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16.323 Principles of Optimal Control
Spring 2008
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16.323
Lecture
3
Dynamic
Programming
•
Principle
of
Optimality
•
Dynamic
Programming
•
Discrete
LQR
Figure by MIT OpenCourseWare.

Spr
2008
16.323
3–1
Dynamic
Programming
•
DP
is
a
central
idea
of
control
theory
that
is
based
on
the
Principle
of
Optimality:
Suppose
the
optimal
solution
for
a
problem
passes
through
some
intermediate
point
(
x
1
, t
1
)
,
then
the
optimal
solution
to
the
same
problem
starting
at
(
x
1
, t
1
)
must
be
the
continuation
of
the
same
path.
•
Proof?
What
would
the
implications
be
if
it
was
false?
•
This
principle
leads
to:
–
Numerical
solution
procedure
called
Dynamic
Programming
for
solving
multi-stage
decision
making
problems.
–
Theoretical
results
on
the
structure
of
the
resulting
control
law.
Texts:
•
–
Dynamic
Programming
(Paperback)
by
Richard
Bellman
(Dover)
–
Dynamic
Programming
and
Optimal
Control
(Vol
1
and
2)
by
D.
P.
Bertsekas
June
18,
2008

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