Stochastic safety for random dynamical systems

Manuela L. Bujorianu; Rafał Wisniewski; Evangelos Boulougouris

doi:10.23919/ACC50511.2021.9483422

Stochastic safety for random dynamical systems

Manuela L. Bujorianu, Rafał Wisniewski, Evangelos Boulougouris

Naval Architecture, Ocean And Marine Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

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Abstract

In the paper, we study the so-called p-safety of a random dynamical system. We generalize the existing results for safety barrier certificates for deterministic dynamical systems and Markov processes. Moreover, we consider the case of random obstacles, modelled as random sets. This leads to the necessity of using integrals with respect to lower and upper distributions. We prove that if there exists at least one barrier certificate then the random dynamical system is safe. The barrier certificates are also defined using such nonlinear distributions. Furthermore, when the family of stochastic Koopman operators has the semigroup property, the barrier certificates are solutions for some type of Dirichlet problems.

Original language	English
Title of host publication	2021 American Control Conference (ACC)
Place of Publication	Piscataway, NJ
Publisher	IEEE
Pages	1340-1345
Number of pages	6
ISBN (Electronic)	9781665441971
DOIs	https://doi.org/10.23919/ACC50511.2021.9483422
Publication status	Published - 28 Jul 2021
Event	2021 American Control Conference - Virtual, New Orleans, United States Duration: 25 May 2021 → 28 May 2021 https://acc2021.a2c2.org/

Publication series

Name	Proceedings of the American Control Conference
Publisher	IEEE
ISSN (Print)	0743-1619
ISSN (Electronic)	2378-5861

Conference

Conference	2021 American Control Conference
Abbreviated title	ACC 2021
Country/Territory	United States
City	New Orleans
Period	25/05/21 → 28/05/21
Internet address	https://acc2021.a2c2.org/

Keywords

Koopman operator
barrier certificates
hitting measure
occupation measure
p-safety
random dynamical system
random set
supermedian function

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10.23919/ACC50511.2021.9483422

Bujorianu-etal-ACC-2021-Stochastic-safety-for-random-dynamical-systemsAccepted author manuscript, 273 KB

Cite this

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title = "Stochastic safety for random dynamical systems",

abstract = "In the paper, we study the so-called p-safety of a random dynamical system. We generalize the existing results for safety barrier certificates for deterministic dynamical systems and Markov processes. Moreover, we consider the case of random obstacles, modelled as random sets. This leads to the necessity of using integrals with respect to lower and upper distributions. We prove that if there exists at least one barrier certificate then the random dynamical system is safe. The barrier certificates are also defined using such nonlinear distributions. Furthermore, when the family of stochastic Koopman operators has the semigroup property, the barrier certificates are solutions for some type of Dirichlet problems.",

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author = "Bujorianu, {Manuela L.} and Rafa{\l} Wisniewski and Evangelos Boulougouris",

note = "{\textcopyright} 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.; 2021 American Control Conference , ACC 2021 ; Conference date: 25-05-2021 Through 28-05-2021",

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T1 - Stochastic safety for random dynamical systems

AU - Bujorianu, Manuela L.

AU - Wisniewski, Rafał

AU - Boulougouris, Evangelos

N1 - © 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.

PY - 2021/7/28

Y1 - 2021/7/28

N2 - In the paper, we study the so-called p-safety of a random dynamical system. We generalize the existing results for safety barrier certificates for deterministic dynamical systems and Markov processes. Moreover, we consider the case of random obstacles, modelled as random sets. This leads to the necessity of using integrals with respect to lower and upper distributions. We prove that if there exists at least one barrier certificate then the random dynamical system is safe. The barrier certificates are also defined using such nonlinear distributions. Furthermore, when the family of stochastic Koopman operators has the semigroup property, the barrier certificates are solutions for some type of Dirichlet problems.

AB - In the paper, we study the so-called p-safety of a random dynamical system. We generalize the existing results for safety barrier certificates for deterministic dynamical systems and Markov processes. Moreover, we consider the case of random obstacles, modelled as random sets. This leads to the necessity of using integrals with respect to lower and upper distributions. We prove that if there exists at least one barrier certificate then the random dynamical system is safe. The barrier certificates are also defined using such nonlinear distributions. Furthermore, when the family of stochastic Koopman operators has the semigroup property, the barrier certificates are solutions for some type of Dirichlet problems.

KW - Koopman operator

KW - barrier certificates

KW - hitting measure

KW - occupation measure

KW - p-safety

KW - random dynamical system

KW - random set

KW - supermedian function

UR - https://acc2021.a2c2.org/

U2 - 10.23919/ACC50511.2021.9483422

DO - 10.23919/ACC50511.2021.9483422

M3 - Conference contribution book

T3 - Proceedings of the American Control Conference

SP - 1340

EP - 1345

BT - 2021 American Control Conference (ACC)

PB - IEEE

CY - Piscataway, NJ

T2 - 2021 American Control Conference

Y2 - 25 May 2021 through 28 May 2021

ER -

Stochastic safety for random dynamical systems

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Keywords

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