Qi Gong - University of California, Santa Cruz (UC Santa Cruz) Computing optimal feedback controls for nonlinear systems generally requires solving Hamilton-Jacobi-Bellman (HJB) equations, a well- known challenging problem. In this talk, we present a model-based data-driven method to approximate solutions to HJB equations for high dimensional nonlinear systems and compute optimal feedback controls in real-time. To accomplish this, we model solutions to HJB equations with neural networks (NNs) trained on data generated without any state space discretization. Training is made more effective and efficient by leveraging the known physics of the problem and generating training date in an adaptive fashion.