<s>
DIDO	B-Application
(	O
)	O
is	O
a	O
MATLAB	B-Language
optimal	O
control	O
toolbox	O
for	O
solving	O
general-purpose	O
optimal	O
control	O
problems	O
.	O
</s>
<s>
Hailed	O
as	O
a	O
breakthrough	O
software	O
,	O
DIDO	B-Application
is	O
based	O
on	O
the	O
pseudospectral	O
optimal	O
control	O
theory	O
of	O
Ross	O
and	O
Fahroo	O
.	O
</s>
<s>
The	O
latest	O
enhancements	O
to	O
DIDO	B-Application
are	O
described	O
in	O
Ross	O
.	O
</s>
<s>
DIDO	B-Application
utilizes	O
trademarked	O
expressions	O
and	O
objects	O
that	O
facilitate	O
a	O
user	O
to	O
quickly	O
formulate	O
and	O
solve	O
optimal	O
control	O
problems	O
.	O
</s>
<s>
Rapidity	O
in	O
formulation	O
is	O
achieved	O
through	O
a	O
set	O
of	O
DIDO	B-Application
expressions	O
which	O
are	O
based	O
on	O
variables	O
commonly	O
used	O
in	O
optimal	O
control	O
theory	O
.	O
</s>
<s>
A	O
user	O
runs	O
DIDO	B-Application
using	O
the	O
one-line	O
command	O
:	O
</s>
<s>
[	O
cost	O
,	O
primal	O
,	O
dual ]	O
=	O
dido(problem, algorithm )	O
,	O
</s>
<s>
In	O
addition	O
to	O
the	O
cost	O
value	O
and	O
the	O
primal	O
solution	O
,	O
DIDO	B-Application
automatically	O
outputs	O
all	O
the	O
dual	O
variables	O
that	O
are	O
necessary	O
to	O
verify	O
and	O
validate	O
a	O
computational	O
solution	O
.	O
</s>
<s>
DIDO	B-Application
implements	O
a	O
spectral	O
algorithm	O
based	O
on	O
pseudospectral	O
optimal	O
control	O
theory	O
founded	O
by	O
Ross	O
and	O
his	O
associates	O
.	O
</s>
<s>
DIDO	B-Application
generates	O
spectrally	O
accurate	O
solutions	O
whose	O
extremality	O
can	O
be	O
verified	O
using	O
Pontryagin	O
's	O
Minimum	O
Principle	O
.	O
</s>
<s>
Because	O
no	O
knowledge	O
of	O
pseudospectral	O
methods	O
is	O
necessary	O
to	O
use	O
it	O
,	O
DIDO	B-Application
is	O
often	O
used	O
as	O
a	O
fundamental	O
mathematical	O
tool	O
for	O
solving	O
optimal	O
control	O
problems	O
.	O
</s>
<s>
That	O
is	O
,	O
a	O
solution	O
obtained	O
from	O
DIDO	B-Application
is	O
treated	O
as	O
a	O
candidate	O
solution	O
for	O
the	O
application	O
of	O
Pontryagin	O
's	O
minimum	O
principle	O
as	O
a	O
necessary	O
condition	O
for	O
optimality	O
.	O
</s>
<s>
DIDO	B-Application
is	O
used	O
world	O
wide	O
in	O
academia	O
,	O
industry	O
and	O
government	O
laboratories	O
.	O
</s>
<s>
Thanks	O
to	O
NASA	O
,	O
DIDO	B-Application
was	O
flight-proven	O
in	O
2006	O
.	O
</s>
<s>
On	O
November	O
5	O
,	O
2006	O
,	O
NASA	O
used	O
DIDO	B-Application
to	O
maneuver	O
the	O
International	O
Space	O
Station	O
to	O
perform	O
the	O
zero-propellant	O
maneuver	O
.	O
</s>
<s>
Since	O
this	O
flight	O
demonstration	O
,	O
DIDO	B-Application
was	O
used	O
for	O
the	O
International	O
Space	O
Station	O
and	O
other	O
NASA	O
spacecraft	O
.	O
</s>
<s>
Most	O
recently	O
,	O
DIDO	B-Application
has	O
been	O
used	O
to	O
solve	O
traveling	B-Algorithm
salesman	I-Algorithm
type	I-Algorithm
problems	I-Algorithm
in	O
aerospace	O
engineering	O
.	O
</s>
<s>
DIDO	B-Application
is	O
primarily	O
available	O
as	O
a	O
stand-alone	O
MATLAB	B-Language
optimal	O
control	O
toolbox	O
.	O
</s>
<s>
That	O
is	O
,	O
it	O
does	O
not	O
require	O
any	O
third-party	O
software	O
like	O
SNOPT	B-Application
or	O
IPOPT	B-Algorithm
or	O
other	O
nonlinear	B-Algorithm
programming	I-Algorithm
solvers	O
.	O
</s>
<s>
In	O
fact	O
,	O
it	O
does	O
not	O
even	O
require	O
the	O
MATLAB	B-Language
Optimization	B-Application
Toolbox	I-Application
.	O
</s>
<s>
The	O
MATLAB/DIDO	O
toolbox	O
does	O
not	O
require	O
a	O
"	O
guess	O
"	O
to	O
run	O
the	O
algorithm	O
.	O
</s>
<s>
This	O
and	O
other	O
distinguishing	O
features	O
have	O
made	O
DIDO	B-Application
a	O
popular	O
tool	O
to	O
solve	O
optimal	O
control	O
problems	O
.	O
</s>
<s>
The	O
MATLAB	B-Language
optimal	O
control	O
toolbox	O
has	O
been	O
used	O
to	O
solve	O
problems	O
in	O
aerospace	O
,	O
robotics	O
and	O
search	O
theory	O
.	O
</s>
<s>
The	O
optimal	O
control	O
toolbox	O
is	O
named	O
after	O
Dido	B-Application
,	O
the	O
legendary	O
founder	O
and	O
first	O
queen	O
of	O
Carthage	O
who	O
is	O
famous	O
in	O
mathematics	O
for	O
her	O
remarkable	O
solution	O
to	O
a	O
constrained	O
optimal	O
control	O
problem	O
even	O
before	O
the	O
invention	O
of	O
calculus	O
.	O
</s>
<s>
Invented	O
by	O
Ross	O
,	O
DIDO	B-Application
was	O
first	O
produced	O
in	O
2001	O
.	O
</s>
<s>
The	O
latest	O
version	O
of	O
DIDO	B-Application
,	O
available	O
from	O
,	O
does	O
not	O
require	O
a	O
"	O
guess	O
"	O
to	O
start	O
the	O
problem	O
and	O
eliminates	O
much	O
of	O
the	O
minutia	O
of	O
coding	O
by	O
simplifying	O
the	O
input-output	O
structure	O
.	O
</s>
