This paper addresses the problem of identifying structured nonlinear dynamical systems, with the goal of using the learned dynamics in model-based reinforcement learning problems. We present in this setting a new class of scalable multi-task estimators which promote sparsity, while preserving the dynamics structure and leveraging available physical insight. An implementation leading to consistent feature selection is suggested, allowing to obtain accurate models. An additional regularizer is also proposed to help in recovering realistic hidden representations of the dynamics. We illustrate our method by applying it to an aircraft trajectory optimization problem. Our numerical results based on real flight data from 25 medium haul aircraft, totaling 8 millions observations, show that our approach is competitive with existing methods for this type of application.