Given that

with the constraint on y(x) such that

and the end condition y(0)=0 and y(1)=1,

prove that F{y(x)} achieves its minimum value for y = x

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- Sep 29th 2010, 04:29 AMpdnhanOptimal control problem
Given that

with the constraint on y(x) such that

and the end condition y(0)=0 and y(1)=1,

prove that F{y(x)} achieves its minimum value for y = x - Sep 29th 2010, 05:20 PMzzzoak

-this is length of a curve from (0,0) to (1,1). Its length is sqrt(2) only if it is a straight line.

y=x.

May be it may be solved to get this solution.

Without length restriction F min is sinx/sin1.