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midterm

# midterm - ME254/ECE217C Midterm Exam Winter 2009 This is a...

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ME254/ECE217C, Midterm Exam Winter 2009 This is a take home exam, it is due back at 1pm, Friday 2/13 in Prof. Bamieh’s mailbox (sharp deadline). You can consult the notes that have been handed out in class or on the course web page, but no other references are allowed. You may not discuss these problems with others in class until you have turned your work in. Please write legibly and make full use of logical reasoning. 1. This problem is a continuation of an example done recently in class with the three integrator cascade system d dt x 1 x 2 x 3 = 0 1 0 0 0 1 0 0 0 x 1 x 2 x 3 + 0 0 1 u, where one desires to transfer the state from x (0) = 0 to the manifold x 2 1 ( T ) + x 2 2 ( T ) = 1, while minimizing the L 2 norm of the control u . You should use what we have done in class for this problem as well as MATLAB. Find the optimal control and the corresponding state trajectory for two cases: T = 1, and T = 10.
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