In this talk, we will demonstrate a novel method for safely modeling or controlling high-dimensional, nonlinear systems arising from interconnected or multi-scale problems. Namely, we will present a reachability-based solution using the Hopf formula, "antagonistic error" and state augmented (SA) linearizations. SA systems are well-known for their ability to outperform standard linear methods in capturing nonlinear dynamics by lifting the system to a high-dimensional space, approximating the Koopman operator. We show through a series of inequalities that it is possible to define a differential game in the SA space whose projected solutions are conservative. It follows that predictions and the optimal controller of this special SA linear game with error are valid in the true system despite any bounded lifting error or disturbance. We demonstrate this in the simple slow-manifold system for clarity and in the Van der Pol system to observe the use of different lifting functions.

The video of this presentation is available here.