Reachability Estimation of Stochastic Dynamical Systems by Semi-definite Programming

Kairong Liu; Meilun Li; Zhikun She

doi:10.1109/CDC40024.2019.9029192

Reachability Estimation of Stochastic Dynamical Systems by Semi-definite Programming

Kairong Liu
, Meilun Li
, Zhikun She^*

^*Corresponding author for this work

School of Mathematical Sciences

Beihang University

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

4 Scopus citations

Abstract

In this paper we present a semi-definite programming based computational method for reachability analysis of stochastic dynamical systems, in which the reachability is characterized by first passage time distribution. Starting from Feynman-Kac formula, we provide over and under approximations of staying probability in a given safety area with explicit algebraical expressions, respectively. Successively, we transform the estimates of over and under approximations into constraint satisfaction problems, which can then be solved efficiently in virtue of SOS programming and global optimization. Two examples are used to show the utility of our method.

Original language	English
Title of host publication	2019 IEEE 58th Conference on Decision and Control, CDC 2019
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	7727-7732
Number of pages	6
ISBN (Electronic)	9781728113982
DOIs	https://doi.org/10.1109/CDC40024.2019.9029192
State	Published - Dec 2019
Event	58th IEEE Conference on Decision and Control, CDC 2019 - Nice, France Duration: 11 Dec 2019 → 13 Dec 2019

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	2019-December
ISSN (Print)	0743-1546
ISSN (Electronic)	2576-2370

Conference

Conference	58th IEEE Conference on Decision and Control, CDC 2019
Country/Territory	France
City	Nice
Period	11/12/19 → 13/12/19

Keywords

Reachability analysis
semi-definite programming.
stochastic dynamical systems

Access to Document

10.1109/CDC40024.2019.9029192

Cite this

Liu, K., Li, M., & She, Z. (2019). Reachability Estimation of Stochastic Dynamical Systems by Semi-definite Programming. In 2019 IEEE 58th Conference on Decision and Control, CDC 2019 (pp. 7727-7732). Article 9029192 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2019-December). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC40024.2019.9029192

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title = "Reachability Estimation of Stochastic Dynamical Systems by Semi-definite Programming",

abstract = "In this paper we present a semi-definite programming based computational method for reachability analysis of stochastic dynamical systems, in which the reachability is characterized by first passage time distribution. Starting from Feynman-Kac formula, we provide over and under approximations of staying probability in a given safety area with explicit algebraical expressions, respectively. Successively, we transform the estimates of over and under approximations into constraint satisfaction problems, which can then be solved efficiently in virtue of SOS programming and global optimization. Two examples are used to show the utility of our method.",

keywords = "Reachability analysis, semi-definite programming., stochastic dynamical systems",

author = "Kairong Liu and Meilun Li and Zhikun She",

note = "Publisher Copyright: {\textcopyright} 2019 IEEE.; 58th IEEE Conference on Decision and Control, CDC 2019 ; Conference date: 11-12-2019 Through 13-12-2019",

year = "2019",

month = dec,

doi = "10.1109/CDC40024.2019.9029192",

language = "英语",

series = "Proceedings of the IEEE Conference on Decision and Control",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

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Liu, K, Li, M & She, Z 2019, Reachability Estimation of Stochastic Dynamical Systems by Semi-definite Programming. in 2019 IEEE 58th Conference on Decision and Control, CDC 2019., 9029192, Proceedings of the IEEE Conference on Decision and Control, vol. 2019-December, Institute of Electrical and Electronics Engineers Inc., pp. 7727-7732, 58th IEEE Conference on Decision and Control, CDC 2019, Nice, France, 11/12/19. https://doi.org/10.1109/CDC40024.2019.9029192

Reachability Estimation of Stochastic Dynamical Systems by Semi-definite Programming. / Liu, Kairong; Li, Meilun; She, Zhikun.
2019 IEEE 58th Conference on Decision and Control, CDC 2019. Institute of Electrical and Electronics Engineers Inc., 2019. p. 7727-7732 9029192 (Proceedings of the IEEE Conference on Decision and Control; Vol. 2019-December).

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

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AU - Li, Meilun

AU - She, Zhikun

PY - 2019/12

Y1 - 2019/12

N2 - In this paper we present a semi-definite programming based computational method for reachability analysis of stochastic dynamical systems, in which the reachability is characterized by first passage time distribution. Starting from Feynman-Kac formula, we provide over and under approximations of staying probability in a given safety area with explicit algebraical expressions, respectively. Successively, we transform the estimates of over and under approximations into constraint satisfaction problems, which can then be solved efficiently in virtue of SOS programming and global optimization. Two examples are used to show the utility of our method.

AB - In this paper we present a semi-definite programming based computational method for reachability analysis of stochastic dynamical systems, in which the reachability is characterized by first passage time distribution. Starting from Feynman-Kac formula, we provide over and under approximations of staying probability in a given safety area with explicit algebraical expressions, respectively. Successively, we transform the estimates of over and under approximations into constraint satisfaction problems, which can then be solved efficiently in virtue of SOS programming and global optimization. Two examples are used to show the utility of our method.

KW - Reachability analysis

KW - semi-definite programming.

KW - stochastic dynamical systems

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DO - 10.1109/CDC40024.2019.9029192

M3 - 会议稿件

AN - SCOPUS:85082456605

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 7727

EP - 7732

BT - 2019 IEEE 58th Conference on Decision and Control, CDC 2019

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 58th IEEE Conference on Decision and Control, CDC 2019

Y2 - 11 December 2019 through 13 December 2019

ER -

Reachability Estimation of Stochastic Dynamical Systems by Semi-definite Programming

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