Discrete-Time Control Barrier Function: High-Order Case and Adaptive Case

Yuhan Xiong; Di Hua Zhai; Mahdi Tavakoli; Yuanqing Xia

doi:10.1109/TCYB.2022.3170607

Discrete-Time Control Barrier Function: High-Order Case and Adaptive Case

Yuhan Xiong, Di Hua Zhai^*, Mahdi Tavakoli, Yuanqing Xia

^*Corresponding author for this work

School of Automation

Research output: Contribution to journal › Article › peer-review

22 Citations (Scopus)

Abstract

This article proposes the novel concepts of the high-order discrete-time control barrier function (CBF) and adaptive discrete-time CBF. The high-order discrete-time CBF is used to guarantee forward invariance of a safe set for discrete-time systems of high relative degree. An optimization problem is then established unifying high-order discrete-time CBFs with discrete-time control Lyapunov functions to yield a safe controller. To improve the feasibility of such optimization problems, the adaptive discrete-time CBF is designed, which can relax constraints on system control input through time-varying penalty functions. The effectiveness of the proposed methods in dealing with high relative degree constraints and improving feasibility is verified on the discrete-time system of a three-link manipulator.

Original language	English
Pages (from-to)	3231-3239
Number of pages	9
Journal	IEEE Transactions on Cybernetics
Volume	53
Issue number	5
DOIs	https://doi.org/10.1109/TCYB.2022.3170607
Publication status	Published - 1 May 2023

Keywords

Control barrier functions (CBFs)
discrete-time systems
optimization problem

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10.1109/TCYB.2022.3170607

Cite this

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title = "Discrete-Time Control Barrier Function: High-Order Case and Adaptive Case",

abstract = "This article proposes the novel concepts of the high-order discrete-time control barrier function (CBF) and adaptive discrete-time CBF. The high-order discrete-time CBF is used to guarantee forward invariance of a safe set for discrete-time systems of high relative degree. An optimization problem is then established unifying high-order discrete-time CBFs with discrete-time control Lyapunov functions to yield a safe controller. To improve the feasibility of such optimization problems, the adaptive discrete-time CBF is designed, which can relax constraints on system control input through time-varying penalty functions. The effectiveness of the proposed methods in dealing with high relative degree constraints and improving feasibility is verified on the discrete-time system of a three-link manipulator.",

keywords = "Control barrier functions (CBFs), discrete-time systems, optimization problem",

author = "Yuhan Xiong and Zhai, {Di Hua} and Mahdi Tavakoli and Yuanqing Xia",

note = "Publisher Copyright: {\textcopyright} 2013 IEEE.",

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AU - Xiong, Yuhan

AU - Zhai, Di Hua

AU - Tavakoli, Mahdi

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AB - This article proposes the novel concepts of the high-order discrete-time control barrier function (CBF) and adaptive discrete-time CBF. The high-order discrete-time CBF is used to guarantee forward invariance of a safe set for discrete-time systems of high relative degree. An optimization problem is then established unifying high-order discrete-time CBFs with discrete-time control Lyapunov functions to yield a safe controller. To improve the feasibility of such optimization problems, the adaptive discrete-time CBF is designed, which can relax constraints on system control input through time-varying penalty functions. The effectiveness of the proposed methods in dealing with high relative degree constraints and improving feasibility is verified on the discrete-time system of a three-link manipulator.

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Discrete-Time Control Barrier Function: High-Order Case and Adaptive Case

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