bv_cvxbook_extra_exercises

Plot pt vt ft and bt versus t comment on what you see

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Unformatted text preview: he simplest is that f is a single, fixed, known loading. In more sophisticated formulations, the loading f might be a random vector with known distribution, or known only to lie in some set F , etc. Show that each of the following four problems is a convex optimization problem, with x as variable. • Design for a fixed known loading. The vector f is known and fixed. The design problem is minimize E (x, f ) subject to l ≤ xi ≤ u, i = 1, . . . , m Wtot (x) ≤ W. • Design for multiple loadings. The vector f can take any of N known values f (i) , i = 1, . . . , N , and we are interested in the worst-case scenario. The design problem is minimize maxi=1,...,N E (x, f (i) ) subject to l ≤ xi ≤ u, i = 1, . . . , m Wtot (x) ≤ W. • Design for worst-case, unknown but bounded load. Here we assume the vector f can take arbitrary values in a ball B = {f | f ≤ α}, for a given value of α. We are interested in minimizing the worst-case stored energy, i.e., minimize sup f ≤α E (x, f (i) ) subject to l ≤ xi ≤ u, i = 1, . . . , m Wtot (x) ≤ W. 118 • Design for a random load with known statistics. We can also use a stochastic model of the uncertainty in the...
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