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Deriving adjoint equation of an Optimal Control Problem

  1. Sep 21, 2015 #1
    Dear all,

    I am investigating a Transient Optimal Heating Problem with distributed control and Dirichlet condition. The following are the mathematical expression of the problem:

    upload_2015-9-21_20-54-19.png


    Where Ω is the domain,
    Γ is the boundary,
    y is the temperature distribution,
    u is the control,
    yΩ is the optimal temperature distribution,
    yD is some known temperature on Γ (i.e. Dirichlet condition),
    λ and κ are some real constant.

    I want to find the adjoint equation for the above problem, I found on some articles that I need to use Lagrangian Function and Divergence Theorem with Integration by Parts to derive the adjoint equation.

    In other words, consider d/dε [L(y+εz,u,λ)] =0 and put ε=0, where L(y,u,λ) is the Lagrangian Function.

    However, I could not keep going and derive the adjoint equation. I do not know how to apply Divergence Theorem with Integration by Parts to get the adjoint equation.

    Can anyone help me to derive the adjoint equation?
     
  2. jcsd
  3. Sep 26, 2015 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
     
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