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Unformatted text preview: erivation or proof; you can
just state how you would ﬁnd this derivative from optimal dual variables for the problem. Verify
your method numerically, by changing the battery capacity a small amount and rerunning the
optimization, and comparing this to the prediction made using dual variables. 3.20 Optimal vehicle speed scheduling. A vehicle (say, an airplane) travels along a ﬁxed path of n
segments, between n + 1 waypoints labeled 0, . . . , n. Segment i starts at waypoint i − 1 and
terminates at waypoint i. The vehicle starts at time t = 0 at waypoint 0. It travels over each
segment at a constant (nonnegative) speed; si is the speed on segment i. We have lower and upper
limits on the speeds: smin
s
smax . The vehicle does not stop at the waypoints; it simply
proceeds to the next segment. The travel distance of segment i is di (which is positive), so the
travel time over segment i is di /si . We let τi , i = 1, . . . , n, denote the time at which the vehicle
21 arrives at waypoint i. The vehicle is required to arrive at waypoint i, for i = 1, . . . , n, between
times τimin and τimax , which are given. The vehicle consumes fuel over segment i at a rate that
depends on its speed, Φ(si ), where Φ is positive, increasing, and c...
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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.
 Fall '13
 F.Borrelli
 The Aeneid

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