EXAMPLE OF APPLICATION OF THE PONTRYAGIN’S MINIMUM PRINCIPLE “PMP EXTENSION”: ZERMELO PROBLEM (WITH CURRENT SPEED MORE THAN BOAT SPEED HYPOTHESIS)

Abstract

We present an example of application covering several cases using the extension of the Pontryaguine minimum principle (PMP) in the case where we add a constraint on reaching a target variety at the final time: the Zermelo problem with current speed more than Boat speed hypothesis, where we consider a boat crossing a channel under a strong current and where we try to reach the opposite bank by minimizing the lateral offset or by minimizing the crossing time.