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Title: A Risk-Sensitive Finite-Time Reachability Approach for Safety of Stochastic Dynamic Systems
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-sensitive reachability approach for safety of stochastic dynamic systems under non-adversarial disturbances over a finite time horizon. Specifically, we first introduce the notion of a risk-sensitive safe set as a 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 theoretical 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 more » from worst-case (which is typical for Hamilton-Jacobi reachability analysis) to risk-neutral (which is the case for stochastic reachability analysis). « less
Authors:
; ; ; ; ; ; ;
Award ID(s):
1740079 1750009
Publication Date:
NSF-PAR ID:
10119092
Journal Name:
AMERICAN CONTROL CONFERENCE
Sponsoring Org:
National Science Foundation
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