impact of a jump during a timestep by averaging the variations at the beginning, twice at the middle point and at the end of the timestep (cf. [@Fortin2011]). Nevertheless, stability questions shall be addressed in the later in order to validate the approach.

Parameter Tuning
----------------

Now that the trajectory generator is defined, we would like to tune the model parameters according to observations. First, there should be a trade-off between the number of parameters and the capacity of the model to approximate real trajectories. As a bad example, instead of using the default thrust controller defined in [@Bada2012], we tried to find the optimal controller for the acceleration mode for a given trajectory. The resulting controller was a Bang-Bang control function where we have observed that the mode switches between accelerating and decelerating at every timestep. Clearly, this function can approximate any real trajectories, but does not generalize from one trajectory to another and does not reflect the real behavior of the aircraft. So, from eq.\[eq:roc\] and eq.\[eq:acceleration\] and the speed schedule $V^*$, the parameters $m$, $V_1$, $V_2$ ,$M$ and $\Delta T$ are good candidates since they are time-invariant, contrary to a discrete control law. Moreover, their values are 