We present a three-step method to perform system identification and optimal control of nonlinear systems. Our approach is mainly data-driven and does not require active excitation of the system to perform system identification. In particular, it is designed for systems for which only historical data under closed-loop control are available and where historical control commands exhibit low variability. In the first step, simple simulation models of the system are built and run under various conditions. In the second step, a neural network architecture is extensively trained on the simulation outputs to learn the system physics and retrained with historical data from the real system with stopping rules. These constraints avoid overfitting that arises by fitting closed-loop controlled systems. By doing so, we obtain one (or many) system model(s), represented by this architecture, whose behavior can be chosen to match more or less the real system. Finally, state-of-the-art reinforcement learning with a variant of domain randomization and distributed learning is used for optimal control of the system. We first illustrate the model identification strategy with a simple example, the pendulum with external torque. We then apply our method to model and optimize the control of a large building facility located in Switzerland. Simulation results demonstrate that this approach generates stable functional controllers that outperform on comfort and energy benchmark rule-based controllers.