Risk-Bounded Control Using Stochastic Barrier Functions

Shakiba Yaghoubi; Keyvan Majd; Georgios Fainekos; Tomoya Yamaguchi; Danil Prokhorov; Bardh Hoxha

doi:10.1109/LCSYS.2020.3043287

Risk-Bounded Control Using Stochastic Barrier Functions

Shakiba Yaghoubi, Keyvan Majd, Georgios Fainekos, Tomoya Yamaguchi, Danil Prokhorov, Bardh Hoxha

Engineering, Ira A. Fulton Schools of (IAFSE)

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

4 Scopus citations

Abstract

In this letter, we design real-time controllers that react to uncertainties with stochastic characteristics and bound the probability of a failure in finite-time to a given desired value. Stochastic control barrier functions are used to derive sufficient conditions on the control input that bound the probability that the states of the system enter an unsafe region within a finite time. These conditions are combined with reachability conditions and used in an optimization problem to find the required control actions that lead the system to a goal set. We illustrate our theoretical development using a simulation of a lane-changing scenario in a highway with dense traffic.

Original language	English (US)
Article number	9286497
Pages (from-to)	1831-1836
Number of pages	6
Journal	IEEE Control Systems Letters
Volume	5
Issue number	5
DOIs	https://doi.org/10.1109/LCSYS.2020.3043287
State	Published - Nov 2021

Keywords

Barrier function
robotics
uncertainty

ASJC Scopus subject areas

Control and Systems Engineering
Control and Optimization

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10.1109/LCSYS.2020.3043287

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title = "Risk-Bounded Control Using Stochastic Barrier Functions",

abstract = "In this letter, we design real-time controllers that react to uncertainties with stochastic characteristics and bound the probability of a failure in finite-time to a given desired value. Stochastic control barrier functions are used to derive sufficient conditions on the control input that bound the probability that the states of the system enter an unsafe region within a finite time. These conditions are combined with reachability conditions and used in an optimization problem to find the required control actions that lead the system to a goal set. We illustrate our theoretical development using a simulation of a lane-changing scenario in a highway with dense traffic. ",

keywords = "Barrier function, robotics, uncertainty",

author = "Shakiba Yaghoubi and Keyvan Majd and Georgios Fainekos and Tomoya Yamaguchi and Danil Prokhorov and Bardh Hoxha",

note = "Funding Information: Manuscript received September 14, 2020; revised November 9, 2020; accepted November 24, 2020. Date of publication December 8, 2020; date of current version January 13, 2021. This work was supported by NSF under Grant OIA 1936997. Recommended by Senior Editor V. Ugrinovskii. (Corresponding author: Bardh Hoxha.) Shakiba Yaghoubi, Tomoya Yamaguchi, Danil Prokhorov, and Bardh Hoxha are with the Toyota North America Research and Development, Ann Arbor, MI 48105 USA (e-mail: shakiba.yaghoubi@ toyota.com; tomoya.yamaguchi@toyota.com; danil.prokhorov@toyota. com; bardh.hoxha@toyota.com). Publisher Copyright: {\textcopyright} 2017 IEEE.",

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AU - Majd, Keyvan

AU - Fainekos, Georgios

AU - Yamaguchi, Tomoya

AU - Prokhorov, Danil

AU - Hoxha, Bardh

N1 - Funding Information: Manuscript received September 14, 2020; revised November 9, 2020; accepted November 24, 2020. Date of publication December 8, 2020; date of current version January 13, 2021. This work was supported by NSF under Grant OIA 1936997. Recommended by Senior Editor V. Ugrinovskii. (Corresponding author: Bardh Hoxha.) Shakiba Yaghoubi, Tomoya Yamaguchi, Danil Prokhorov, and Bardh Hoxha are with the Toyota North America Research and Development, Ann Arbor, MI 48105 USA (e-mail: shakiba.yaghoubi@ toyota.com; tomoya.yamaguchi@toyota.com; danil.prokhorov@toyota. com; bardh.hoxha@toyota.com). Publisher Copyright: © 2017 IEEE.

PY - 2021/11

Y1 - 2021/11

N2 - In this letter, we design real-time controllers that react to uncertainties with stochastic characteristics and bound the probability of a failure in finite-time to a given desired value. Stochastic control barrier functions are used to derive sufficient conditions on the control input that bound the probability that the states of the system enter an unsafe region within a finite time. These conditions are combined with reachability conditions and used in an optimization problem to find the required control actions that lead the system to a goal set. We illustrate our theoretical development using a simulation of a lane-changing scenario in a highway with dense traffic.

AB - In this letter, we design real-time controllers that react to uncertainties with stochastic characteristics and bound the probability of a failure in finite-time to a given desired value. Stochastic control barrier functions are used to derive sufficient conditions on the control input that bound the probability that the states of the system enter an unsafe region within a finite time. These conditions are combined with reachability conditions and used in an optimization problem to find the required control actions that lead the system to a goal set. We illustrate our theoretical development using a simulation of a lane-changing scenario in a highway with dense traffic.

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Risk-Bounded Control Using Stochastic Barrier Functions

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