PhD thesis by Daniel González Arribas. Intended Title: “Stochastic Optimal Control towards Enhanced Predictability of four-dimensional Trajectories using Weather Ensemble Prediction Forecasts”. Supervisors: Manuel Soler and Manuel Sanjurjo. Con-Funded by HALA! Reserach Network (SESAR WP-E within FP7).


The research activities included in this proposal aim at studying the problem of optimizing trajectories under the effects of weather uncertainties, exploring algorithms for efficient, yet predictable strategic trajectory planning in ATM. Specific objectives include:

  1. the characterization of weather uncertainty based on Ensemble Prediction Forecasts (EPF);
  2. the development of algorithms to optimize trajectories under uncertainty;
  3. the validation of the results via simulations which must be first defined and thereafter executed.

The overall goal is to contribute towards acquiring a better understanding on how the information of weather EPFs could be included in optimal control problems with the purpose of developing stochastic optimal control algorithms capable of finding 4D trajectories at strategic level that are efficient, yet predictable.

Theory, methods and tools to be used during the development of the PhD thesis include:

  • probabilistic weather forecasts based on EPFs;
  • BADA 4.1 and WGS-84 models for aircraft performance and the Earth, respectively;
  • deterministic and stochastic optimal control theory;
  • numerical methods for uncertainty representation (Monte Carlo, Polynomial Chaos), coupled with numerical methods on deterministic and stochastic optimal control;
  • the definition of validation scenarios that are to be analyzed and executed in the facilities of a center for air traffic controllers training.

The following results are expected:

  1. a tool to obtain the optimal ensemble 4D trajectory at strategic level;
  2. a robust and stochastic optimal control algorithmic framework to find at strategic level optimal and predictable trajectories. These results are to be validated to quantitatively assess both the predictability and the efficiency of the trajectory in terms of: (a) time buffers from a given Required Time of Arrival (RTA); and (b) air traffic control tactical modifications in the planned trajectory (and thus loss of efficiency) required in a particular volume of airspace due to deviations from the planned RTAs.

The problems of optimizing trajectories and characterizing uncertainty around them have been studied over the last years. However, and this is the main innovative aspect of this proposal, there is a powerful need of tackling the problem in an integrated way, developing algorithms that combine optimality and uncertainty in the scope of 4D trajectory planning in ATM. The research activities included in this proposal aims at contributing to HALA! by discussing the automation role at the best time layer: minimizing the loss of accuracy in the trajectory data (associated to atmospheric behavior) would certainly reduce tactical intervention and result in expanded trajectory planning time-frames, which would empower automation capabilities at strategic level.