  The vertical trajectory optimization for the en route descent phase is
studied in the presence of both along track and cross winds, which are both
modeled as functions of altitude. The flight range covers some portion of a
cruise segment and ends at a meter fix. The descent trajectory is assumed as a
flight idle descent. The problem is formulated as an optimal control problem
with both mixed state path constraints and pure state constraints. For
minimizing environmental impacts, we optimize descent trajectory with respect
to two cost functionals: fuel and emissions cost. We analyze both singular arc
and boundary arc using the necessary conditions of the optimality. From the
analysis result, we propose the optimal trajectory generation method, in which
the optimal trajectory is generated by the backward and forward integration.
The trajectory from the proposed algorithm is compared to the numerical optimal
solution of the original optimal control problem. The result shows that
proposed algorithm generates the same solution as the numerical optimal
solution. The wind speed, wind shear, and cross wind effects on the optimal
trajectory are analyzed with two aircraft type, Boeing 737-500 and Boeing
767-400.
