A risk-sensitive finite-time reachability approach for safety of stochastic dynamic systems

Margaret P. Chapman, Jonathan Lacotte, Aviv Tamar, Donggun Lee, Kevin M. Smith, Victoria Cheng, Jaime F. Fisac, Susmit Jha, Marco Pavone, Claire J. Tomlin

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

A classic reachability problem for safety of dynamic systems is to compute the set of initial states from which the state trajectory is guaranteed to stay inside a given constraint set over a given time horizon. In this paper, we leverage existing theory of reachability analysis and risk measures to devise a risk-sensitivereachability approach for safety of stochasticdynamic systems under non-adversarial disturbances over a finite time horizon. Specifically, we first introduce the notion of a risk-sensitive safe set asa set of initial states from which the risk of large constraint violations can be reduced to a required level via a control policy, where risk is quantified using the Conditional Value-at-Risk(CVaR) measure. Second, we show how the computation of a risk-sensitive safe set can be reduced to the solution to a Markov Decision Process (MDP), where cost is assessed according to CVaR. Third, leveraging this reduction, we devise a tractable algorithm to approximate a risk-sensitive safe set and provide arguments about its correctness. Finally, we present a realistic example inspired from stormwater catchment design to demonstrate the utility of risk-sensitive reachability analysis. In particular, our approach allows a practitioner to tune the level of risk sensitivity from worst-case (which is typical for Hamilton-Jacobi reachability analysis) to risk-neutral (which is the case for stochastic reachability analysis).

Original languageEnglish (US)
Title of host publication2019 American Control Conference, ACC 2019
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2958-2963
Number of pages6
ISBN (Electronic)9781538679265
DOIs
StatePublished - Jul 2019
Externally publishedYes
Event2019 American Control Conference, ACC 2019 - Philadelphia, United States
Duration: Jul 10 2019Jul 12 2019

Publication series

NameProceedings of the American Control Conference
Volume2019-July
ISSN (Print)0743-1619

Conference

Conference2019 American Control Conference, ACC 2019
CountryUnited States
CityPhiladelphia
Period7/10/197/12/19

All Science Journal Classification (ASJC) codes

  • Electrical and Electronic Engineering

Fingerprint Dive into the research topics of 'A risk-sensitive finite-time reachability approach for safety of stochastic dynamic systems'. Together they form a unique fingerprint.

  • Cite this

    Chapman, M. P., Lacotte, J., Tamar, A., Lee, D., Smith, K. M., Cheng, V., Fisac, J. F., Jha, S., Pavone, M., & Tomlin, C. J. (2019). A risk-sensitive finite-time reachability approach for safety of stochastic dynamic systems. In 2019 American Control Conference, ACC 2019 (pp. 2958-2963). [8815169] (Proceedings of the American Control Conference; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/acc.2019.8815169