2638961
[13]	Xu Y, Sun Y, Chen Y Y, Tao H F. Safety predefined time tracking control of second-order nonlinear systems. In: Proceedings of the 12th Data Driven Control and Learning Systems Conference (DDCLS). Xiangtan, China: IEEE, 2023. 1320−1324
[14]	Cortez W S, Dimarogonas D V. Correct-by-design control barrier functions for Euler-Lagrange systems with input constraints. In: Proceedings of the American Control Conference (ACC). Denver, USA: IEEE, 2020. 950−955
[15]	Cortez W S, Dimarogonas D V. Safe-by-design conrtrol for Euler-Lagrange systems. Automatica, 2022, 146: Article No. 110620 doi: 10.1016/j.automatica.2022.110620
[16]	Das E, Murray R M. Robust Safe control synthesis with disturbance observer-based control barrier functions. In: Proceedings of the 61st Conference on Decision and Control (CDC). Cancun, Mexico: IEEE, 2022. 5566−5573
[17]	Nguyen Q, Sreenath K. Exponential control barrier function for enforcing high relative-degree safety-critical constraints. In: Proceedings of the American Control Conference (ACC). Boston, USA: IEEE, 2016. 322−328
[18]	Xiao W, Belta C. Control barrier functions for systems with high relative degree. In: Proceedings of the 58th IEEE Conference on Decision and Control (CDC). Nice, France: IEEE, 2019. 474−479
[19]	Xiao W, Belta C. High-order control barrier functions. IEEE Transactions on Automatic Control, 2022, 67(7): 3655−3662 doi: 10.1109/TAC.2021.3105491
[20]	Tan X, Cortez W S, Dimarogonas D V. High-order barrier functions: Robustness, safety, and performance-critical control. IEEE Transactions on Automatic Control, 2021, 67(6): 3021−3028
[21]	Wang H, Peng J, Xu J, Zhang F, Wang Y. High-order control barrier function based optimization control for time-varying nonlinear systems with full-state constraints: A dynamic sub-safe set approach. International Journal of Robust and Nonlinear Control, 2023, 33(8): 4490−4503 doi: 10.1002/rnc.6624
[22]	Zhang D H, Van M Mcllvanna S, Sun Y, McLoone S. Adaptive safety critical control with uncertainty estimation for human–robot collaboration. IEEE Transactions on Automation Science and Engineering, DOI: 10.1109/TASE.2023.3320873
[23]	Molnar T G, Cosner R K, Singletary A W, Ubellacker W, Ames A D. Model-free safety critical control for robotic systems. IEEE Robotics and Automation Letters, 2022, 7(2): 944−951 doi: 10.1109/LRA.2021.3135569
[24]	Xu J X, Gu N, Wang D, Li T S, Han B, Peng Z H. Safety critical parallel trajectory tracking control of maritime autonomous surface ships based on integral control barrier functions. IEEE Transactions on Intelligent Vehicles, 9 (5): 4979−4988, 2024 doi: 10.1109/TIV.2024.3361477
[25]	Xu X. Constrained control of input-output linearizable systems using control sharing barrier funcion. Automatica, 2018, 87: 195−201 doi: 10.1016/j.automatica.2017.10.005
[26]	Taylor A J, Ong P, Molnar T G, Ames A D. Safe backstepping with control barrier functions. In: Proceedings of the 61st IEEE Conference on Decision and Control (CDC). Cancun, Mexico: IEEE, 2022. 5775−5782
[27]	Abel I, Steeves D, KritićM, JankovićM. Prescribed time safety design for strict-feedback nonlinear systems. IEEE Transactions on Automatic Control, 2024, 69(3): 1464−1479 doi: 10.1109/TAC.2023.3326393
[28]	马知恩, 周义仓, 李承治. 常微分方程定性与稳定性方法. 第2版. 北京: 科学出版社, 2015. Ma Zhi-En, Zhou Yi-Cang, Li Cheng-Zhi. Qualitative and Stability Theory of Ordinary Differential Equations, II. Beijing: Science Press, 2015.
[29]	Ames A D, Coogan S, Egerstedt M, Notomista G, Sreenath K and Tabuada P. Control barrier functions: Theory and applications. In: Proceedings of the 18th European Control Conference (ECC). Naples, Italy: IEEE, 2019. 3420−3431
[30]	Li L H, Zhao K, Zhang Z Z, Song Y D. Dual-channel event-triggered robust adaptive control of strict-feedback system with flexible prescribed performance. IEEE Transactions on Automatic Control, 2024, 69(3): 1752−1759 doi: 10.1109/TAC.2023.3328167
[31]	Cheng H, Huang X C, Cao H W. Asymptotic tracking control for uncertain nonlinear strict-feedback systems with unknown time-varying delays. IEEE Transactions on Neural Networks and Learning Systems, 2023, 34(12): 9821−9831 doi: 10.1109/TNNLS.2022.3160803
[32]	Yip P P, Hedrick J K. Adaptive dynamic surface control: a simplified algorithm for adaptive backstepping control of nonlinear systems. International Journal of Control, 1998, 71(5): 959−979 doi: 10.1080/002071798221650
[33]	Khalil H K. Nonlinear Systems. Upper Saddle River: Prentice Hall, 2002
[34]	Wang H, Margellos K, Papachristodoulou A. Explicit solutions for safety problems using control barrier functions. In: Proceedings of the 61st IEEE Conference on Decision and Control (CDC). Cancun, Mexico: IEEE, 2022. 5680−5685
[35]	Saviolo A, Loianno G. Learning quadrotor dynamics for precise, safe, and agile flight control. Annual Reviews in Control, 2023, 55: 45−60 doi: 10.1016/j.arcontrol.2023.03.009
[36]	Yuan W, Liu Y H, Su C Y, Zhao F. Whole-body control of an autonomous mobile manipulator using model predictive control and adaptive fuzzy technique. IEEE Transactions on Fuzzy Systems, 2024, 31(3): 799−809
[37]	Yuan W, Liu Y, Liu Y H, Su C Y. Differential flatness-based adaptive robust tracking control for wheeled mobile robots with slippage disturbances. ISA Transactions, 2024, 144: 482−489 doi: 10.1016/j.isatra.2023.11.008