2007midterm2

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

This preview shows pages 1–4. Sign up to view the full content.

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 .

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
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
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 first order necessary condition is ∂g d ∂g ∂x dt ∂x ˙ = 0 subject to various (assumed to be well defined) 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 that is a linear function of time.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern