Zermelo's Navigation Problem
Proposed in 1931, the Zermelo's navigation problem is a classic optimal control problem. The problems deals with a boat navigating on a body of water, originating from a point O to a destination point D. The boat is capable of a certain maximum speed, and we want to derive the best possible control to reach D in the least possible time.
Without considering external forces such as current and wind, the optimal control is to follow a straight line segment from O to D. With consideration of current and wind, the shortest path from O to D is in fact, not the optimal solution.
Read more about this topic: Ernst Zermelo
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