bv_cvxbook_extra_exercises

# the force comes from two thrusters and from gravity

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Unformatted text preview: or the original problem. Solving this problem multiple times, with diﬀerent c’s, will generate (perhaps diﬀerent) ǫ-suboptimal points. If 18 the problem has a strong minimum, these points will all be close to each other; if the problem has a weak minimum, they can be quite diﬀerent. There are diﬀerent strategies for choosing c in these experiments. The simplest is to choose the c’s randomly; another method is to choose c to have the form ±ei , for i = 1, . . . , n. (This method gives the ‘range’ of each component of x, over the ǫ-suboptimal set.) You will carry out this method for the following problem, to determine whether it has a strong minimum or a weak minimum. You can generate the vectors c randomly, with enough samples for you to come to your conclusion. You can pick ǫ = 0.01p⋆ , which means that we are considering the set of 1% suboptimal points. The problem is a minimum fuel optimal control problem for a vehicle moving in R2 . The position at time kh is g...
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## This note was uploaded on 09/10/2013 for the course C 231 taught by Professor F.borrelli during the Fall '13 term at Berkeley.

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