2007midterm1

2007midterm1 - MIT OpenCourseWare http:/ocw.mit.edu 16.323...

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MIT OpenCourseWare http://ocw.mit.edu 16.323 Principles of Optimal Control Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .
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16.323, #15 March 8th, 2007 16.323 Midterm #1 This is a closed-book exam, but you are allowed 1 page of notes (both sides). You have 1.5 hours. There are three 3 questions of equal value . Hint: To maximize your score, initially give a brief explanation of your approach before getting too bogged down in the equations. 1
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1. For the following cost function, F = x 2 + y 2 6 xy 4 x 5 y (a) Minimize the cost subject to the constraints, f 1 : 2 x + y + 1 0 f 2 : x + y 4 0 (b) How is the optimal cost affected if the constraint f 1 is changed to, f = 2 x + y + 1 . 1 0 1 Estimate this difference and explain your answer. 2. The ±rst order discrete system, x k +1 = x k + u k is to be transferred to the origin in two stages ( x 2 = 0). The performance measure to be minimized is, 1 J = ( | x
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2007midterm1 - MIT OpenCourseWare http:/ocw.mit.edu 16.323...

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