We are working on a helicopter game, and encountered a rather difficult problem:
For sake of simplicity, let's consider this to be a one-dimensional problem.
I have a helicopter traveling at speed $V$ and an arbitrary pitch angle $A$. The acceleration of the helicopter is defined as thrust $t$ and mass $m$ as $\frac{t \cdot \cos(A)}{m}$.
The pitch rate has a max of dAMAX, and a maximum rate of change of ddAMAX.
Also there's simplified air drag $R = \frac{1}{2}v^2 \cdot \text{dragCoefficient}$, although that might be a needless complication for this problem.
So the goal is to achieve $V=0$ and $A=0$ simultaneously in the least amount of time as possible.
Made a little animation to show the approximate scenario: hover sample
