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Unformatted text preview: MAE 288A Assignment 5/TakeHome Final Due Wednesday, 9 Dec., 2009 Note: You may find it helpful to write code in order to solve some of these problems. You may work in Matlab, C, C++, Java, Fortran, Maple, or Mathematica. Please include copies of any codes used. 1. (10) Consider the optimal control problem of exit type given by dy namics ˙ ξ t = u t , ξ = x ∈ ( − 1 , 1) , payoff J ( x ; u · ) = integraldisplay τ ρ + ( u 2 t / 2) dt, and value V ( x ) = inf u ∈U J ( x ; u · ) , where ρ = 1, τ = inf { t ≥  ξ t negationslash∈ ( − 1 , 1) } , and U is the set of L 2 controls taking values in U = IR , as indicated in class. Construct the gridbased numerical scheme as discussed in class to numerically obtain the value function. You will need to be a bit careful about the time and space stepsizes in order to ensure the you obtain a reasonable solution approximation. Use at least 21 grid points over [ − 1 , 1]. You do not need to take limits as time and space step sizes converge to zero.do not need to take limits as time and space step sizes converge to zero....
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 Spring '10
 Mceneaney,W
 Compact space, MAE 288A Assignment

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