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 - 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).
UR - http://www.scopus.com/inward/record.url?scp=85072301299&partnerID=8YFLogxK
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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 -