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Math Help - Optimal control problem

  1. #1
    Junior Member
    Joined
    Sep 2009
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    35

    Post Optimal control problem

    Given that
    F\{y(x)\}= \int\begin{array}{cc}1\\0\end{array} (y'^2-y^2) dx
    with the constraint on y(x) such that
     \int \begin{array}{cc}1\\0\end{array} \sqrt{1+y'^2}dx = \sqrt{2}
    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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  2. #2
    Senior Member
    Joined
    Mar 2010
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    <br />
\int \begin{array}{cc}1\\0\end{array} \sqrt{1+y'^2}dx = \sqrt{2} <br />
    -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.
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