Risk-sensitive safety analysis via state-space augmentation.

Risk-sensitive safety analysis is a safety analysis method for stochastic systems on Borel spaces that uses a risk functional from finance called Conditional Value-at-Risk (CVaR). CVaR provides a particularly expressive way to quantify the safety of a control system, as it represents the average cost in a fraction of worst cases. In prior work, the notion of a risk-sensitive safe set was defined in terms of a non-standard optimal control problem, in which a maximum cost is assessed via CVaR. Here, we provide a method to compute risk-sensitive safe sets exactly in principle by utilizing a state-space augmentation technique. In addition, we prove the existence of an optimal pre-commitment policy under a measurable selection condition. The proposed framework assumes continuous system dynamics and cost functions, but is otherwise flexible. In particular, it can accommodate probabilistic control policies, fairly general disturbance distributions, and control-dependent, non-monotonic, and non-convex stage costs. We demonstrate how risk-sensitive safety analysis is useful for a stormwater infrastructure application. Our numerical examples are inspired by current challenges that cities face in managing precipitation uncertainty.