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.
Highlights
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
The theorem of the Pontryagin’s minimum principle PMP: If is an optimal control, by noting and by defining the deputy state the trajectory associated with the control solution of
The PMP here provides only a necessary condition for optimization. It does not say anything about the existence of optimal control and it does not provide a sufficient condition a priori
Summary
A triplet Remark: satisfying the above conditions is called an extremal. The PMP here provides only a necessary condition for optimization. It does not say anything about the existence of optimal control and it does not provide a sufficient condition a priori. We consider the extremes and we sort
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