The notion of a safe operating space for humanity has recently emerged as a conceptual guide for global-scale sustainability policy challenges. While the Planetary Boundaries Framework defines this space and has spurred empirical work to determine where the Earth system is relative to its boundaries, even less is known regarding the capacity of globally interconnected societies to navigate towards or remain within a safe operating space when constrained by imperfect information. This study leverages notions of observability and controllability from modern control systems theory to explore the link between information and the capacity to navigate Earth system dynamics in three interrelated sustainability problems. The analysis highlights the critical dependence of the notion of a safe operating space on information and decision processes and the subtle interplay between how past, real-time, and projected information on a particular observation is weighted and the controllability of a system.