Reduced-order models (ROMs) provide a viable avenue to enable (near) real-time decision-making and control with a digital twin, due to their rigorous mathematical derivation and fast simulation. However, not all ROM techniques are “fit-for-purpose” to serve as a digital twin, as decision-making and control require special properties of ROMs. In this talk, we focus on the system-theoretic aspects of controllability and observability, and describe ways to derive nonlinear ROMs that preserve those properties. In particular, we focus on nonlinear balanced truncation ROMs as initializations of the digital twin before the physical-to-digital data stream starts. To obtain the relevant balancing transforms, special forms of Hamilton-Jacobi-Bellman equations have to be solved, which we do so with Taylor-series-based techniques to produce scalable algorithms with 1,000s of state variables.