<s>
Differential	B-Algorithm
dynamic	I-Algorithm
programming	I-Algorithm
(	O
DDP	O
)	O
is	O
an	O
optimal	O
control	O
algorithm	O
of	O
the	O
trajectory	O
optimization	O
class	O
.	O
</s>
<s>
The	O
algorithm	O
uses	O
locally-quadratic	O
models	O
of	O
the	O
dynamics	O
and	O
cost	O
functions	O
,	O
and	O
displays	O
quadratic	B-Architecture
convergence	I-Architecture
.	O
</s>
<s>
Setting	O
,	O
the	O
dynamic	B-Algorithm
programming	I-Algorithm
principle	I-Algorithm
reduces	O
the	O
minimization	O
over	O
an	O
entire	O
sequence	O
of	O
controls	O
to	O
a	O
sequence	O
of	O
minimizations	O
over	O
a	O
single	O
control	O
,	O
proceeding	O
backwards	O
in	O
time	O
:	O
</s>
<s>
Differential	B-Algorithm
dynamic	I-Algorithm
programming	I-Algorithm
is	O
a	O
second-order	O
algorithm	O
like	O
Newton	O
's	O
method	O
.	O
</s>
<s>
Regularization	O
in	O
the	O
DDP	O
context	O
means	O
ensuring	O
that	O
the	O
matrix	O
in	O
is	O
positive	B-Algorithm
definite	I-Algorithm
.	O
</s>
<s>
Line-search	B-Algorithm
in	O
DDP	O
amounts	O
to	O
scaling	O
the	O
open-loop	O
control	O
modification	O
by	O
some	O
.	O
</s>
<s>
Sampled	O
differential	B-Algorithm
dynamic	I-Algorithm
programming	I-Algorithm
(	O
SaDDP	O
)	O
is	O
a	O
Monte	O
Carlo	O
variant	O
of	O
differential	B-Algorithm
dynamic	I-Algorithm
programming	I-Algorithm
.	O
</s>
<s>
It	O
is	O
based	O
on	O
treating	O
the	O
quadratic	O
cost	O
of	O
differential	B-Algorithm
dynamic	I-Algorithm
programming	I-Algorithm
as	O
the	O
energy	O
of	O
a	O
Boltzmann	O
distribution	O
.	O
</s>
<s>
Sampled	O
differential	B-Algorithm
dynamic	I-Algorithm
programming	I-Algorithm
has	O
been	O
extended	O
to	O
Path	O
Integral	O
Policy	O
Improvement	O
with	O
Differential	B-Algorithm
Dynamic	I-Algorithm
Programming	I-Algorithm
.	O
</s>
<s>
This	O
creates	O
a	O
link	O
between	O
differential	B-Algorithm
dynamic	I-Algorithm
programming	I-Algorithm
and	O
path	O
integral	O
control	O
,	O
which	O
is	O
a	O
framework	O
of	O
stochastic	O
optimal	O
control	O
.	O
</s>
<s>
Interior	O
Point	O
Differential	B-Algorithm
dynamic	I-Algorithm
programming	I-Algorithm
(	O
IPDDP	O
)	O
is	O
an	O
interior-point	B-Algorithm
method	I-Algorithm
generalization	O
of	O
DDP	O
that	O
can	O
address	O
the	O
optimal	O
control	O
problem	O
with	O
nonlinear	O
state	O
and	O
input	O
constraints	O
.	O
</s>
