2007midterm2

2007midterm2 - 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 April 19th, 2007 16.323 Midterm #2 This is a closed-book exam, but you are allowed 2 page of notes (both sides). You have 1.5 hours. There are three 3 questions with values as given . 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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± ² 1. (35pts) In the calculus of variations problem, where the goal is to minimize t f J = x,t ) dt g ( x, ˙ t 0 we showed that the Frst order necessary condition is ∂g d ∂g ∂x dt ∂x ˙ = 0 subject to various (assumed to be well deFned) initial and terminal conditions, de- pending on the problem statement. Now consider the following: (a) If we can write g g ( ˙ x ) (i.e. the function g is not an explicit function of x or time), show that there always exists a solution
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This note was uploaded on 11/07/2011 for the course AERO 16.323 taught by Professor Jonathanhow during the Spring '08 term at MIT.

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2007midterm2 - MIT OpenCourseWare http:/ocw.mit.edu 16.323...

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