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Unformatted text preview: (in terms of the objective) for
the inequality to be tight. You can ﬁx this in (at least) two ways. One is to go back and adjust
certain variables, without aﬀecting the objective and maintaining feasibility, so that the relaxed
constraints hold with equality. Another simple method is to add to the objective a term of the
form
T ǫ
t=1 max{0, −Pmg (t)}, where ǫ is small and positive. This makes it more attractive to use the brakes to extract power
from the wheels, even when the battery is (or will be) full (which removes any fuel incentive).
Find the optimal fuel consumption, and compare to the fuel consumption with a nonhybrid version of the same vehicle (i.e., one without a battery). Plot the braking power, engine power,
motor/generator power, and battery energy versus time.
max
How would you use optimal dual variables for this problem to ﬁnd ∂Ftotal /∂Ebatt , i.e., the partial
derivative of optimal fuel consumption with respect to battery capacity? (You can just assume
that this partial derivative exists.) You do not have to give a long d...
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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.
 Fall '13
 F.Borrelli
 The Aeneid

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