<s>
GPOPS-II	B-Application
(	O
pronounced	O
"	O
GPOPS	O
2	O
"	O
)	O
is	O
a	O
general-purpose	O
MATLAB	B-Language
software	I-Language
for	O
solving	O
continuous	O
optimal	O
control	O
problems	O
using	O
hp-adaptive	O
Gaussian	O
quadrature	O
collocation	O
and	O
sparse	O
nonlinear	O
programming	O
.	O
</s>
<s>
The	O
acronym	O
GPOPS	O
stands	O
for	O
"	O
General	O
Purpose	O
OPtimal	O
Control	O
Software	O
"	O
,	O
and	O
the	O
Roman	O
numeral	O
"	O
II	O
"	O
refers	O
to	O
the	O
fact	O
that	O
GPOPS-II	B-Application
is	O
the	O
second	O
software	O
of	O
its	O
type	O
(	O
that	O
employs	O
Gaussian	O
quadrature	O
integration	O
)	O
.	O
</s>
<s>
GPOPS-II	B-Application
is	O
designed	O
to	O
solve	O
multiple-phase	O
optimal	O
control	O
problems	O
of	O
the	O
following	O
mathematical	O
form	O
(	O
where	O
is	O
the	O
number	O
of	O
phases	O
)	O
:	O
</s>
<s>
GPOPS-II	B-Application
uses	O
a	O
class	O
of	O
methods	O
referred	O
to	O
as	O
-adaptive	O
Gaussian	O
quadrature	O
collocation	O
where	O
the	O
collocation	O
points	O
are	O
the	O
nodes	O
of	O
a	O
Gauss	O
quadrature	O
(	O
in	O
this	O
case	O
,	O
the	O
Legendre-Gauss-Radau	O
 [ LGR ] 	O
points	O
)	O
.	O
</s>
<s>
The	O
development	O
of	O
GPOPS-II	B-Application
began	O
in	O
2007	O
.	O
</s>
<s>
The	O
code	O
development	O
name	O
for	O
the	O
software	O
was	O
OptimalPrime	O
,	O
but	O
was	O
changed	O
to	O
GPOPS-II	B-Application
in	O
late	O
2012	O
in	O
order	O
to	O
keep	O
with	O
the	O
lineage	O
of	O
the	O
original	O
version	O
of	O
GPOPS	O
which	O
implemented	O
global	O
collocation	O
using	O
the	O
Gauss	O
pseudospectral	O
method	O
.	O
</s>
<s>
The	O
development	O
of	O
GPOPS-II	B-Application
continues	O
today	O
,	O
with	O
improvements	O
that	O
include	O
the	O
open-source	O
algorithmic	O
differentiation	O
package	O
ADiGator	O
and	O
continued	O
development	O
of	O
-adaptive	O
mesh	O
refinement	O
methods	O
for	O
optimal	O
control	O
.	O
</s>
<s>
GPOPS-II	B-Application
has	O
been	O
used	O
extensively	O
throughout	O
the	O
world	O
both	O
in	O
academia	O
and	O
industry	O
.	O
</s>
<s>
Published	O
academic	O
research	O
where	O
GPOPS-II	B-Application
has	O
been	O
used	O
includes	O
Refs	O
.	O
</s>
