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Safety-critical systems, such as autonomous vehicles, often incorporateperception modules that can anticipate upcoming disturbances to systemdynamics, expecting that such preview information can improve the performanceand safety of the system in complex and uncertain environments. However, thereis a lack of formal analysis of the impact of preview information on safety. Inthis work, we introduce a notion of safety regret, a properly defineddifference between the maximal invariant set of a system with finite previewand that of a system with infinite preview, and show that this quantitycorresponding to finite-step preview decays exponentially with preview horizon.Furthermore, algorithms are developed to numerically evaluate the safety regretof the system for different preview horizons. Finally, we demonstrate theestablished theory and algorithms via multiple examples from differentapplication domains.

Quantifying the Value of Preview Information for Safety Control