Convex Synthesis of Control Barrier Functions Under Input Constraints

Pan Zhao; Reza Ghabcheloo; Yikun Cheng; Hossein Abdi; Naira Hovakimyan

doi:10.1109/LCSYS.2023.3293765

Convex Synthesis of Control Barrier Functions Under Input Constraints

Pan Zhao^*
, Reza Ghabcheloo
, Yikun Cheng
, Hossein Abdi
, Naira Hovakimyan

^*Corresponding author for this work

Automation Technology and Mechanical Engineering

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

20 Citations (Scopus)

123 Downloads (Pure)

Abstract

This letter presents a systematic method based on the sum of square (SOS) optimization to synthesize control barrier functions (CBFs) for nonlinear polynomial systems subject to input constraints. The approach consists of two design steps. In the first step, using a linear-like representation of the nonlinear dynamics, an SOS optimization problem is formulated to search for an initial CBF and controller jointly. In the second step, an iterative optimization procedure involving the solution of a series of SOS problems is proposed to alternatively update the CBF and the controller to increase the invariant set defined by the CBF. The efficacy of the proposed approach is validated using numerical examples.

Original language	English
Pages (from-to)	3102-3107
Number of pages	6
Journal	IEEE Control Systems Letters
Volume	7
DOIs	https://doi.org/10.1109/LCSYS.2023.3293765
Publication status	Published - 2023
Publication type	A1 Journal article-refereed

Funding

This work was supported in part by the Air Force Office of Scientific Research (AFOSR) under Grant FA9550-21-1-0411

Keywords

Constrained control
nonlinear systems
optimization
safety

Publication forum classification

Publication forum level 1

ASJC Scopus subject areas

Control and Systems Engineering
Control and Optimization

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10.1109/LCSYS.2023.3293765Licence: CC BY

Convex Synthesis of ControlFinal published version, 944 KBLicence: CC BY

https://urn.fi/URN:NBN:fi:tuni-202309138134Licence: CC BY

Cite this

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title = "Convex Synthesis of Control Barrier Functions Under Input Constraints",

abstract = "This letter presents a systematic method based on the sum of square (SOS) optimization to synthesize control barrier functions (CBFs) for nonlinear polynomial systems subject to input constraints. The approach consists of two design steps. In the first step, using a linear-like representation of the nonlinear dynamics, an SOS optimization problem is formulated to search for an initial CBF and controller jointly. In the second step, an iterative optimization procedure involving the solution of a series of SOS problems is proposed to alternatively update the CBF and the controller to increase the invariant set defined by the CBF. The efficacy of the proposed approach is validated using numerical examples.",

keywords = "Constrained control, nonlinear systems, optimization, safety",

author = "Pan Zhao and Reza Ghabcheloo and Yikun Cheng and Hossein Abdi and Naira Hovakimyan",

note = "Funding Information: This work was supported in part by the Air Force Office of Scientific Research (AFOSR) under Grant FA9550-21-1-0411 Publisher Copyright: {\textcopyright} 2017 IEEE.",

year = "2023",

doi = "10.1109/LCSYS.2023.3293765",

language = "English",

volume = "7",

pages = "3102--3107",

journal = "IEEE Control Systems Letters",

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T1 - Convex Synthesis of Control Barrier Functions Under Input Constraints

AU - Zhao, Pan

AU - Ghabcheloo, Reza

AU - Cheng, Yikun

AU - Abdi, Hossein

AU - Hovakimyan, Naira

PY - 2023

Y1 - 2023

N2 - This letter presents a systematic method based on the sum of square (SOS) optimization to synthesize control barrier functions (CBFs) for nonlinear polynomial systems subject to input constraints. The approach consists of two design steps. In the first step, using a linear-like representation of the nonlinear dynamics, an SOS optimization problem is formulated to search for an initial CBF and controller jointly. In the second step, an iterative optimization procedure involving the solution of a series of SOS problems is proposed to alternatively update the CBF and the controller to increase the invariant set defined by the CBF. The efficacy of the proposed approach is validated using numerical examples.

AB - This letter presents a systematic method based on the sum of square (SOS) optimization to synthesize control barrier functions (CBFs) for nonlinear polynomial systems subject to input constraints. The approach consists of two design steps. In the first step, using a linear-like representation of the nonlinear dynamics, an SOS optimization problem is formulated to search for an initial CBF and controller jointly. In the second step, an iterative optimization procedure involving the solution of a series of SOS problems is proposed to alternatively update the CBF and the controller to increase the invariant set defined by the CBF. The efficacy of the proposed approach is validated using numerical examples.

KW - Constrained control

KW - nonlinear systems

KW - optimization

KW - safety

U2 - 10.1109/LCSYS.2023.3293765

DO - 10.1109/LCSYS.2023.3293765

M3 - Article

AN - SCOPUS:85164410245

SN - 2475-1456

VL - 7

SP - 3102

EP - 3107

JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

ER -

Convex Synthesis of Control Barrier Functions Under Input Constraints

Abstract

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Keywords

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