TY - GEN
T1 - A risk-sensitive finite-time reachability approach for safety of stochastic dynamic systems
AU - Chapman, Margaret P.
AU - Lacotte, Jonathan
AU - Tamar, Aviv
AU - Lee, Donggun
AU - Smith, Kevin M.
AU - Cheng, Victoria
AU - Fisac, Jaime F.
AU - Jha, Susmit
AU - Pavone, Marco
AU - Tomlin, Claire J.
N1 - Funding Information:
We thank Dr. Sumeet Singh, Dr. Mo Chen, Dr. Murat Arcak, Dr. Alessandro Abate, and Dr. David Freyberg for discussions. M.C. and V.C. are supported by NSF GRFP. This work is supported by NSF CPS 1740079, NSF PIRE UNIV59732, and NSF DGE 1633740.
Publisher Copyright:
© 2019 American Automatic Control Council.
PY - 2019/7
Y1 - 2019/7
N2 - 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).
AB - 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).
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U2 - 10.23919/acc.2019.8815169
DO - 10.23919/acc.2019.8815169
M3 - Conference contribution
AN - SCOPUS:85072301299
T3 - Proceedings of the American Control Conference
SP - 2958
EP - 2963
BT - 2019 American Control Conference, ACC 2019
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2019 American Control Conference, ACC 2019
Y2 - 10 July 2019 through 12 July 2019
ER -