ME254/ECE217C,Midterm ExamWinter 2009This is a take home exam, it is due back at 1pm, Friday 2/13 in Prof. Bamieh’s mailbox (sharpdeadline). You can consult the notes that have been handed out in class or on the course webpage, but no other references are allowed. You may not discuss these problems with others in classuntil 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 integratorcascade systemddtx1x2x3=010001000x1x2x3+001u,where one desires to transfer the state fromx(0) = 0 to the manifoldx21(T) +x22(T) = 1,while minimizing theL2norm of the controlu.You should use what we have done in class for this problem as well as MATLAB. Find theoptimal control and the corresponding state trajectory for two cases:T= 1, andT= 10.
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course web page, MATLAB command plot3, corresponding state trajectory