A Risk-Sensitive Finite-Time Reachability Approach for Safety of Stochastic Dynamic Systems
A Risk-Sensitive Finite-Time Reachability Approach for Safety of Stochastic Dynamic Systems
复制标题
DOI：
10.23919/acc.2019.8815169
复制
发表时间：
2019-02
期刊：
影响因子：
--
通讯作者：
Margaret P. Chapman;Jonathan Lacotte;Aviv Tamar;Donggun Lee;K. Smith;Victoria Cheng;J. Fisac;Susmit Jha;M. Pavone;C. Tomlin
中科院分区：
文献类型：
--
作者：
Margaret P. Chapman;Jonathan Lacotte;Aviv Tamar;Donggun Lee;K. Smith;Victoria Cheng;J. Fisac;Susmit Jha;M. Pavone;C. Tomlin
动态系统安全的一个经典可达性问题是计算初始状态集，保证状态轨迹在给定的时间范围内保持在给定的约束集内。在本文中，我们利用现有的理论的可达性分析和风险措施，设计一个风险敏感的可达性方法的安全性随机动态系统在有限的时间范围内的非对抗性干扰。具体来说，我们首先引入的概念，风险敏感的安全集阿萨一组初始状态，从大的约束违反的风险可以减少到所需的水平，通过控制策略，其中风险量化使用的条件风险价值（CVaR）措施。其次，我们展示了如何计算一个风险敏感的安全集可以减少到马尔可夫决策过程（MDP）的解决方案，根据CVaR的成本进行评估。第三，利用这种减少，我们设计了一个易于处理的算法来近似一个风险敏感的安全集，并提供有关其正确性的参数。最后，我们提出了一个现实的例子，从雨水集水区设计的启发，以证明风险敏感的可达性分析的效用。特别是，我们的方法允许从业者调整的风险敏感性水平，从最坏的情况下（这是典型的汉密尔顿-雅可比可达性分析）的风险中性（这是随机可达性分析的情况下）。
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).