Dynamical systems complexity with a view towards air traffic management applications

The growth of air traffic in future years requires a paradigm shift in the way the aircraft are controlled. Major innovative projects (SESAR in Europe, NexGen in USA) have started in order to define and implement control tools based on time-space constraints on aircraft trajectories. As a consequence, an increasing level of automation is expected. In this framework, it is of primary importance to be able to quantify the hardness to produce conflict free trajectories for a given situation and the robustness of the solution found. In this paper, a characterisation based on the Lyapunov exponents of a dynamical system interpolating the observed data will be presented. A first part will be devoted to vector field fitting, and a second one to efficient lyapunov exponents computation. Then, some practical implementation issues will be discussed.