Brachistochrone problem (TACO) - Revision history

JonasSchulze: Text replacement - "\(.*)\<\/bibref\>" to ""

2015-12-30T20:32:09Z

Text replacement - "\<bibref\>(.*)\<\/bibref\>" to "<bib id="$1" />"

← Older revision		Revision as of 20:32, 30 December 2015
Line 1:		Line 1:
	This page contains a model of the classical [[Brachistochrone problem]] (Johann Bernoulli, 1696), see e.g. [http://en.wikipedia.org/wiki/Brachistochrone_curve Wikipedia] or <~~bibref>~~Betts1993</~~bibref~~>, in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions.		This page contains a model of the classical [[Brachistochrone problem]] (Johann Bernoulli, 1696), see e.g. [http://en.wikipedia.org/wiki/Brachistochrone_curve Wikipedia] or <bib id="Betts1993" />, in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions.
	Note that you will need to include a generic [[support AMPL files\|AMPL/TACO support file]], OptimalControl.mod.		Note that you will need to include a generic [[support AMPL files\|AMPL/TACO support file]], OptimalControl.mod.
	To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.		To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.

JonasSchulze: Text replacement - "" to ""

2015-12-30T20:28:25Z

Text replacement - "<bibreferences/>" to "<biblist />"

← Older revision		Revision as of 20:28, 30 December 2015
Line 63:		Line 63:
	== References ==		== References ==

	<~~bibreferences~~/>		<biblist />

	[[Category:AMPL/TACO]]		[[Category:AMPL/TACO]]

Ckirches: brachistochrone: Cited Bernoulli, Betts1993

2011-09-29T17:42:50Z

brachistochrone: Cited Bernoulli, Betts1993

← Older revision		Revision as of 17:42, 29 September 2011
Line 1:		Line 1:
	This page contains a model of the classical [[Brachistochrone problem]] in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions.		This page contains a model of the classical [[Brachistochrone problem]] (Johann Bernoulli, 1696), see e.g. [http://en.wikipedia.org/wiki/Brachistochrone_curve Wikipedia] or <bibref>Betts1993</bibref>, in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions.
	Note that you will need to include a generic [[support AMPL files\|AMPL/TACO support file]], OptimalControl.mod.		Note that you will need to include a generic [[support AMPL files\|AMPL/TACO support file]], OptimalControl.mod.
	To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.		To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.

Ckirches: /* Other Descriptions */

2011-09-29T17:37:22Z

Other Descriptions

← Older revision		Revision as of 17:37, 29 September 2011
Line 60:		Line 60:

	* Mathematical notation at [[Brachistochrone problem]]		* Mathematical notation at [[Brachistochrone problem]]
	* [[:Category:AMPL \| AMPL]] (using a fixed discretization) at [[Brachistochrone problem (AMPL)]]
			== References ==

			<bibreferences/>

	[[Category:AMPL/TACO]]		[[Category:AMPL/TACO]]

Ckirches: Brachistochrone problem (AMPL/TACO)

2011-09-29T17:19:57Z

Brachistochrone problem (AMPL/TACO)

New page

This page contains a model of the classical [[Brachistochrone problem]] in [http://www.ampl.org AMPL] format, making use of the TACO toolkit for AMPL control optimization extensions.
Note that you will need to include a generic [[support AMPL files|AMPL/TACO support file]], OptimalControl.mod.
To solve this model, you require an optimal control or NLP code that uses the TACO toolkit to support the AMPL optimal control extensions.

=== AMPL ===

This is the source file brac_taco.mod
<source lang="AMPL">
# ----------------------------------------------------------------
# Brachistochrone problem using AMPL and TACO
# (c) Christian Kirches, Sven Leyffer
# ----------------------------------------------------------------
include OptimalControl.mod;

var t;
var tf := 1.0, >= 0.1, <= 1.0;
let tf.scale := 0.5; # improves convergence

var x := 0, >= 0, <= 1;
var y := 0, >= 0, <= 1;
var v := 0, >= 0, <= 8;

var a := 0.5, >= 0, <= 1.57079327;
let a.type := "u1";
let a.slope_min := -10.0;
let a.slope_max := +10.0;

param gravity := 32.174; # in ft/s^2

minimize

EndTime: eval (t,tf);
let EndTime.scale := 0.1;

subject to

ODE_x: diff(x,t) = v*cos(a);
ODE_y: diff(y,t) = v*sin(a);
ODE_v: diff(v,t) = gravity*sin(a);

IVC_x: eval(x,0) = 0;
IVC_y: eval(y,0) = 0;
IVC_v: eval(v,0) = 0;
TC_x: eval(x,tf) = 1.0;

# treating IVCs as boundary constraints improves convergence
let IVC_x.type := "dpc";
let IVC_y.type := "dpc";
let IVC_v.type := "dpc";

option solver ...;

solve;

</source>

== Other Descriptions ==

Other descriptions of this problem are available in

* Mathematical notation at [[Brachistochrone problem]]
* [[:Category:AMPL | AMPL]] (using a fixed discretization) at [[Brachistochrone problem (AMPL)]]

[[Category:AMPL/TACO]]