Safety-Aware Optimal Control of Stochastic Systems Using Conditional Value-at-Risk
For control engineers and researchers, this work offers a new safety verification tool (risk-constrained safe sets) and a computationally feasible approach to multi-objective stochastic control with safety constraints.
This paper introduces a safety risk measure using conditional value-at-risk and set distance to formulate a risk-constrained optimal control problem for stochastic systems, providing a tractable dynamic programming solution. The method is validated through an inventory control problem, demonstrating tradeoffs between risk tolerance and mean performance.
In this paper, we consider a multi-objective control problem for stochastic systems that seeks to minimize a cost of interest while ensuring safety. We introduce a novel measure of safety risk using the conditional value-at-risk and a set distance to formulate a safety risk-constrained optimal control problem. Our reformulation method using an extremal representation of the safety risk measure provides a computationally tractable dynamic programming solution. A useful byproduct of the proposed solution is the notion of a risk-constrained safe set, which is a new stochastic safety verification tool. We also establish useful connections between the risk-constrained safe sets and the popular probabilistic safe sets. The tradeoff between the risk tolerance and the mean performance of our controller is examined through an inventory control problem.