Quantifying the Value of Preview Information for Safety Control

Safety-critical systems, such as autonomous vehicles, often incorporate perception modules that can anticipate upcoming disturbances to system dynamics, expecting that such preview information can improve the performance and safety of the system in complex and uncertain environments. However, there is a lack of formal analysis of the impact of preview information on safety. In this work, we introduce a notion of safety regret, a properly defined difference between the maximal invariant set of a system with finite preview and that of a system with infinite preview, and show that for linear systems, this quantity corresponding to finite-step preview decays exponentially with the preview horizon. Furthermore, algorithms are developed to numerically evaluate the safety regret of a system for different preview horizons. Finally, we demonstrate the established theory and algorithms via multiple examples from different application domains.