Stephen Tu

Model-based control synthesis relies on an accurate description of the system dynamics and the environment. When such models are unavailable or difficult to derive from first principles, they must be learned from system trajectories. Latent world models have recently emerged as a promising general-purpose approach, learning low-dimensional representations together with dynamics that evolve these representations to predict future behavior. However, it remains unclear which dynamical properties these models preserve, and whether they support control synthesis with guarantees of closed-loop stability and safety. Resolving these questions is essential to establishing latent world modeling as a reliable tool for control design. In this talk, we initiate a study of the dynamical properties captured by latent world model designs. For trajectory data generated by a linear dynamical system, we show that multi-step backward latent reconstruction losses recover the system’s unstable subspace, provided the latent dimension is large enough to represent the unstable modes. We then show that an H-infinity controller synthesized using the learned latent dynamics stabilizes the original system. Crucially, both multi-step prediction and reconstruction in the original space (i.e., backward reconstruction) are necessary for this guarantee: removing either can lead to an unstable closed-loop system. Although our analysis focuses on linear systems, experiments on high-dimensional nonlinear systems reveal behavior consistent with our theoretical findings.