<s>
The	O
PROPT	B-Application
MATLAB	B-Language
Optimal	O
Control	O
Software	O
is	O
a	O
new	O
generation	O
platform	O
for	O
solving	O
applied	O
optimal	O
control	O
(	O
with	O
ODE	O
or	O
DAE	O
formulation	O
)	O
and	O
parameters	O
estimation	O
problems	O
.	O
</s>
<s>
The	O
platform	O
was	O
developed	O
by	O
MATLAB	B-Language
Programming	O
Contest	O
Winner	O
,	O
in	O
2008	O
.	O
</s>
<s>
PROPT	B-Application
is	O
a	O
combined	O
modeling	O
,	O
compilation	B-Application
and	O
solver	O
engine	O
,	O
built	O
upon	O
the	O
TomSym	B-Application
modeling	O
class	O
,	O
for	O
generation	O
of	O
highly	O
complex	O
optimal	O
control	O
problems	O
.	O
</s>
<s>
PROPT	B-Application
uses	O
a	O
pseudospectral	O
Collocation	B-Algorithm
method	I-Algorithm
(	O
with	O
Gauss	O
or	O
Chebyshev	O
points	O
)	O
for	O
solving	O
optimal	O
control	O
problems	O
.	O
</s>
<s>
This	O
means	O
that	O
the	O
solution	O
takes	O
the	O
form	O
of	O
a	O
Polynomial	O
,	O
and	O
this	O
polynomial	O
satisfies	O
the	O
DAE	O
and	O
the	O
path	O
constraints	B-Application
at	O
the	O
collocation	B-Algorithm
points	I-Algorithm
.	O
</s>
<s>
In	O
general	O
PROPT	B-Application
has	O
the	O
following	O
main	O
functions	O
:	O
</s>
<s>
Computation	O
of	O
the	O
constant	O
matrices	B-Architecture
used	O
for	O
the	O
differentiation	B-Algorithm
and	O
integration	O
of	O
the	O
polynomials	O
used	O
to	O
approximate	O
the	O
solution	O
to	O
the	O
Trajectory	O
optimization	O
problem	O
.	O
</s>
<s>
Source	O
transformation	O
to	O
turn	O
user-supplied	O
expressions	O
into	O
MATLAB	B-Language
code	O
for	O
the	O
cost	O
function	O
and	O
constraint	B-Application
function	I-Application
that	O
are	O
passed	O
to	O
a	O
Nonlinear	B-Algorithm
programming	I-Algorithm
solver	O
in	O
TOMLAB	B-Application
.	O
</s>
<s>
The	O
source	O
transformation	O
package	O
TomSym	B-Application
automatically	O
generates	O
first	O
and	O
second	O
order	O
derivatives	B-Algorithm
.	O
</s>
<s>
Simple	O
bounds	O
,	O
linear	O
and	O
nonlinear	O
constraints	B-Application
.	O
</s>
<s>
The	O
PROPT	B-Application
system	O
uses	O
the	O
TomSym	B-Application
symbolic	O
source	O
transformation	O
engine	O
to	O
model	O
optimal	O
control	O
problems	O
.	O
</s>
<s>
A	O
variety	O
of	O
boundary	O
,	O
path	O
,	O
event	O
and	O
integral	O
constraints	B-Application
are	O
shown	O
below	O
:	O
</s>
<s>
To	O
solve	O
the	O
problem	O
with	O
PROPT	B-Application
the	O
following	O
code	O
can	O
be	O
used	O
(	O
with	O
60	O
collocation	B-Algorithm
points	I-Algorithm
)	O
:	O
</s>
<s>
The	O
problem	O
is	O
solved	O
with	O
PROPT	B-Application
by	O
creating	O
two	O
phases	O
and	O
connecting	O
them	O
:	O
</s>
<s>
In	O
the	O
code	O
below	O
the	O
problem	O
is	O
solved	O
with	O
a	O
fine	O
grid	O
(	O
10	O
collocation	B-Algorithm
points	I-Algorithm
)	O
.	O
</s>
<s>
This	O
solution	O
is	O
subsequently	O
fine-tuned	O
using	O
40	O
collocation	B-Algorithm
points	I-Algorithm
:	O
</s>
