Approximate Abstractions of Stochastic Hybrid Systems

L.M. Bujorianu; M.C. Bujorianu; H.A.P. Blom

doi:10.3182/20080706-5-KR-1001.4232

Approximate Abstractions of Stochastic Hybrid Systems

L.M. Bujorianu, M.C. Bujorianu, H.A.P. Blom

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

2 Citations (Scopus)

137 Downloads (Pure)

Abstract

This paper considers the issue of developing approximate abstractions of stochastic hybrid systems. The stochastic continuous behaviour breaks many essential properties of hybrid automata. Our approach departs from the progress in stochastic reachability analysis and Markov chain approximations. For this purpose we have to introduce a new approximation scheme and look for a suitable metric. We construct an exponential timestepping approximation scheme for general Markov processes. This approximation scheme relies on the complex space of system trajectories involving a sensible choice of the metric. Fortunately, the Skorokhod metric is sly enough to overcome the problems.

Original language	Undefined
Title of host publication	Proceedings of the 17th IFAC World Congress
Place of Publication	USA
Publisher	IFAC
Pages	8978-8983
Number of pages	6
ISBN (Print)	978-3-902661-00-5
DOIs	https://doi.org/10.3182/20080706-5-KR-1001.4232
Publication status	Published - 2008
Event	17th IFAC World Congress 2008 - Seoul, Korea, Republic of Duration: 5 Jul 2008 → 12 Jul 2008 Conference number: 17

Publication series

Name
Publisher	IFAC
Volume	17,1

Conference

Conference	17th IFAC World Congress 2008
Country/Territory	Korea, Republic of
City	Seoul
Period	5/07/08 → 12/07/08

Keywords

EWI-15269
stochastic hybrid systems
step processes
METIS-263804
Approximations
Model Checking
approximate abstraction
IR-65452

Access to Document

10.3182/20080706-5-KR-1001.4232

Cite this

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title = "Approximate Abstractions of Stochastic Hybrid Systems",

abstract = "This paper considers the issue of developing approximate abstractions of stochastic hybrid systems. The stochastic continuous behaviour breaks many essential properties of hybrid automata. Our approach departs from the progress in stochastic reachability analysis and Markov chain approximations. For this purpose we have to introduce a new approximation scheme and look for a suitable metric. We construct an exponential timestepping approximation scheme for general Markov processes. This approximation scheme relies on the complex space of system trajectories involving a sensible choice of the metric. Fortunately, the Skorokhod metric is sly enough to overcome the problems.",

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T1 - Approximate Abstractions of Stochastic Hybrid Systems

AU - Bujorianu, L.M.

AU - Bujorianu, M.C.

AU - Blom, H.A.P.

N1 - Conference code: 17

PY - 2008

Y1 - 2008

N2 - This paper considers the issue of developing approximate abstractions of stochastic hybrid systems. The stochastic continuous behaviour breaks many essential properties of hybrid automata. Our approach departs from the progress in stochastic reachability analysis and Markov chain approximations. For this purpose we have to introduce a new approximation scheme and look for a suitable metric. We construct an exponential timestepping approximation scheme for general Markov processes. This approximation scheme relies on the complex space of system trajectories involving a sensible choice of the metric. Fortunately, the Skorokhod metric is sly enough to overcome the problems.

AB - This paper considers the issue of developing approximate abstractions of stochastic hybrid systems. The stochastic continuous behaviour breaks many essential properties of hybrid automata. Our approach departs from the progress in stochastic reachability analysis and Markov chain approximations. For this purpose we have to introduce a new approximation scheme and look for a suitable metric. We construct an exponential timestepping approximation scheme for general Markov processes. This approximation scheme relies on the complex space of system trajectories involving a sensible choice of the metric. Fortunately, the Skorokhod metric is sly enough to overcome the problems.

KW - EWI-15269

KW - stochastic hybrid systems

KW - step processes

KW - METIS-263804

KW - Approximations

KW - Model Checking

KW - approximate abstraction

KW - IR-65452

U2 - 10.3182/20080706-5-KR-1001.4232

DO - 10.3182/20080706-5-KR-1001.4232

M3 - Conference contribution

SN - 978-3-902661-00-5

SP - 8978

EP - 8983

BT - Proceedings of the 17th IFAC World Congress

PB - IFAC

CY - USA

T2 - 17th IFAC World Congress 2008

Y2 - 5 July 2008 through 12 July 2008

ER -