Inner approximations of stochastic programs for data-driven stochastic barrier function design

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Abstract

This paper proposes a new framework to compute finite-horizon safety guarantees for discrete-time piece-wise affine systems with stochastic noise of unknown distributions. The approach is based on a novel approach to synthesise a stochastic barrier function (SBF) from noisy data and rely on the scenario optimization theory. In particular, we show that the stochastic program to synthesize a SBF can be relaxed into a chance-constrained optimisation problem on which scenario approach theory applies. We further show that the resulting program can be reduced to a linear programming problem, thus guaranteeing efficiency. In contrast to existing approaches, this method is data efficient as it only requires the number of data to be proportional to the logarithm in the negative inverse of the confidence level and is computationally efficient due to its reduction to linear programming. The efficacy of the method is empirically evaluated on various verification benchmarks. Experiments show a significant improvement with respect to state-of-the-art, obtaining tighter certificates with a confidence that is several orders of magnitude higher.
Original languageEnglish
Title of host publicationProceedings of the 62nd IEEE Conference on Decision and Control (CDC 2023)
PublisherIEEE
Pages3073-3080
Number of pages8
ISBN (Electronic)979-8-3503-0124-3
DOIs
Publication statusPublished - 2023
Event62nd IEEE Conference on Decision and Control, CDC 2023 - Singapore, Singapore
Duration: 13 Dec 202315 Dec 2023

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370

Conference

Conference62nd IEEE Conference on Decision and Control, CDC 2023
Country/TerritorySingapore
CitySingapore
Period13/12/2315/12/23

Bibliographical note

Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.

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