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Unformatted text preview: rgy function φ(st ) = α + βst + γs2 . (The parameters α, β , and γ are given
t
in the data ﬁle.) Executing this ﬁle will also give a plot showing the availability times and
deadlines for the jobs.
Give the energy obtained by your speed proﬁle and allocations. Plot these using the command
bar((s*ones(1,n)).*theta,1,’stacked’), where s is the T × 1 vector of speeds, and θ is
the T × n matrix of allocations with components θti . This will show, at each time period, how
much eﬀective speed is allocated to each job. The top of the plot will show the speed st . (You
don’t need to turn in a color version of this plot; B&W is ﬁne.)
16.6 AC power ﬂow analysis via convex optimization. This problem concerns an AC (alternating current)
power system consisting of m transmission lines that connect n nodes. We describe the topology
by the nodeedge incidence matrix A ∈ Rn×m , where
Aij = +1 line j leaves node i −1 line j enters node i
otherwise. 0 The power ﬂow on line j is p...
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 Fall '13
 F.Borrelli
 The Aeneid

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