Title: Learning System Dynamics from Sensory Input under Optimal Control Principles. Abstract: Identifying the underlying dynamics of actuated physical systems from sensory input is of high interest in control, robotics, and engineering in general. In the context of control problems, existing approaches decouple the construction of the feature space where the dynamics identification process occurs from the target control tasks, potentially leading to a mismatch between feature and real state spaces: the systems may not be controllable in feature space, and synthesized controls may not be applicable in the state space. Borrowing from the Koopman formalism, we propose instead to learn an embedding of both the states and con- trols in feature spaces where the dynamics are linear, and to include the target control task in the learning objective in the form of a differentiable and robust optimal control problem. We validate this approach with simulation experiments of systems with non-linear dynamics, demonstrating that the controls obtained in feature space can be used to drive the corresponding physical systems and that the learned model can serve for future state prediction.