|Description of work
To achieve the stated objectives of this work package, two tasks will be performed:
P03.01 – Establishing a basis for the work. The research and operational context for the work needs to be clarified. Based on the characterization of uncertainty described in WP 02, the first step of this WP will be a more precise identification of the techniques that can be applied and of the questions that have to be answered. More precisely, we would define the content of a probabilistic traffic prediction in term of traffic distribution and flight dependencies. In order to define these dependencies, we will look at flights interaction, as explained hereunder. Based on existing modelling techniques in ATM, we will determine the best model that will allow us to (first) represent, and (second) optimize our actuations in order to manage, probabilistic traffic situations (including elements, relationships and probability distributions).
P03.02 – Combination of Probable Trajectories. Based on EUROCONTROL Data, the characterization of uncertainty described in WP 02 and the results of P03.01, modelling and work on the raised questions will be done. Two main fields of applied mathematics are foreseen as areas of research for these methods: the robust and stochastic control and the big data fields. In these two areas, the following preliminary questions will be posed in order to develop a global model.
The application of big data-techniques will target the design of ‘add-on tools’, limited in scope, but enabling quick conversion into practically usable tools. The first tracks to explore would be the following:
These two points would allow to increase our understanding of the overall interaction of flights and uncertainty, and could already lead to our goal of predicting a model for uncertainty and combination of probable trajectories. Depending on the outcome of this first research topic, a second goal would be to control the uncertainty. In order to do so, we will use (computational) techniques from robust control theory. Indeed, robust control techniques allow to represent uncertain sets and their evolution in a dynamical system. In particular, robust control has thrived on the rise of new programming techniques like semi-definite programming, sum of squares methods, convex optimization and other geometrical and algebraic tools in order to represent these uncertainty sets and their evolution.
Typical applications of robust control are e.g., bioprocesses , where the state of the system can be known only up to a certain accuracy, or control of aircraft , where the true value of some variables is only known up to a certain accuracy, while some safety constraints guarantee the good behaviour of the controlled systems even though the knowledge at the disposal of the controller is limited.
Modern control theory has proposed diverse mechanisms for controlling dynamic system, not only for systems with a few defined continuous input parameters, but also for systems with discrete binary possible actions   In our case, these particular actions could range widely, going from a change in the altitude of a precisely predicted flight, or a change in the trajectory, requiring more accuracy, forbidding some actions, etc. Our aim would be to minimize and/or control the resulting uncertainty of the network by taking advantage of any available actions in the overall network. Regarding this second research part, the research questions are not yet completely settled, as they will be dictated by the previous results. However, we foresee the following points:
Trade-off between computability and accuracy will be an important criterion in our methods. In addition to that, critical needs from the ATM field will have to be taken into account (safety, user-friendliness, implementability in a legacy environment).
In addition to the graphical model that presents the delay inducing couplings between the flights in the traffic, a higher level capacity/service-rate model will be developed. This model will be built with tools from stochastic queuing network theory  and will represent time-dependent arrival and departure service-rates of airports and airspaces. The utilization of advanced theoretical concepts from queuing theory (time-varying parameters, networks with ring queues etc.) will be implemented based on the domain-expertise to develop a realistic capacity model. The parameters of the model will be inferred from the historical flight data and capacity declaration data using statistical methods. This networked queuing model will be integrated with the traffic model to simulate the delay propagation in the network based on the stochastic service-rate limits due to the emergent events and coupled with the trajectory uncertainties in the traffic. The potential interaction between those layers, such as the centric aircraft network and the airport/airspace centric network, will further be investigated to establish better understanding on such complex system. The layered approach will be addressing structure of the current ATM system with the multi-decision makers at the different level of the decision process (i.e., pilots and ground controllers). Hence, these uncertainty mapping tools will be enabling the potential control on the sensitive parameters including capacity and service rate at high-level or directly intervening to the flight trajectories at lower-level. In that sense, this WP will allow us to discuss future needs of the airspace and the flight operations by considering quantified uncertainties coupled with the flight trajectories.