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16.323 Principles of Optimal Control
Spring 2008
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View Full Document 16.323
Handout
#5
Prof.
J.
P.
How
April
10,
2008
Due:
April
24,
2008
16.323
Homework
Assignment
#5
1.
Suppose
that
the
stock
of
a
species
of
Fsh
increases
at
a
constant
rate
when
they
are
not
harvested.
±ishing
regulations
set
a
maximum
permitted
rate
for
the
harvesting
of
Fsh,
which
is
proportional
to
the
size
of
the
stock.
The
system
model
is
then
that:
x
˙ =
x
−
ux
0
≤
u
≤
h
where
x
(
t
)
is
the
normalized
size
of
the
stock
of
Fsh,
ux
is
the
harvesting
rate,
and
h <
1
is
the
maximum
proportional
rate.
Suppose
that
initially
x
=
1
and
that
the
terminal
time
T
is
Fxed.
The
goal
is
to
determine
how
to
maximize
the
total
number
of
Fsh
caught,
so
the
cost
functional
is
given
by
T
min
J
uxdt
=
−
0
and
obviously
x
(
T
)
is
free.
(a)
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This note was uploaded on 11/07/2011 for the course AERO 16.323 taught by Professor Jonathanhow during the Spring '08 term at MIT.
 Spring '08
 jonathanhow

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