Zermelo's navigation problem

In mathematical optimization, Zermelo's navigation problem, proposed in 1931 by Ernst Zermelo, is a classic optimal control problem that deals with a boat navigating on a body of water, originating from a point ${\displaystyle A}$ to a destination point ${\displaystyle B}$. The boat is capable of a certain maximum speed, and the goal is to derive the best possible control to reach ${\displaystyle B}$ in the least possible time.

Without considering external forces such as current and wind, the optimal control is for the boat to always head towards ${\displaystyle B}$. Its path then is a line segment from ${\displaystyle A}$ to ${\displaystyle B}$, which is trivially optimal. With consideration of current and wind, if the combined force applied to the boat is non-zero the control for no current and wind does not yield the optimal path.

...
Wikipedia