2019/02/28 by Margaret P. Chapman, Chapman, Margaret P., Jonathan Lacotte +17 · 3 citations
Decision Sciences · Engineering · #FOS: Electrical engineering #Infrastructure Resilience and Vulnerability Analysis #Probabilistic and Robust Engineering Design #Risk and Safety Analysis #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1902.11277
openalex publication_date 2019/02/28 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28
A classic reachability problem for safety of dynamic systems is to compute\nthe set of initial states from which the state trajectory is guaranteed to stay\ninside a given constraint set over a given time horizon. In this paper, we\nleverage existing theory of reachability analysis and risk measures to devise a\nrisk-sensitive reachability approach for safety of stochastic dynamic systems\nunder non-adversarial disturbances over a finite time horizon. Specifically, we\nfirst introduce the notion of a risk-sensitive safe set as a set of initial\nstates from which the risk of large constraint violations can be reduced to a\nrequired level via a control policy, where risk is quantified using the\nConditional Value-at-Risk (CVaR) measure. Second, we show how the computation\nof a risk-sensitive safe set can be reduced to the solution to a Markov\nDecision Process (MDP), where cost is assessed according to CVaR. Third,\nleveraging this reduction, we devise a tractable algorithm to approximate a\nrisk-sensitive safe set, and provide theoretical arguments about its\ncorrectness. Finally, we present a realistic example inspired from stormwater\ncatchment design to demonstrate the utility of risk-sensitive reachability\nanalysis. In particular, our approach allows a practitioner to tune the level\nof risk sensitivity from worst-case (which is typical for Hamilton-Jacobi\nreachability analysis) to risk-neutral (which is the case for stochastic\nreachability analysis).\n