bv_cvxbook_extra_exercises

# Such a partition is called a cut of the graph the

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Unformatted text preview: ove, we have y = (I − GF )−1 v, u = F (I − GF )−1 v. (You can simply assume that I − GF will be invertible.) The disturbance v is random, with E v = 0, E vv T = σ 2 I , where σ is known. The objective is to 2 minimize maxi=1,...,n E yi , the maximum mean square value of the output components, subject to 2 ≤ 1, i = 1, . . . , n, i.e., each input component has a mean square value not the constraint that E ui exceeding one. The variable to be chosen is the matrix F ∈ Rn×n . (a) Explain how to use convex (or quasi-convex) optimization to ﬁnd an optimal feedback gain matrix. As usual, you must fully explain any change of variables or other transformations you carry out, and why your formulation solves the problem described above. A few comments: • You can assume that matrices arising in your change of variables are invertible; you do not need to worry about the special cases when they are not. • You can assume that G is invertible if you need to, but we will deduct a few points from these answers. (b) Carry out your method...
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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 University of California, Berkeley.

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