hw4_f08 - = T dt x x u J 2 2 2 1 2 8 3 2 1 subject to the...

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Homework Set #4: MAE 4720/7720 – Modern Control Fall 2008 Due October 28, 2008 Problem 1: Given the quadratic scalar function F to be minimized: Minimize 2 3 2 2 2 1 3 . 0 6 2 ) ( u u u F + + = u subject to the two linear equality constraints 0 8 2 3 ) ( 0 4 ) ( 3 2 1 2 2 1 1 = - + - = = - = u u u h u u h u u Determine the optimal solution vector u * and show your steps. Problem 2: A fixed-time optimal control problem is shown below: Determine the optimal control u* ( t ), 0 < t < T , which minimizes Minimize ( 29
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Unformatted text preview: + + = T dt x x u J 2 2 2 1 2 8 3 2 1 subject to the dynamical equations u x x x x 2 5 1 2 2 1 + = = where the initial state is x (0) = [ 2 -0.5 ] T and end-time T = 4 (fixed). a) Define the Hamiltonian, H ( x , u ) b) Present all first-order necessary conditions for an optimal solution (i.e., derive the 2PBVP). c) Is the Hamiltonian constant? Explain....
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This note was uploaded on 01/12/2011 for the course MAE 4720 taught by Professor Dr.kluever during the Spring '10 term at Missouri (Mizzou).

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