This paper addresses an aircraft dynamical system identification problem, with the goal of using the learned models for trajectory optimization purposes. Our approach is based on multi-task regression. We present in this setting a new class of estimators that we call Block sparse Lasso, which conserves a certain structure between the tasks and some groups of variables, while promoting sparsity within these groups. An implementation leading to consistent feature selection is suggested, allowing to obtain accurate models, which are suitable for trajectory optimization. An additional regularizer is also proposed to help in recovering hidden representations of the initial dynamical system. We illustrate our method with numerical results based on real flight data from 25 medium haul aircraft, totaling 8 million observations.